2024-03-28T20:16:53Zhttp://nur.nu.edu.kz/oai/requestoai:nur.nu.edu.kz:123456789/9692018-08-15T03:49:48Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Families without minimal numberings
Abeshev, K. Sh.
Badaev, S. A.
Mustafa, M.
Research Subject Categories::MATHEMATICS
computable numbering
Ershov hierarchy
minimal numbering
2015-12-25T04:37:03Z
2015-12-25T04:37:03Z
2014
Article
Abeshev K. Sh., Badaev S. A., Mustafa M.; 2014; Families without minimal numberings
http://nur.nu.edu.kz/handle/123456789/969
en
oai:nur.nu.edu.kz:123456789/9702018-08-15T03:49:50Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Friedberg numberings in the Ershov hierarchy
Badaev, S. A.
Mustafa, M.
Sorbi, Andrea
Research Subject Categories::MATHEMATICS
minimal numberings
We show that for every n 1, there exists a 1n -computable family which up to equivalence has exactly one Friedberg numbering which does not induce the least element of the corresponding Rogers semilattice.
2015-12-25T04:57:24Z
2015-12-25T04:57:24Z
2014
Article
Badaev S. A., Mustafa M., Sorbi Andrea; 2014; Friedberg numberings in the Ershov hierarchy
http://nur.nu.edu.kz/handle/123456789/970
en
oai:nur.nu.edu.kz:123456789/9712018-08-15T03:49:50Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Positive undecidable numberings in the Ershov hierarchy
Mustafa, M.
Sorbi, Andrea
Research Subject Categories::MATHEMATICS
numbering
We give a su cient condition for an in nite computable family of 1
a sets, to have computable positive but undecidable numberings, where a
is a notation for a nonzero computable ordinal. This extends a theorem
proved by Talasbaeva for the nite levels of the Ershov hierarchy. In par-
ticular the family of all 1 a sets has positive undecidable numberings: this
veri es for all levels of the Ershov hierarchy a conjecture due to Badaev
and Goncharov. We point out also that for every ordinal notation a of a
nonzero ordinal, there are families of 1 a sets having positive numberings,
but no Friedberg numberings: this answers for all levels (whether nite
or in nite) of the Ershov hierarchy, a question originally raised, only for
the nite levels over level 1, by Badaev and Goncharov.
2015-12-25T05:34:30Z
2015-12-25T05:34:30Z
2012
Article
Mustafa Manat, Sorbi Andrea; 2012; Positive undecidable numberings in the Ershov hierarchy
http://nur.nu.edu.kz/handle/123456789/971
en
oai:nur.nu.edu.kz:123456789/9722018-08-15T03:50:23Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Rogers semilattices of families of two embedded sets in the Ershov hierarchy
Badaev, Serikzhan A.
Mustafa, M.
Research Subject Categories::MATHEMATICS
Ershov hierarchy
Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, the Rogers semilattice of the family is in nite. This condition is satis ed by every notation of !; moreover every nonzero computable ordinal that is not sum of any two smaller ordinals has a notation that satis es this condition. On the other hand, we also give a su cient condition on a,
that yields that there is a 1 a {computable family of two embedded sets,
whose Rogers semilattice consists of exactly one element; this condition is
satis ed by all notations of every successor ordinal bigger than 1, and by
all notations of the ordinal !+!; moreover every computable ordinal that
is sum of two smaller ordinals has a notation that satis es this condition.
We also show that for every nonzero n 2 !, or n = !, and every notation
of a nonzero ordinal there exists a 1 a {computable family of cardinality
n, whose Rogers semilattice consists of exactly one element.
2015-12-25T05:41:04Z
2015-12-25T05:41:04Z
2012
Article
Badaev Serikzhan A., Mustafa M.; 2012; Rogers semilattices of families of two embedded sets in the Ershov hierarchy
http://nur.nu.edu.kz/handle/123456789/972
en
oai:nur.nu.edu.kz:123456789/9732018-08-15T03:49:49Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Positive entropy invariant measures on the space of lattices with escape of mass
Kadyrov, Shirali
Research Subject Categories::MATHEMATICS
unimodular lattices
On the space of unimodular lattices, we construct a sequence of
invariant probability measures under a singular diagonal element with high
entropy and show that the limit measure is 0
2015-12-25T06:10:37Z
2015-12-25T06:10:37Z
2010
Article
Kadyrov Shirali; 2010; Positive entropy invariant measures on the space of lattices with escape of mass
http://nur.nu.edu.kz/handle/123456789/973
en
oai:nur.nu.edu.kz:123456789/9742018-08-15T03:49:46Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Algebraic numbers, hyperbolicity, and density modulo one
Kadyrov, Shirali
Gorodnik, A.
Research Subject Categories::MATHEMATICS
Algebraic numbers
hyperbolicity
density modulo one
2015-12-25T06:19:54Z
2015-12-25T06:19:54Z
2011
Article
Kadyrov Shirali, Gorodnik A.; 2011; Algebraic numbers, hyperbolicity, and density modulo one
http://nur.nu.edu.kz/handle/123456789/974
en
oai:nur.nu.edu.kz:123456789/9752018-08-15T03:49:48Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Singular systems of linear forms and non-escape of mass in the space of lattices
Kadyrov, Shirali
Kleinbock, D.
Lindenstrauss, E.
Margulis, G.A.
Research Subject Categories::MATHEMATICS
lattices
Singular systems of linear forms were introduced by Khintchine
in the 1920s, and it was shown by Dani in the 1980s that they
are in one-to-one correspondence with certain divergent orbits of oneparameter
diagonal groups on the space of lattices. We give a (conjecturally
sharp) upper bound on the Hausdor dimension of the set of
singular systems of linear forms (equivalently the set of lattices with divergent
trajectories) as well as the dimension of the set of lattices with
trajectories `escaping on average' (a notion weaker than divergence).
This extends work by Cheung, as well as by Chevallier and Cheung.
Our method di ers considerably from that of Cheung and Chevallier,
and is based on the technique of integral inequalities developed by Eskin,
Margulis and Mozes.
2015-12-25T06:34:06Z
2015-12-25T06:34:06Z
2014
Article
Kadyrov Shirali, Kleinbock D., Lindenstrauss E., Margulis G.A.; 2014; Singular systems of linear forms and non-escape of mass in the space of lattices
http://nur.nu.edu.kz/handle/123456789/975
en
oai:nur.nu.edu.kz:123456789/9762018-08-15T03:49:49Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension
Kadyrov, Shirali
Pohl, A.
Research Subject Categories::MATHEMATICS
Hausdorff dimension
Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal
ows on homogeneous spaces nG, where G is any connected semisimple Lie group of real rank 1 with nite center, and is any nonuniform lattice in G. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.
2015-12-28T05:40:46Z
2015-12-28T05:40:46Z
2012
Article
Kadyrov Shirali, Pohl A.; 2012; Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension
http://nur.nu.edu.kz/handle/123456789/976
en
oai:nur.nu.edu.kz:123456789/9772018-08-15T03:49:50Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Escape of mass and entropy for diagonal flows in real rank one situations
Einsiedler, M.
Kadyrov, Shirali
Pohl, A.
Research Subject Categories::MATHEMATICS
Hausdorff dimension
Let G be a connected semisimple Lie group of real rank 1 with finite center, let be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting on the homogeneous space \G and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of a) which miss a fixed open set is not full.
2015-12-28T05:56:48Z
2015-12-28T05:56:48Z
2011
Article
Einsiedler M., Kadyrov Shirali, Pohl A; 2011; Escape of mass and entropy for diagonal flows in real rank one situations
http://nur.nu.edu.kz/handle/123456789/977
en
oai:nur.nu.edu.kz:123456789/9782018-08-15T03:49:50Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Bernstein-walsh inequalities in higherdimensions over exponential curves
Kadyrov, Shirali
Lawrence, Mark
Research Subject Categories::MATHEMATICS
bernstein-walsh inequalities
Let x = (x1; : : : ; xd) 2 [1; 1]d be linearly independent over Z, set K = f(ez; ex1z; ex2z : : : ; exdz) : jzj 1g:We prove sharp estimates for the growth of a polynomial of degree n, in terms of En(x) := supfkPk d+1 : P 2 Pn(d + 1); kPkK 1g; where d+1 is the unit polydisk. For all x 2 [1; 1]d with linearly independent entries, we have the lower estimate logEn(x) nd+1 (d 1)!(d + 1) log n O(nd+1); for Diophantine x, we have
logEn(x) nd+1 (d 1)!(d + 1) log n + O(nd+1): In particular, this estimate holds for almost all x with respect to Lebesgue measure. The results here generalize those of [6] for d = 1, without relying on estimates for best approximants of rational numbers which do not hold in the vector-valued setting.
2015-12-28T06:13:51Z
2015-12-28T06:13:51Z
2011
Article
Kadyrov Shirali, Lawrence Mark; 2011; Bernstein-walsh inequalities in higherdimensions over exponential curves
http://nur.nu.edu.kz/handle/123456789/978
en
oai:nur.nu.edu.kz:123456789/9792018-08-15T03:49:48Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Exceptional sets in homogeneous spaces and hausdorff dimension
Kadyrov, Shirali
Research Subject Categories::MATHEMATICS
Hausdorff dimension
In this paper we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable ows in compact homogeneous spaces X to show that the Hausdorff dimension of set of points that lie on trajectories missing a particular open ball of radius r is at most dimX + C rdimX log r; where C > 0 is a constant independent of r > 0. Meanwhile, we also describe a general method for computing the least cardinality of open covers of dynamical sets using volume estimates.
2015-12-28T06:22:51Z
2015-12-28T06:22:51Z
2015
Article
Kadyrov Shirali; 2015; Exceptional sets in homogeneous spaces and hausdorff dimension
http://nur.nu.edu.kz/handle/123456789/979
en
oai:nur.nu.edu.kz:123456789/9802018-08-15T03:49:38Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Effective uniqueness of parry measure and exceptional sets in ergodic theory
Kadyrov, Shirali
Research Subject Categories::MATHEMATICS
Hausdorff dimension
It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension of exceptional sets arising from dynamics.
2015-12-28T08:04:59Z
2015-12-28T08:04:59Z
2014
Article
Kadyrov Shirali; 2014; Effective uniqueness of parry measure and exceptional sets in ergodic theory
http://nur.nu.edu.kz/handle/123456789/980
en
oai:nur.nu.edu.kz:123456789/9812018-08-15T03:49:40Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Entropy and escape of mass for SL3(Z)n SL3(R)
Einsiedler, Manfred
Kadyrov, Shirali
Research Subject Categories::MATHEMATICS
measure theoretic entropy
We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices
2015-12-28T08:17:27Z
2015-12-28T08:17:27Z
2011
Article
Einsiedler Manfred, Kadyrov Shirali; 2011; Entropy and escape of mass for SL3(Z)n SL3(R)
http://nur.nu.edu.kz/handle/123456789/981
en
oai:nur.nu.edu.kz:123456789/11952018-08-15T03:50:25Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_905
Characterization of Corneal Indentation Hysteresis
Wei, Dongming
Ko, Match W. L.
Leung, Christopher K.S
Corneal Indentation
Research Subject Categories::MATHEMATICS
The aim of this study is to design and develop a noninvasive
corneal indentation method to measure the corneal
hysteresis behavior under dynamic corneal indentation. Corneal
indentation method is adapted for the design and development of
a measurement method for the characterization of Corneal
Indentation Hysteresis (CIH). Fourteen porcine eyes were tested
using the corneal indentation method. The CIH measured in
enucleated porcine eyes showed indentation rate and intraocular
pressure dependences. The CIH increased with the indentation
rate at lower IOP (< 25 mmHg) and the CIH decreased with the
indentation rate at higher IOP (> 25 mmHg). The CIH was linear
proportional to the IOP within an individual eye. The CIH was
positively correlated with the IOP, corneal in-plane tensile stress
and corneal tangent modulus (E). A new method based on corneal
indentation for the measurement of Corneal Indentation
Hysteresis in vivo is developed. To our knowledge, this is the first
study to introduce the corneal indentation hysteresis and correlate
the corneal indentation hysteresis and the corneal tangent
modulus
2016-02-08T10:36:38Z
2016-02-08T10:36:38Z
2015
Article
Match W. L. Ko, Dongming Wei, Christopher K.S Leung; 2015; Characterization of Corneal Indentation Hysteresis
http://nur.nu.edu.kz/handle/123456789/1195
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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oai:nur.nu.edu.kz:123456789/11962018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
A Lumped-Parameter Model for Nonlinear Waves in Graphene
Wei, Dongming
Hazim, Hamad
Elgindi, Mohamed
Soukiassian, Yeran
Graphene
Research Subject Categories::MATHEMATICS
Resonance
Nonlinear Vibration
Phase Diagram
Frequency Sweep
A lumped-parameter nonlinear spring-mass model which takes into
account the third-order elastic sti ness constant is considered for mod-
eling the free and forced axial vibrations of a graphene sheet with one
xed end and one free end with a mass attached. It 's demonstrated
through this simple model that, in free vibration, within certain initial
energy level and depending upon its length and the nonlinear elas-
tic constants, there exist bounded periodic solutions which are non-
sinusoidal, and that for each xed energy level, there is a bifurcation
point depending upon material constants, beyond which the periodic
solutions disappear. The amplitude, frequency, and the corresponding
wave solutions for both free and forced harmonic vibrations are cal-
culated analytically and numerically. Energy sweep is also performed
for resonance applications.
2016-02-08T10:46:42Z
2016-02-08T10:46:42Z
2015
Article
Hamad Hazim, Dongming Wei, Mohamed Elgindi, Yeran Soukiassian; 2015; A Lumped-Parameter Model for Nonlinear Waves in Graphene
http://nur.nu.edu.kz/handle/123456789/1196
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
oai:nur.nu.edu.kz:123456789/12032018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Realization of abstract convex geometries by point configurations. Part I
Adaricheva, Kira
Wild, Marcel
Research Subject Categories::MATHEMATICS
abstract convex geometries
The Edelman-Jamison problem is to characterize those abstract
convex geometries that are representable by a set of points in the plane. We
show that some natural modification of the Edelman-Jamison problem is equivalent
to the well known NP-hard order type problem
2016-02-09T04:05:08Z
2016-02-09T04:05:08Z
2007
Article
Adaricheva Kira; Wild Marcel; 2007; Realization of abstrack convex geometries by point configurations. Part I; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1203
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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oai:nur.nu.edu.kz:123456789/12042018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Stasheff polytope as a sublattice of permutohedron
Adaricheva, Kira
Research Subject Categories::MATHEMATICS
Stasheff polytope
An assosiahedron Kn, known also as Stasheff polytope, is a multifaceted
combinatorial object, which, in particular, can be realized as a convex
hull of certain points in Rn, forming (n − 1)-dimensional polytope1.
A permutahedron Pn is a polytope of dimension (n−1) in Rn with vertices
forming various permutations of n-element set. There exists well-known orderings
of vertices of Pn and Kn that make these objects into lattices: the first
known as permutation lattices, and the latter as Tamari lattices. We provide a
new proof to the statement that the vertices of Kn can be naturally associated
with particular vertices of Pn in such a way that the corresponding lattice
operations are preserved. In lattices terms, Tamari lattices are sublattices
of permutation lattices. The fact was established in 1997 in paper by Bjorner
and Wachs, but escaped the attention of lattice theorists. Our approach to the
proof is based on presentation of points of an associahedron Kn via so-called
bracketing functions. The new fact that we establish is that the embedding
preserves the height of elements
2016-02-09T04:19:43Z
2016-02-09T04:19:43Z
2011
Article
Adaricheva Kira; 2011; Stasheff polytope as a sublattice of permutohedron; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1204
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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oai:nur.nu.edu.kz:123456789/12052018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Representing finite convex geometries by relatively convex sets
Adaricheva, Kira
Research Subject Categories::MATHEMATICS
finite convex geometries
A closure system with the anti-exchange axiom is called a convex
geometry. One geometry is called a sub-geometry of the other if its closed sets
form a sublattice in the lattice of closed sets of the other. We prove that convex
geometries of relatively convex sets in n-dimensional vector space and their
nite sub-geometries satisfy the n-Carousel Rule, which is the strengthening
of the n-Carath eodory property. We also nd another property, that is similar
to the simplex partition property and does not follow from 2-Carusel Rule,
which holds in sub-geometries of 2-dimensional geometries of relatively convex
sets.
2016-02-09T04:56:58Z
2016-02-09T04:56:58Z
2011
Article
Adaricheva Kira; 2011; Representing finite convex geometries by relatively convex sets; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1205
en
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oai:nur.nu.edu.kz:123456789/12062018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part I
Adaricheva, Kira
Nation, J. B.
Research Subject Categories::MATHEMATICS
lattices of quasi-equational theories
We show that for every quasivariety K of structures (where
both functions and relations are allowed) there is a semilattice S with
operators such that the lattice of quasi-equational theories of K (the dual
of the lattice of sub-quasivarieties of K) is isomorphic to Con(S;+; 0; F).
As a consequence, new restrictions on the natural quasi-interior operator
on lattices of quasi-equational theories are found.
2016-02-09T08:19:14Z
2016-02-09T08:19:14Z
2012
Article
Adaricheva Kira, Nation J.B.; 2012; Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part I; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1206
en
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oai:nur.nu.edu.kz:123456789/12072018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II
Adaricheva, Kira
Nation, J.B.
Research Subject Categories::MATHEMATICS
lattices of quasi-equational theories
Part I proved that for every quasivariety K of structures
(which may have both operations and relations) there is a semilattice
S with operators such that the lattice of quasi-equational theories of
K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to
Con(S;+; 0; F). It is known that if S is a join semilattice with 0 (and no
operators), then there is a quasivariety Q such that the lattice of theories
of Q is isomorphic to Con(S;+; 0). We prove that if S is a semilattice
having both 0 and 1 with a group G of operators acting on S, and each
operator in G xes both 0 and 1, then there is a quasivariety W such
that the lattice of theories of W is isomorphic to Con(S;+; 0; G).
2016-02-09T08:26:23Z
2016-02-09T08:26:23Z
2012
Article
Adaricheva Kira, Nation J. B.; 2012; Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1207
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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oai:nur.nu.edu.kz:123456789/12082018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Ordered direct implication basis of a finite closure system
Adaricheva, Kira
Nation, J.B.
Rand, R.
Research Subject Categories::MATHEMATICS
finite closure system
Closure system on a nite set is a unifying concept in logic programming,
relational data bases and knowledge systems. It can also be presented
in the terms of nite lattices, and the tools of economic description of a
nite lattice have long existed in lattice theory. We present this approach by
describing the so-called D-basis and introducing the concept of ordered direct
basis of an implicational system. A direct basis of a closure operator, or an
implicational system, is a set of implications that allows one to compute the
closure of an arbitrary set by a single iteration. This property is preserved by
the D-basis at the cost of following a prescribed order in which implications
will be attended. In particular, using an ordered direct basis allows to optimize
the forward chaining procedure in logic programming that uses the Horn
fragment of propositional logic. One can extract the D-basis from any direct
unit basis in time polynomial in the size s( ), and it takes only linear time
of the cardinality of the D-basis to put it into a proper order. We produce
examples of closure systems on a 6-element set, for which the canonical basis
of Duquenne and Guigues is not ordered direct
2016-02-09T08:58:28Z
2016-02-09T08:58:28Z
2012
Article
Adaricheva Kira, Nation J.B., Rand R.; 2012; Ordered direct implication basis of a finite closure system; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1208
en
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oai:nur.nu.edu.kz:123456789/12092018-08-15T03:50:25Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On implicational bases of closure system with unique critical sets
Adaricheva, Kira
Nation, J.B.
Research Subject Categories::MATHEMATICS
finite closure system
We show that every optimum basis of a nite closure system,
in D. Maier's sense, is also right-side optimum, which is a parameter of a
minimum CNF representation of a Horn Boolean function. New parameters
for the size of the binary part are also established. We introduce the K-basis
of a general closure system, which is a re nement of the canonical basis of
V. Duquenne and J.L. Guigues, and discuss a polynomial algorithm to obtain
it. We study closure systems with unique critical sets, and some subclasses
of these where the K-basis is unique. A further re nement in the form of the
E-basis is possible for closure systems without D-cycles. There is a polynomial
algorithm to recognize the D-relation from a K-basis. Thus, closure systems
without D-cycles can be e ectively recognized. While the E-basis achieves an
optimum in one of its parts, the optimization of the others is an NP-complete
problem
2016-02-09T09:08:20Z
2016-02-09T09:08:20Z
2013
Article
Adaricheva Kira, Nation J.B.; 2013; On implicational bases of closure system with unique critical sets; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1209
en
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oai:nur.nu.edu.kz:123456789/12102018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Optimum basis of finite convex geometry
Adaricheva, Kira
Research Subject Categories::MATHEMATICS
finite convex geometry
Convex geometries form a subclass of closure systems with unique
criticals, or UC-systems. We show that the F-basis introduced in [6] for UC-
systems, becomes optimum in convex geometries, in two essential parts of the
basis: right sides (conclusions) of binary implications and left sides (premises)
of non-binary ones. The right sides of non-binary implications can also be
optimized, when the convex geometry either satis es the Carousel property,
or does not have D-cycles. The latter generalizes a result of P.L. Hammer
and A. Kogan for acyclic Horn Boolean functions. Convex geometries of order
convex subsets in a poset also have tractable optimum basis. The problem of
tractability of optimum basis in convex geometries in general remains to be
open
2016-02-09T09:16:44Z
2016-02-09T09:16:44Z
2016
Article
Adaricheva Kira; 2016; Optimum basis of finite convex geometry; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1210
en
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oai:nur.nu.edu.kz:123456789/12132018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Notes on the description of join-distributive lattices by permutations
Adaricheva, Kira
Cz´edli, G´abor
Research Subject Categories::MATHEMATICS
join-distributive lattices
Let L be a join-distributive lattice with length n and width (Ji L) k.
There are two ways to describe L by k − 1 permutations acting on an n-element set:
a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent
lattice theoretical way of the second author. We prove that these two approaches are
equivalent. Also, we characterize join-distributive lattices by trajectories
2016-02-09T09:29:33Z
2016-02-09T09:29:33Z
2012
Article
Kira Adaricheva, G´abor Cz´edli; 2012; Notes on the description of join-distributive lattices by permutations; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1213
en
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oai:nur.nu.edu.kz:123456789/12142018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Algebraic convex geometries revisited
Adaricheva, Kira
Research Subject Categories::MATHEMATICS
algebraic convex geometries
Representation of convex geometry as an appropriate join of compatible
orderings of the base set can be achieved, when closure operator of
convex geometry is algebraic, or finitary. This bears to the finite case proved
by P. Edelman and R. Jamison to the greater extent than was thought earlier
2016-02-09T09:36:45Z
2016-02-09T09:36:45Z
2014
Article
Adaricheva Kira; 2014; Algebraic convex geometries revisited; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1214
en
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oai:nur.nu.edu.kz:123456789/12152018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
A class of infinite convex geometries
Adaricheva, Kira
Nation, J.B.
Research Subject Categories::MATHEMATICS
infinite convex geometries
Various characterizations of finite convex geometries
are well known. This note provides similar characterizations for
possibly infinite convex geometries whose lattice of closed sets is
strongly coatomic and lower continuous. Some classes of examples
of such convex geometries are given
2016-02-09T09:43:08Z
2016-02-09T09:43:08Z
2015
Article
Adaricheva Kira, Nation J.B.; 2015; A class of infinite convex geometries; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1215
en
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oai:nur.nu.edu.kz:123456789/12162018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Discovery of the D-basis in binary tables based on hypergraph dualization
Adaricheva, Kira
Nation, J.B.
Research Subject Categories::MATHEMATICS
hypergraph dualization
Discovery of (strong) association rules, or implications, is an important
task in data management, and it nds application in arti cial intelligence,
data mining and the semantic web. We introduce a novel approach
for the discovery of a speci c set of implications, called the D-basis, that provides
a representation for a reduced binary table, based on the structure of
its Galois lattice. At the core of the method are the D-relation de ned in
the lattice theory framework, and the hypergraph dualization algorithm that
allows us to e ectively produce the set of transversals for a given Sperner hypergraph.
The latter algorithm, rst developed by specialists from Rutgers
Center for Operations Research, has already found numerous applications in
solving optimization problems in data base theory, arti cial intelligence and
game theory. One application of the method is for analysis of gene expression
data related to a particular phenotypic variable, and some initial testing is
done for the data provided by the University of Hawaii Cancer Center
2016-02-09T09:59:06Z
2016-02-09T09:59:06Z
2016
Article
Adaricheva Kira, Nation J. B.; 2016; Discovery of the D-basis in binary tables based on hypergraph dualization; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1216
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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oai:nur.nu.edu.kz:123456789/12172018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On scattered convex geometries
Adaricheva, Kira
Pouzet, Maurice
Research Subject Categories::MATHEMATICS
convex geometries
A convex geometry is a closure space satisfying the anti-exchange axiom. For several
types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice ( ), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets
2016-02-09T10:09:36Z
2016-02-09T10:09:36Z
2015
Article
Adaricheva Kira, Pouzet Maurice; 2015; On scattered convex geometries; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1217
en
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oai:nur.nu.edu.kz:123456789/12182018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Join-semidistributive lattices of relatively convex sets
Adaricheva, Kira
Research Subject Categories::MATHEMATICS
join-semidistributive lattices
We give two sufficient conditions for the lattice Co(Rn,X) of rel-
atively convex sets of Rn to be join-semidistributive, where X is a finite union
of segments. We also prove that every finite lower bounded lattice can be
embedded into Co(Rn,X), for a suitable finite subset X of Rn
2016-02-09T10:20:45Z
2016-02-09T10:20:45Z
2004
Article
Adaricheva Kira; 2004; Join-semidistributive lattices of relatively convex sets; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1218
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
oai:nur.nu.edu.kz:123456789/12192018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Embedding finite lattices into finite biatomic lattices
Adaricheva, Kira
Wehrung, Freidrich
Research Subject Categories::MATHEMATICS
embedding finite lattices
For a class C of finite lattices, the question arises whether any
lattice in C can be embedded into some atomistic, biatomic lattice in C. We
provide answers to the question above for C being, respectively,
— The class of all finite lattices;
— The class of all finite lower bounded lattices (solved by the first author’s
earlier work).
— The class of all finite join-semidistributive lattices (this problem was,
until now, open).
We solve the latter problem by finding a quasi-identity valid in all finite, atomistic,
biatomic, join-semidistributive lattices but not in all finite join-semidistributive
lattices
2016-02-09T10:40:24Z
2016-02-09T10:40:24Z
2005
Article
Adaricheva Kira, Wehrung Freidrich; 2005; Embedding finite lattices into finite biatomic lattices; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1219
en
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oai:nur.nu.edu.kz:123456789/12202018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On complex algebras of subalgebras
Adaricheva, Kira
Pilitowska, Agata
Stanovsky, David
Research Subject Categories::MATHEMATICS
complex algebras
subalgebras
Let V be a variety of algebras. We establish a condition (so called
generalized entropic property), equivalent to the fact that for every algebra
A 2 V, the set of all subalgebras of A is a subuniverse of the complex algebra of
A. We investigate the relationship between the generalized entropic property
and the entropic law. Further, provided the generalized entropic property is
satisfied in V, we study the identities satisfied by the complex algebras of
subalgebras of algebras from V
2016-02-09T10:51:07Z
2016-02-09T10:51:07Z
2006
Article
Adaricheva Kira, Pilitowska Agata, Stanovsky David; 2006; On complex algebras of subalgebras; arXiv.org
http://nur.nu.edu.kz/handle/123456789/1220
en
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oai:nur.nu.edu.kz:123456789/12232018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_907
Increasing the role of the D-basis in applications
Adaricheva, Kira
Research Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis
2016-02-15T05:26:47Z
2016-02-15T05:26:47Z
2015-06-06
Presentation
Kira Adaricheva; 2015; Increasing the role of the D-basis in applications; http://sites.dmi.uns.ac.rs/aaa90/
http://nur.nu.edu.kz/handle/123456789/1223
en
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oai:nur.nu.edu.kz:123456789/12242018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_907
Measuring implications of the D-basis in biomedical applications
Adaricheva, Kira
Research Subject Categories::MATHEMATICS
algebra
2016-02-15T05:34:22Z
2016-02-15T05:34:22Z
2015-06-26
Presentation
Kira Adaricheva; 2015; Measuring implications of the D-basis in biomedical applications; http://www.matap.uma.es/icfca2015/blog-7/index.html
http://nur.nu.edu.kz/handle/123456789/1224
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
oai:nur.nu.edu.kz:123456789/12252018-08-15T03:49:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_907
Representations of Convex Geometries
Adaricheva, Kira
Research Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis::Algebra and geometry
2016-02-15T05:44:38Z
2016-02-15T05:44:38Z
2015-06
Presentation
Kira Adaricheva; 2015; Representations of Convex Geometries
http://nur.nu.edu.kz/handle/123456789/1225
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
oai:nur.nu.edu.kz:123456789/12262018-08-15T03:49:51Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_907
Efficient bases of finite closure systems
Adaricheva, Kira
Research Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis
2016-02-15T05:56:08Z
2016-02-15T05:56:08Z
2014-05-13
Presentation
Kira Adaricheva; 2014; Efficient bases of finite closure systems; http://www.dagstuhl.de/en/program/calendar/semhp/?semnr=14201
http://nur.nu.edu.kz/handle/123456789/1226
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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oai:nur.nu.edu.kz:123456789/15572019-12-26T09:18:05Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
On logistic-normal distribution
Almagambetova, Ayanna
Zakiyeva, Nazgul
Research Subject Categories
logistic-normal distribution
Existing distributions do not always provide an adequate fit to the complex real world data. Hence, the interest in developing more flexible statistical distributions remains strong in statistics profession. In this project, we present a family of generalized normal distributions, the T-normal family. We study in some details a member of the proposed family namely, the logistic-normal (LN) distribution. Some properties of the LN distribution including moments, tail behavior, and modes are examined. The distribution is symmetric and can be unimodal or bimodal. The tail of the LN distribution can be heavier or lighter than the tail of the normal distribution. The performance of the maximum likelihood estimators is evaluated through small simulation study. Two bimodal data sets are used to show the applicability of the LN distribution
2016-05-31T08:31:02Z
2016-05-31T08:31:02Z
2016-04
Capstone Project
Ayanna Almagambetova and Nazgul Zakiyeva. 2016. On logistic-normal distribution. Nazarbayev University, Department of Mathematics. http://nur.nu.edu.kz/handle/123456789/1557
http://nur.nu.edu.kz/handle/123456789/1557
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15582019-12-26T09:18:12Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
On the well-posedness of the Boltzmann's moment system of equations in fourth approximation
Issagali, Aizhan
Boltzmann equation
moment system
initial and boundary value problem
hyperbolic partial differential equations
a-priori estimate
We study the one-dimensional non-linear non-stationary Boltzmann's moment system of equations in fourth approxi-
mation with the tools developed by Sakabekov in [4],[5] and [6]. For the third approximation system Sakabekov proves the
mass conservation law (cf. Theorem 2.1 in [4]) and discusses the existence and uniqueness of the solution (cf. Theorem
in [6]). We extend the analysis of the existence and uniqueness of the solution to the fourth approximation system. In
particular, for the fourth approximation system we discuss the well-posed initial and boundary value problem and obtain
the a-priori estimate of the solution belonging to the space of functions, continuous in time and square summable by spatial
variable.
2016-05-31T08:40:29Z
2016-05-31T08:40:29Z
2016-05
Capstone Project
Aizhan Issagali. 2016. On the well-posedness of the Boltzmann's moment system of equations in fourth approximation. Nazarbayev University. Capstone Project. Report. http://nur.nu.edu.kz/handle/123456789/1558
http://nur.nu.edu.kz/handle/123456789/1558
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15592019-12-26T09:15:52Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Modeling of corneal deformation under air-puff by nonlinear differential equations
Jangabylova, Aliya
Zhalgas, Aidana
nonlinear differential equations
corneal deformation
Intraocular Pressure (IOP) is a main factor for the diagnosis of glaucoma. In this report,
the kinematic viscoelastic corneal models, specifcally the Maxwell and the Kelvin-Voight
models, of human eye ball will be proposed for determining the displacement of the cornea
during the air-puff tonometry simulations and its relationship to IOP. The purpose of
project is to study the in
uence of elasticity and viscosity to the corneal deformations
under an air puff.
2016-05-31T08:54:22Z
2016-05-31T08:54:22Z
2016-05
Capstone Project
Aliya Jangabylova and Aidana Zhalgas. 2016. Modeling of corneal deformation under air-puff by nonlinear differential equations. SCHOOL OF SCIENCE AND TECHNOLOGY, NAZARBAYEV UNIVERSITY, May 2016. http://nur.nu.edu.kz/handle/123456789/1559
http://nur.nu.edu.kz/handle/123456789/1559
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15602019-12-26T09:07:26Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Stable holomorphic polynomials on the half-plane and generalizations
Kairzhan, Adilbek
Research Subject Categories
Stable holomorphic polynomials
The study of locations of zeroes of functions became popular among mathematicians
many years ago. This investigation contributes a lot to wide range of
theories and topics in Mathematics and Physics.
2016-05-31T09:16:16Z
2016-05-31T09:16:16Z
2015-04
Capstone Project
Adilbek Kairzhan. 2015. Stable holomorphic polynomials on the half-plane and generalizations. NAZARBAYEV UNIVERSITY, Department of Mathematics. http://nur.nu.edu.kz/handle/123456789/1560
http://nur.nu.edu.kz/handle/123456789/1560
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15612019-12-26T09:09:10Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
A Short Note On Solving 1-D Porous Medium Equation by Finite Element Methods
Matayev, Chingis
Research Subject Categories
Porous Medium Equation
Porous Medium Equation (PME) is one of the simplest types of of nonlinear evolution equation
of parabolic type. It emerges in the description of di erent natural phenomena, and its theory and
properties depart strongly from the heat equation, ut = u, its most famous relative. Hence the
interest of its study, both for the pure mathematician and the applied scientist (Vazquez, 2006).
The aim of this paper is to study the Porous Medium Equation in one dimension.
2016-05-31T09:23:08Z
2016-05-31T09:23:08Z
2016-05-20
Capstone Project
Chingis Matayev. 2016. A Short Note On Solving 1-D Porous Medium Equation by Finite Element Methods. Nazarbaev University. http://nur.nu.edu.kz/handle/123456789/1561
http://nur.nu.edu.kz/handle/123456789/1561
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15622019-12-26T09:20:29Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Statistical Morphological Disambiguation for Kazakh Language
Azamat, Daiana
Research Subject Categories
Kazakh language
natural language processing
This paper presents the results of developing a statistical model for morphological
disambiguation of Kazakh text. Starting with basic assumptions we tried
to cope with the complex morphology of Kazakh language by breaking up lexical
forms across their derivational boundaries into inflectional groups and modeling
their behavior with statistical methods. We also provide maximum likelihood estimates
for the parameters and an effective way to perform disambiguation with
the Viterbi algorithm.
2016-05-31T09:33:28Z
2016-05-31T09:33:28Z
2016
Capstone Project
Daiana Azamat. 2016. Statistical Morphological Disambiguation for Kazakh Language. NAZARBAYEV UNIVERSITY, SCHOOL OF SCIENCE AND TECHNOLOGY. http://nur.nu.edu.kz/handle/123456789/1562
http://nur.nu.edu.kz/handle/123456789/1562
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15632019-12-26T09:15:08Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Finite element solutions of the nonlinear RAPM Black-Scholes model
Zhexembay, Laila
Pak, Andrey
Research Subject Categories
Black-Scholes equation
The main purpose of our Capstone project is to study the Risk-Adjusted
Pricing Methodology (RAMP) Black-Scholes model and to find the finite
element solutions of the nonlinear Black-Scholes equation. The RAPM
is one of the many nonlinear models in option pricing considering factors
which affect the volatility in the original Black-Scholes equation. This
model can be simplifed to a nonlinear parabolic equation in a new vari-
able which equals the product of Gamma and the price of the underlying
asset. Galerkin nite element method is applied to the parabolic equation.
Two types of solutions will be presented: one using the linear elements
and the other using quadratic elements. Local finite element equations
for the linear and quadratic elements are derived with some specifc inter-
polations of the nonlinear terms. Numerical solutions are obtained and
compared to the results in literature. The explanation of the discrepancies
will be given together with the future goals of this study.
2016-05-31T09:42:36Z
2016-05-31T09:42:36Z
2016-05-09
Capstone Project
Laila Zhexembay and Andrey Pak. 2016. Finite element solutions of the nonlinear RAPM Black-Scholes model. Nazarbayev University. http://nur.nu.edu.kz/handle/123456789/1563
http://nur.nu.edu.kz/handle/123456789/1563
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15642019-12-26T09:20:06Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Representation of Convex Geometries by Convex Structures on a Plane
Bolat, Madina
Research Subject Categories
Convex geometries
Convex geometries are closure systems satisfying anti-exchange axiom with
combinatorial properties. Every convex geometry is represented by a convex
geometry of points in n-dimensional space with a special closure operator.
Some convex geometries are represented by circles on a plane. This paper
proves that not all convex geometries are represented by circles on a plane
by providing a counterexample. We introduce Weak n-Carousel rule and
prove that it holds for confgurations of circles on a plane.
2016-05-31T09:48:20Z
2016-05-31T09:48:20Z
2016-05
Capstone Project
Madina Bolat. 2016. Representation of Convex Geometries by Convex Structures on a Plane. School of Science and Technology, Nazarbayev University, Astana, Kazakhstan. http://nur.nu.edu.kz/handle/123456789/1564
http://nur.nu.edu.kz/handle/123456789/1564
en
Attribution-NonCommercial-ShareAlike 3.0 United States
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15652019-12-26T09:17:59Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
On a stochastic interacting particle system with pushing dynamics
Abdukadyrov, Nurlan
Research Subject Categories
stochastic interacting particle system
In this paper we study a stochastic two-particle system on Z where
particles interact each other by pushing dynamics. We derive the explicit formulas
of the transition probability and of the probability distributions of each particle's
position at time t. Finally, we discuss about the generalization of our works to
N-particle system.
2016-05-31T09:56:12Z
2016-05-31T09:56:12Z
2016
Capstone Project
Nurlan Abdukadyrov. 2016. On a stochastic interacting particle system with pushing dynamics. School of Science and Technology, Nazarbayev University, Astana, Kazakhstan. http://nur.nu.edu.kz/handle/123456789/1565
http://nur.nu.edu.kz/handle/123456789/1565
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/15662019-12-26T09:14:57Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Finite Element Solution of Thermal Gee-Lyon Flows in a Circular Tube
Aimambet, Narken
Research Subject Categories
Non-Newtonian fluid
finite element method
temperature distribution
extrusion
The goal of this project is to calculate the temperature distribu-
tion of certain pressure-driven non-Newtonian
ows inside a circular tube.
The rheology under consideration is the type in which the shear stress is an
implicit function of the shear rate de ned as the inverse function of an odd
function. The
uid velocity in the tube is approximated by the steady state
velocity pro le along the tube length and the viscosity is assumed to be
independent of the temperature. The velocity pro le is computed by using
Mathematica's build-in ODE solver semi-analytically. The corresponding
steady state temperature pro le at tube length is then calculated taking
into account of heat source generated by shear rate from the
uid
ow by
solving an ODE. The temperature distribution from the entrance to the fully
developed region is then approximated numerically by using the axisymmet-
ric linear triangular nite elements. Material and geometric constants and
data for extrusion of chemical Lucite through the tube in literature are used
for the numerical example. Comparison of the numerical result with the
industrial experimental result is made at a point along the central axis of
the tube.
2016-05-31T10:01:15Z
2016-05-31T10:01:15Z
2016-05
Capstone Project
Narken Aimambet. 2016. Finite Element Solution of Thermal Gee-Lyon Flows in a Circular Tube. Department of Mathematics, Nazarbayev University, Astana, Kazakhstan. http://nur.nu.edu.kz/handle/123456789/1566
http://nur.nu.edu.kz/handle/123456789/1566
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16172019-12-26T09:18:28Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Optimization of convex geometries: component quadratic and general
Myrzakul, Zhanbota
Capstone Project
convex geometries
In this Capstone Project, we worked with a class of closure systems called convex
geometries, which are closure systems with a closure operator that satisfies the
anti-exchange property. We first looked at the result of optimization algorithm of
component quadratic systems, which are discussed in [4], and reproved it for the
case of convex geometries. We then investigated the following question: if a convex
geometry is given by a set of implications, is it possible to find its optimum basis
in polynomial time when the convex geometry does not have particular properties
(for instance, not component quadratic)?
2016-06-06T04:42:02Z
2016-06-06T04:42:02Z
2016
Capstone Project
Myrzakul Zhanbota. 2016. Optimization of convex geometries: component quadratic and general. Nazarbayev University. School of Science and Technology. Mathematics Department. http://nur.nu.edu.kz/handle/123456789/1617
http://nur.nu.edu.kz/handle/123456789/1617
en
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16332019-12-26T09:17:37Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Multiple Point Compression on Elliptic Curves
Otemissov, Adilet
Capstone Project
Elliptic Curves
Elliptic Curve Cryptography
The paper aims at developing new point compression algorithms which are useful in mobile communication systems where Elliptic Curve Cryptography is employed to achieve secure data storage and transmission. Compression algorithms allow elliptic curve points to be represented in the form that balances the usage of memory and computational power. The two- and three-point compression algorithms developed by Khabbazian, Gulliver and Bhargava [4] are reviewed and extended to generic cases of four and five points.
The proposed methods use only basic operations (multiplication, division,
etc.) and avoids square root finding. In addition, a new two-point compression method which is heavy in compression phase and light in decompression
is developed.
2016-06-14T02:48:58Z
2016-06-14T02:48:58Z
2015
Capstone Project
Otemissov Adilet. 2015. Multiple Point Compression on Elliptic Curves. School of Science and Technology. Mathematics Department. http://nur.nu.edu.kz/handle/123456789/1633
http://nur.nu.edu.kz/handle/123456789/1633
en
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16342019-12-26T09:20:23Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Stability Analysis of SEIS model with spatial variations
Baki, Zhuldyzay
SEIS model
Capstone Project
In this report we present an SEIS model for infectious diseases with
latent period and no immune response for spatially heterogeneous environment. Spatial heterogeneity is designed by several metapopulations. It was shown that global dynamics of an epidemics completely
depends on basic reproduction number R0. By fxing the number of
patches to two, we use next generation matrix method to obtain basic
reproduction number and make further analysis on it. Migration rates
of individuals are considered as one of the main factors that influence R0. Moreover, some numerical simulations for the dynamics of the system with different initial conditions is presented.
2016-06-15T02:53:11Z
2016-06-15T02:53:11Z
2016-05
Capstone Project
Baki Zhuldyzay. 2016. Stability Analysis of SEIS model with spatial variations. School of Science and Technology. Mathematics Department. http://nur.nu.edu.kz/handle/123456789/1634
http://nur.nu.edu.kz/handle/123456789/1634
en
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16352019-12-26T09:18:40Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Pairwise Overlap and Misclassification in Cluster Analysis
Akynkozhayev, Birzhan
Research Subject Categories
Cluster Analysis
Separation of data into distinct groups is one of the most important tools of learning and means of obtaining valuable information from data. Cluster analysis studies the ways of distributing objects into groups with similar characteristics. Real-world examples of such applications are age separation of a population, loyalty grouping of customers, classification of living organisms into kingdoms, etc. In particular, cluster analysis is an important objective of data mining, which focuses on studying ways of extracting key information from data and converting it into some more understandable form. There is no single best algorithm for producing data partitions in cluster analysis, but many that perform well in various circumstances (Jain, 2008). Many popular clustering algorithms are based on an iterative partitioning method, where single items are moved step-by-step from one cluster to another based on optimization of some parameter. One of such algorithms, which will be mentioned in this paper is K-means algorithm, where data points are partitioned based on optimization of sum of squared distances within clusters (MacQueen, 1967). Another large class of algorithms are based on finite mixture model clustering methods. For example, stochastic emEMclustering method, which will also be covered in this article, is based on maximum likelihood estimation of statistical model parameters (Melnykov & Maitra). Misclassification of data is not a rare situation in cluster analysis. For instance, we can observe that several points have been misclassified on the previous figure (Figure 1) of true partition (a) versus the solution found by the K-means algorithm (b). Various factors lead to misclassification in clustering algorithms. The main goal of this paper is to analyze the effect of pairwise overlap, number of dimensions of data, and number of clusters on misclassification. The simplest case where misclassification can occur is when there are two clusters. The overlap is exact in this case, thus, we proceeded to use one of the simplest algorithms – K-means. At the higher number of clusters, when overlap is estimated, we considered more complex emEM algorithm
2016-06-16T03:18:44Z
2016-06-16T03:18:44Z
2015
Capstone Project
Akynkozhayev Birzhan.2015. Pairwise Overlap and Misclassification in Cluster Analysis. School of Science and Technology. Mathematics Department. http://nur.nu.edu.kz/handle/123456789/1635
http://nur.nu.edu.kz/handle/123456789/1635
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16362019-12-26T09:09:15Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Boundary Element Method for Stokes Flow in Incompressible Newtonian Fluids
Tazhimbetov, Nurbek Akhmetuly
Research Subject Categories
Capstone Project
Stokes flow
In this thesis, I present different discretization techniques for boundary integral
method for Stokes flow in case of an incompressible Newtonian fluid. Boundary
integral method (BIM) is one of many techniques that are used to solve Partial
Differencial Equations (PDE) numerically. However, the basic advantage of the BIM
is that it reduces the problem from n-dimensional domain to n - 1; for example,
the two-dimensional square-box that contains viscous liquid can be solved by using
the values of an unkown function at the boundary of square. Nevertheless, the BIM
exhibits some challenges in finding the Green's function for a particular domain or
differential operator, solving the integral equations and, especially, in computing the
values of a complex domain. The latter one is quite diffcult because the flow diverges
at corners (exhibits singularity). The goal of this work is to derive general analytical solution for Stokes equation (in integral equations form) and to compute the discretized integral equations using different quadrature rules for cavity problem.
2016-06-20T02:57:37Z
2016-06-20T02:57:37Z
2015-04
Capstone Project
Tazhimbetov Nurbek Akhmetuly. 2015. Boundary Element Method for Stokes Flow in Incompressible Newtonian Fluids. School of Science and Technology. Mathematics Department. http://nur.nu.edu.kz/handle/123456789/1636
http://nur.nu.edu.kz/handle/123456789/1636
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16842020-07-14T04:38:40Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1683
The implementation of the computer system Aleks for placement in mathematical courses at Nazarbayev university
Adaricheva, Kira
Assylbekov, Zh.
computer system Aleks
mathematical courses at Nazarbayev university
teaching tool
The ALEKS computer system, well-known on the American con-
tinent as an individualized teaching tool and placement test into a series of
high school and college level courses, was implemented by the Mathematics
Department of Nazarbayev University, most likely as the frst experiment of
this sort in the heart of Asia. This paper summarizes the results of the placement testing of several hundreds of Kazakhstani students passing from the
preparatory study focused on biology, economics or engineering mathematics
to the typical curriculum of science departments at the School of Science and
Technology of Nazarbayev University.
2016-08-09T03:49:27Z
2016-08-09T03:49:27Z
2013
Technical Report
K. Adaricheva and Zh. Assylbekov; 2013; The implementation of the computer system Aleks for placement in mathematical courses at Nazarbayev university; Nazarbayev University, SST, Math Department
http://nur.nu.edu.kz/handle/123456789/1684
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Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/16922018-08-15T03:50:00Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_905
A free/open-source hybrid morphological disambiguation tool for Kazakh
Assylbekov, Zhenisbek
Washington, Jonathan
Tyers, Francis
Nurkas, Assulan
Sundetova, Aida
Karibayeva, Aidana
Abduali, Balzhan
Amirova, Dina
open-source
morphological disambiguation
hybrid morphological disambiguation tool
tool for Kazakh
Research Subject Categories::MATHEMATICS
This paper presents the results of developing a
morphological disambiguation tool for Kazakh. Starting with a
previously developed rule-based approach, we tried to cope with
the complex morphology of Kazakh by breaking up lexical forms
across their derivational boundaries into inflectional groups
and modeling their behavior with statistical methods. A hybrid
rule-based/statistical approach appears to benefit morphological
disambiguation demonstrating a per-token accuracy of 91% in
running text.
2016-09-05T04:16:09Z
2016-09-05T04:16:09Z
2016-04
Conference Paper
Assylbekov, Zhenisbek; North, Jonathan; Tyers, Francis; Nurkas, Assulan; Sundetova, Aida; Karibayeva, Aidana; Abduali, Balzhan; Amirova, Dina. (2016). A free/open-source hybrid morphological disambiguation tool for Kazakh.; Conference Paper.
http://nur.nu.edu.kz/handle/123456789/1692
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DOI: 10.13140/RG.2.2.12467.43045
oai:nur.nu.edu.kz:123456789/16942018-08-15T03:49:58Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_905
Experiments with Russian to Kazakh sentence alignment
Assylbekov, Zhenisbek
Myrzakhmetov, Bagdat
Makazhanov, Aibek
sentence alignment
sentence splitting
lemmatization
parallel corpus
Kazakh language
выравнивание по предложениям
разбивка по предложениям
лемматизация
параллельный корпус
казахский язык
Research Subject Categories::MATHEMATICS
Sentence alignment is the final step in building parallel corpora, which arguably has the greatest impact on the quality of a resulting corpus and the accuracy of machine translation systems that use it for training. However, the quality of sentence alignment itself depends on a number of factors. In this paper we investigate the impact of several data processing techniques on the quality of sentence alignment. We develop and use a number of automatic evaluation metrics, and provide empirical evidence that application of all of the considered data processing techniques yields bitexts with the lowest ratio of noise and the highest ratio of parallel sentences.
2016-09-20T10:26:55Z
2016-09-20T10:26:55Z
2016
Conference Paper
Zhenisbek Assylbekov , Bagdat Myrzakhmetov and Aibek Makazhanov (2016) Experiments with Russian to Kazakh sentence alignment. The 4-th International Conference on Computer Processing of Turkic Languages “TurkLang 2016”.
http://nur.nu.edu.kz/handle/123456789/1694
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The 4-th International Conference on Computer Processing of Turkic Languages “TurkLang 2016”
oai:nur.nu.edu.kz:123456789/19142018-08-15T03:50:05Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Existence, Uniqueness, and Numerical Analysis of Solutions of a Quasilinear ParabolicProblem
Wei, Dongming
quasilinear parabolic problem
method of lines
finite element method
L2 estimates
A quasilinear parabolic problem is studied. By using the method of lines, the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown. Also given are L2 error estimates for the error between the extended fully discrete finite element solutions and the exact solution.
2016-11-23T06:02:09Z
2016-11-23T06:02:09Z
1992-04
Article
Dongming Wei; 1992; Society for Industrial and Applied Mathematics. SIAM Journal on Numerical Analysis; Journal on Numerical Analysis; http://nur.nu.edu.kz/handle/123456789/1914
http://nur.nu.edu.kz/handle/123456789/1914
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Society for Industrial and Applied Mathematics. SIAM Journal on Numerical Analysis
oai:nur.nu.edu.kz:123456789/19152018-08-15T03:50:06Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Some Generalized Trigonometric Sine Functions and Their Applications
Wei, Dongming
Liu, Yu
generalized sine
Hamilton system
nonlinear spring
vibration
analytic solution
In this paper, it is shown that D. Shelupsky's generalized sine func-
tion, and various general sine functions developed by P. Drabek, R.
Manasevich and M. Otani, P. Lindqvist, including the generalized Ja-
cobi elliptic sine function of S. Takeuchi can be defned by systems of
first order nonlinear ordinary differential equations with initial condi-
tions. The structure of the system of differential equations is shown to
be related to the Hamilton System in Lagrangian Mechanics. Numer-
ical solutions of the ODE systems are solved to demonstrate the sine
functions graphically. It is also demonstrated that the some of the gen-
eralized sine functions can be used to obtain analytic solutions to the
equation of a nonlinear spring-mass system.
2016-11-23T06:16:00Z
2016-11-23T06:16:00Z
2012
Article
Dongming Wei and Yu Liu; 2012; Some Generalized Trigonometric Sine Functions and Their Applications; Applied Mathematical Sciences; http://nur.nu.edu.kz/handle/123456789/1915
http://nur.nu.edu.kz/handle/123456789/1915
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Applied Mathematical Sciences
oai:nur.nu.edu.kz:123456789/19182018-08-15T03:50:07Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Penalty finite element approximations of the stationary power- law Stokes problem
Lefton, Lew
Wei, Dongming
Power-law flows
penalty method
stationary Stokes problem
non-Newtonian flows
finite element method
convergence and error estimates
BB condition
Finite element approximations of the stationary power-law Stokes problem using penalty
formulation are considered. A priori error estimates under appropriate smoothness assumptions on the
solutions are established without assuming a discrete version of the BB condition. Numerical solutions
are presented by implementing a nonlinear conjugate gradient method
2016-11-23T06:31:20Z
2016-11-23T06:31:20Z
2003
Article
Lew Lefton and Dongming Wei; 2003; Penalty finite element approximations of the stationary power- law Stokes problem; Journal of Numerical Mathematics; http://nur.nu.edu.kz/handle/123456789/1918
http://nur.nu.edu.kz/handle/123456789/1918
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Journal of Numerical Mathematics
oai:nur.nu.edu.kz:123456789/19202018-08-15T03:50:00Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Finite Element Analysis of the Ramberg-Osgood Bar
Wei, Dongming
Elgindi, Mohamed B. M.
Nonlinear Two Point Boundary Value Problem
Ramberg-Osgood Axial Bar
Existence and Uniqueness of Solutions
Finite Element Analysis
Convergence and a Priori Error Estimates
In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to the associated nonlinear two point boundary value problem is established and used as a foundation for the finite element analysis.
2016-11-23T08:07:42Z
2016-11-23T08:07:42Z
2013
Article
Dongming Wei, Mohamed B. M. Elgindi; 2013; Finite Element Analysis of the Ramberg-Osgood Bar; American Journal of Computational Mathematics; http://nur.nu.edu.kz/handle/123456789/1920
http://nur.nu.edu.kz/handle/123456789/1920
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American Journal of Computational Mathematics
oai:nur.nu.edu.kz:123456789/19212018-08-15T03:50:01Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load
Elgindi, Mohamed B. M.
Wei, Dongming
Soukiassian, Yeran
Liu, Yu
Critical Buckling Load
Graphene
Euler-Bernoulli Beam
Non-Linear Eigenvalue Problem
Shooting Method
In this paper, we consider the buckling of an Euler-Bernoulli graphene beam due to an axial compressive
load. We formulate the problem as a non-linear (eigenvalue) two-point boundary value
problem, prove some properties of the eigenpairs and introduce a suitable numerical shooting
method scheme for approximating them. We present the perturbation and the numerical approximations
of the first and second buckling loads and the corresponding shapes
2016-11-23T08:20:15Z
2016-11-23T08:20:15Z
2014
Article
Mohamed B. M. Elgindi1, Dongming Wei, Yeran Soukiassian, Yu Liu; 2014; On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load; World Journal of Engineering and Technology; http://nur.nu.edu.kz/handle/123456789/1921
http://nur.nu.edu.kz/handle/123456789/1921
en
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World Journal of Engineering and Technology
oai:nur.nu.edu.kz:123456789/19222018-08-15T03:50:01Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Existence of Equilibrium States of Hollow Hollomon Cylinders Submerged in a Fluid
Elgindi, Mohamed B. M.
Wei, Dongming
Existence of equilibrium states
Hollomon power-law material
hollow plastic cylinders
nonlinear eigenvalue problem
nonlinear integro-differential equation
minimization of functional with constraints
Browder Theorem
This paper is concerned with the existence of equilibrium states of a thin-walled hollow
elasto-plastic cylinders fully or partially submerged in a fluid. This problem serves as a
model for many problems with engineering importance. Previous studies on the
deformation of such a shell assumed that the material is linear elastic. This paper takes
into consideration the nonlinear Hollomon materials that (are plastic) can deform
plastically. The effect of gravity on pressure is also taken into account
2016-11-23T08:30:43Z
2016-11-23T08:30:43Z
2013
Article
M. B. M. Elgindi and Dongming Wei; 2013; Existence of Equilibrium States of Hollow Hollomon Cylinders Submerged in a Fluid; Applied Mathematical Sciences; http://nur.nu.edu.kz/handle/123456789/1922
http://nur.nu.edu.kz/handle/123456789/1922
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Applied Mathematical Sciences
oai:nur.nu.edu.kz:123456789/19242018-08-15T03:50:03Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On the Global Solvability of a Class of Fourth- Order Nonlinear Boundary Value Problems
Elgindi, Mohamed B. M.
Wei, Dongming
Global solvability
fourth-order nonlinear boundary value problems
monotone operator
Leray-Schauder fixed point theorem
coercivity
In this paper we prove the global solvability of a class of fourth-order
nonlinear boundary value problems that govern the deformation of a Hollomon’s
power-law plastic beam subject to an axial compression and nonlinear lateral
constrains. For certain ranges of the acting axial compression force, the
solvability of the equations follows from the monotonicity of the fourth order
nonlinear differential operator. Beyond these ranges the monotonicity of the
operator is lost. It is shown that, in this case, the global solvability may be
generated by the lower order nonlinear terms of the equations for a certain type of
constrains.
2016-11-23T08:44:40Z
2016-11-23T08:44:40Z
2012
Article
Elgindi, M.B.M. and Wei, Dongming; 2012; On the Global Solvability of a Class of Fourth- Order Nonlinear Boundary Value Problems; Mathematics Faculty Publications; http://nur.nu.edu.kz/handle/123456789/1924
http://nur.nu.edu.kz/handle/123456789/1924
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Mathematics Faculty Publications
oai:nur.nu.edu.kz:123456789/19252018-08-15T03:50:03Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Optimal Design of Helical Springs of Power Law Materials
Wei, Dongming
Fyrillas, Marios
Otemissov, Adilet
Bekishev, Rustam
Helical Spring
Power Law Materials
Geometric Programming
Optimal Design
In this paper the geometric dimensions of a compressive helical spring
made of power law materials are optimized to reduce the amount of material. The
mechanical constraints are derived to form the geometric programming problem.
Both the prime and the dual problem are examined and solved semi-analytically for
a range of spring index. A numerical example is provided to validate the solutions
2016-11-23T08:57:50Z
2016-11-23T08:57:50Z
2016
Article
Dongming Wei, Marios Fyrillas, Adilet Otemissov, Rustam Bekishev; 2016; Optimal Design of Helical Springs of Power Law Materials; arXiv.org; http://nur.nu.edu.kz/handle/123456789/1925
http://nur.nu.edu.kz/handle/123456789/1925
en
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arXiv.org
oai:nur.nu.edu.kz:123456789/19272018-08-15T03:50:02Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On the solvability of the Brinkman-forchheimer-extended darcy Equation
Skrzypacz, Piotr
Wei, Dongming
Brinkman-Forchheimer Equation
Packed Bed Reactors
Existence and Uniqueness of Solution
The nonlinear Brinkman-Forchheimer-extended Darcy equation is used to model some
porous medium
ow in chemical reactors of packed bed type. The results concerning the
existence and uniqueness of a weak solution are presented for nonlinear convective
ows
in medium with nonconstant porosity and for small data. Furthermore, the finite element
approximations to the
ow profiles in the fixed bed reactor are presented for several
Reynolds numbers at the non-Darcy's range
2016-11-23T09:05:20Z
2016-11-23T09:05:20Z
2016
Article
Piotr Skrzypacz and Dongming Wei; 2016; On the solvability of the Brinkman-forchheimer-extended darcy Equation; arXiv.org; http://nur.nu.edu.kz/handle/123456789/1927
http://nur.nu.edu.kz/handle/123456789/1927
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arXiv.org
oai:nur.nu.edu.kz:123456789/19302018-08-15T03:50:05Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
A Lumped-Parameter Model for Nonlinear Waves in Graphene
Hazim, Hamad
Wei, Dongming
Elgindi, Mohamed B. M.
Soukiassian, Yeran
Graphene
Resonance
Nonlinear Vibration
Phase Diagram
Frequency Sweep
A lumped-parameter nonlinear spring-mass model which takes into account the third-order elastic
stiffness constant is considered for modeling the free and forced axial vibrations of a graphene
sheet with one fixed end and one free end with a mass attached. It is demonstrated through this
simple model that, in free vibration, within certain initial energy level and depending upon its
length and the nonlinear elastic constants, that there exist bounded periodic solutions which are
non-sinusoidal, and that for each fixed energy level, there is a bifurcation point depending upon
material constants, beyond which the periodic solutions disappear. The amplitude, frequency, and
the corresponding wave solutions for both free and forced harmonic vibrations are calculated
analytically and numerically. Energy sweep is also performed for resonance applications
2016-11-23T09:28:40Z
2016-11-23T09:28:40Z
2015
Article
Hamad Hazim, Dongming Wei, Mohamed Elgindi, Yeran Soukiassian; 2015; A Lumped-Parameter Model for Nonlinear Waves in Graphene; World Journal of Engineering and Technology; http://nur.nu.edu.kz/handle/123456789/1930
http://nur.nu.edu.kz/handle/123456789/1930
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World Journal of Engineering and Technology
oai:nur.nu.edu.kz:123456789/19322018-08-15T03:50:07Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On the solvability of euler graphene beam subject to axial compressive load
Elgindi, Mohamed B. M.
Wei, Dongming
Elgindi, T.M.
Materials Science
Analysis of PDEs
In this paper we formulate the equilibrium equation for a beam made of graphene sub-
jected to some boundary conditions and acted upon by axial compression and nonlinear lateral
constrains as a fourth-order nonlinear boundary value problem. We first study the nonlinear
eigenvalue problem for buckling analysis of the beam. We show the solvability of the eigen-
value problem as an asymptotic expansion in a ratio of the elastoplastic parameters. We
verify that the spectrum is a closed set bounded away from zero and contains a discrete in-
finite sequence of eigenvalues. In particular, we prove the existence of a minimal eigenvalue
for the graphene beam corresponding to a Lipschitz continuous eigenfunction, providing a
lower bound for the critical buckling load of the graphene beam column. We also proved that
the eigenfunction corresponding to the minimal eigenvalue is positive and symmetric. For a
certain range of lateral forces, we demonstrate the solvability of the general equation by using
energy methods and a suitable iteration scheme.
2016-11-23T09:49:51Z
2016-11-23T09:49:51Z
2014
Article
Mohamed B. Elgindi, Dongming Wei and Tarek M. Elgindi; 2014; On the solvability of euler graphene beam subject to axial compressive load; arXiv.org; http://nur.nu.edu.kz/handle/123456789/1932
http://nur.nu.edu.kz/handle/123456789/1932
en
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arXiv.org
oai:nur.nu.edu.kz:123456789/19342018-08-15T03:50:04Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
A Penalty Method for Approximations of the Stationary Power-Law Stokes Problem
Lefton, Lew
Wei, Dongming
We study approximations of the steady state Stokes problem governed
by the power-law model for viscous incompressible non-Newtonian flow
using the penalty formulation. We establish convergence and find error estimates.
2016-11-23T10:19:56Z
2016-11-23T10:19:56Z
2001
Article
Lew Lefton, Dongming Wei; 2001; A Penalty Method for Approximations of the Stationary Power-Law Stokes Problem; Electronic journal of differential equations; http://nur.nu.edu.kz/handle/123456789/1934
http://nur.nu.edu.kz/handle/123456789/1934
en
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Electronic journal of differential equations
oai:nur.nu.edu.kz:123456789/19352018-08-15T03:50:09Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Decay Estimates of Heat Transfer to Melton Polymer Flow in Pipes with Viscous Dissipation
Wei, Dongming
Zhang, Zhenbu
In this work, we compare a parabolic equation with an elliptic
equation both of which are used in modeling temperature profile of a powerlaw
polymer
ow in a semi-infinite straight pipe with circular cross section.
We show that both models are well-posed and we derive exponential rates of
convergence of the two solutions to the same steady state solution away from
the entrance. We also show estimates for difference between the two solutions
in terms of physical data.
2016-11-23T10:26:39Z
2016-11-23T10:26:39Z
2001
Article
Dongming Wei, Zhenbu Zhang; 2001; Decay Estimates of Heat Transfer to Melton Polymer Flow in Pipes with Viscous Dissipation; Electronic journal of differential equations; http://nur.nu.edu.kz/handle/123456789/1935
http://nur.nu.edu.kz/handle/123456789/1935
en
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Electronic journal of differential equations
oai:nur.nu.edu.kz:123456789/21912018-08-15T03:50:09Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Adaptive cross approximation for ill-posed problems
Mach, Thomas
Reichel, Lothar
Van Barel, Marc
Vandebril, R.
adaptive cross approximation
Ill-posed problem
inverse problem
regularization
sparse discretization
Integral equations of the first kind with a smooth kernel and perturbed right-hand side, which represents available contaminated data, arise in many applications. Discretization gives rise to linear systems of equations with a matrix whose singular values cluster at the origin. The solution of these systems of equations requires regularization, which has the effect that components in the computed solution connected to singular vectors associated with small singular values are damped or ignored. In order to compute a useful approximate solution typically approximations of only a fairly small number of the largest singular values and associated singular vectors of the matrix are required. The present paper explores the possibility of determining these approximate singular values and vectors by adaptive cross approximation. This approach is particularly useful when a fine discretization of the integral equation is required and the resulting linear system of equations is of large dimensions, because adaptive cross approximation makes it possible to compute only fairly few of the matrix entries.
2017-01-06T09:32:09Z
2017-01-06T09:32:09Z
2016-09-01
Article
Mach, T., Reichel, L., Van Barel, M., & Vandebril, R. (2016). Adaptive cross approximation for ill-posed problems. Journal of Computational and Applied Mathematics, 303, 206-217. DOI: 10.1016/j.cam.2016.02.020
http://nur.nu.edu.kz/handle/123456789/2191
en
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Journal of Computational and Applied Mathematics
oai:nur.nu.edu.kz:123456789/21922018-08-15T03:50:09Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
A New Weibull–Pareto Distribution: Properties and Applications
Tahir, M. H.
Cordeiro, Gauss M.
Alzaatreh, Ayman
Mansoor, M.
Zubair, M.
hazard function
likelihood estimation
moment
pareto distribution
Weibull-G class
Many distributions have been used as lifetime models. In this article, we propose a new three-parameter Weibull–Pareto distribution, which can produce the most important hazard rate shapes, namely, constant, increasing, decreasing, bathtub, and upsidedown bathtub. Various structural properties of the new distribution are derived including explicit expressions for the moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, and generating and quantile functions. The Rényi and q entropies are also derived. We obtain the density function of the order statistics and their moments. The model parameters are estimated by maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of two real datasets on Wheaton river flood and bladder cancer. In the two applications, the new model provides better fits than the Kumaraswamy–Pareto, beta-exponentiated Pareto, beta-Pareto, exponentiated Pareto, and Pareto models.
2017-01-06T09:46:56Z
2017-01-06T09:46:56Z
2016-11-25
Article
Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., & Zubair, M. (2016). A New Weibull–Pareto Distribution: Properties and Applications. Communications in Statistics: Simulation and Computation, 45(10), 3548-3567. DOI: 10.1080/03610918.2014.948190
http://nur.nu.edu.kz/handle/123456789/2192
en
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Communications in Statistics: Simulation and Computation
oai:nur.nu.edu.kz:123456789/21952018-08-15T03:50:09Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
An extended Hessenberg form for Hamiltonian matrices
Ferranti, Micol
Iannazzo, Bruno
Mach, Thomas
Vandebril, Raf
extended hessenberg forms
hamiltonian eigenvalue problems
QR algorithm
A unitary symplectic similarity transformation for a special class of Hamiltonian matrices to extended Hamiltonian Hessenberg form is presented. Whereas the classical Hessenberg form links to Krylov subspaces, the extended Hessenberg form links to extended Krylov subspaces. The presented algorithm generalizes thus the classic reduction to Hamiltonian Hessenberg form and offers more freedom in the choice of Hamiltonian condensed forms, to be used within an extended Hamiltonian QR algorithm. Theoretical results identifying the structure of the extended Hamiltonian Hessenberg form and proofs of uniqueness of the reduction process are included. Numerical experiments confirm the validity of the approach.
2017-01-06T10:02:29Z
2017-01-06T10:02:29Z
2016-06-01
Article
Ferranti, M., Iannazzo, B., Mach, T., & Vandebril, R. (2016). An extended Hessenberg form for Hamiltonian matrices. Calcolo, 1-31. DOI: 10.1007/s10092-016-0192-1
http://nur.nu.edu.kz/handle/123456789/2195
en
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Calcolo
oai:nur.nu.edu.kz:123456789/22022018-08-15T03:50:00Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Convergence rates for inverse-free rational approximation of matrix functions
Jagels, Carl
Mach, Thomas
Reichel, Lothar
Vandebril, Raf
approximation
convergence rate
iterative method
matrix function
rational Krylov
This article deduces geometric convergence rates for approximating matrix functions via inverse-free rational Krylov methods. In applications one frequently encounters matrix functions such as the matrix exponential or matrix logarithm; often the matrix under consideration is too large to compute the matrix function directly, and Krylov subspace methods are used to determine a reduced problem. If many evaluations of a matrix function of the form f(A)v with a large matrix A are required, then it may be advantageous to determine a reduced problem using rational Krylov subspaces. These methods may give more accurate approximations of f(A)v with subspaces of smaller dimension than standard Krylov subspace methods. Unfortunately, the system solves required to construct an orthogonal basis for a rational Krylov subspace may create numerical difficulties and/or require excessive computing time. This paper investigates a novel approach to determine an orthogonal basis of an approximation of a rational Krylov subspace of (small) dimension from a standard orthogonal Krylov subspace basis of larger dimension. The approximation error will depend on properties of the matrix A and on the dimension of the original standard Krylov subspace. We show that our inverse-free method for approximating the rational Krylov subspace converges geometrically (for increasing dimension of the standard Krylov subspace) to a rational Krylov subspace. The convergence rate may be used to predict the dimension of the standard Krylov subspace necessary to obtain a certain accuracy in the approximation. Computed examples illustrate the theory developed.
2017-01-09T03:33:16Z
2017-01-09T03:33:16Z
2016-12-01
Article
Jagels, C., Mach, T., Reichel, L., & Vandebril, R. (2016). Convergence rates for inverse-free rational approximation of matrix functions. Linear Algebra and Its Applications, 510, 291-310. DOI: 10.1016/j.laa.2016.08.029
http://nur.nu.edu.kz/handle/123456789/2202
en
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Linear Algebra and Its Applications
oai:nur.nu.edu.kz:123456789/22032018-08-15T03:50:03Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Fast and backward stable computation of the eigenvalues of matrix polynomials
Aurentz, Jared
Mach, Thomas
Robol, Leonardo
Vandebril, Raf
Watkins, David S.
math.NA
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues. In this article we propose a new backward stable method for computing a factored Schur form of the associated companion pencil. The algorithm has a quadratic cost in the degree of the polynomial and a cubic one in the size of the coefficient matrices. The algorithm is a variant of Francis's implicitly shifted QR algorithm applied on the associated companion pencil. A preprocessing unitary equivalence is executed on the matrix polynomial to simultaneously bring the leading matrix coefficient and the constant matrix term to triangular form before forming the companion pencil. The resulting structure allows us to stably factor both matrices of the pencil into $k$ matrices which are of unitary-plus-rank-one form admitting cheap and numerically reliable storage. The problem is then solved as a product core chasing eigenvalue problem. The numerical experiments illustrate stability and efficiency of the proposed methods.
2017-01-09T04:09:00Z
2017-01-09T04:09:00Z
2016-11-30
Article
Aurentz, J., Mach, T., Robol, L., Vandebril, R., & Watkins, D. S. (2016). Fast and backward stable computation of the eigenvalues of matrix polynomials. arXiv, 1611(10142).
http://nur.nu.edu.kz/handle/123456789/2203
en
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arXiv
oai:nur.nu.edu.kz:123456789/22092018-08-15T03:50:26Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Neutron monitor generated data distributions in quantum variational Monte Carlo
Kussainov, A. S.
Pya, N.
neutrons
inverse transforms
splines
We have assessed the potential applications of the neutron monitor hardware as random number generator for normal and uniform distributions. The data tables from the acquisition channels with no extreme changes in the signal level were chosen as the retrospective model. The stochastic component was extracted by fitting the raw data with splines and then subtracting the fit. Scaling the extracted data to zero mean and variance of one is sufficient to obtain a stable standard normal random variate. Distributions under consideration pass all available normality tests. Inverse transform sampling is suggested to use as a source of the uniform random numbers. Variational Monte Carlo method for quantum harmonic oscillator was used to test the quality of our random numbers. If the data delivery rate is of importance and the conventional one minute resolution neutron count is insufficient, we could always settle for an efficient seed generator to feed into the faster algorithmic random number generator or create a buffer.
2017-01-09T04:45:12Z
2017-01-09T04:45:12Z
2016-09-05
Article
Kussainov, A. S., & Pya, N. (2016). Neutron monitor generated data distributions in quantum variational Monte Carlo. Journal of Physics: Conference Series, 738(1), [012076]. DOI: 10.1088/1742-6596/738/1/012076
http://nur.nu.edu.kz/handle/123456789/2209
en
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Journal of Physics: Conference Series
oai:nur.nu.edu.kz:123456789/22142018-08-15T03:50:08Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Roots of Polynomials: on twisted QR methods for companion matrices and pencils
Aurentz, Jared L.
Mach, Thomas
Robol, Leonardo
Vandebril, Raf
Watkins, David S.
polynomial rootfinding
companion matrix
companion pencil
eigenvalue
QR algorithm
QZ algorithm
rotators
core transformation
backward stability
Root
AMS subject classification: 65F15, 65H17, 15A18, 65H04
Two generalizations of the companion QR algorithm by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015, to compute the roots of a polynomial are presented. First, we will show how the fast and backward stable QR algorithm for companion matrices can be generalized to a QZ algorithm for companion pencils. Companion pencils admit a greater flexibility in scaling the polynomial and distributing the matrix coefficients over both matrices in the pencil. This allows for an enhanced stability for polynomials with largely varying coefficients. Second, we will generalize the pencil approach further to a twisted QZ algorithm. Whereas in the classical QZ case Krylov spaces govern the convergence, the convergence of the twisted case is determined by a rational Krylov space. A backward error analysis to map the error back to the original pencil and to the polynomial coefficients shows that in both cases the error scales quadratically with the input. An extensive set of numerical experiments supports the theoretical backward error, confirms the numerical stability and shows that the computing time depends quadratically on the problem size.
2017-01-09T05:13:22Z
2017-01-09T05:13:22Z
2016-11-08
Article
Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., & Watkins, D. S. (2016). Roots of Polynomials: on twisted QR methods for companion matrices and pencils. arXiv, 1611(02435).
http://nur.nu.edu.kz/handle/123456789/2214
en
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arXiv
oai:nur.nu.edu.kz:123456789/22192018-08-15T03:50:09Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
The gamma half-Cauchy distribution: Properties and applications
Alzaatreh, Ayman
Mansoory, M.
Tahirz, M. H.
Zubair, M.
Ghazalik, Shakir Ali
folded Cauchy distribution
gamma distribution
Half-Cauchy distribution
Shannon entropy
A new distribution, namely, the Gamma-Half-Cauchy distribution is proposed. Various properties of the Gamma-Half-Cauchy distribution are studied in detail such as limiting behavior, moments, mean deviations and Shannon entropy. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is obtained. Two data sets are used to illustrate the applications of Gamma-Half-Cauchy distribution.
2017-01-09T05:41:25Z
2017-01-09T05:41:25Z
2016
Article
Alzaatreh, A., Mansoory, M., Tahirz, M. H., Zubair, M., & Ghazalik, S. A. (2016). The gamma half-Cauchy distribution: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 45(4), 1143-1159. DOI: 10.15672/HJMS.20157011058
http://nur.nu.edu.kz/handle/123456789/2219
en
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Hacettepe Journal of Mathematics and Statistics
oai:nur.nu.edu.kz:123456789/22202018-08-15T03:50:01Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
The logistic-X family of distributions and its applications
Tahir, M. H.
Cordeiro, Gauss M.
Alzaatreh, Ayman
Mansoor, M.
Zubair, M.
estimation
Fréchet distribution
logistic distribution
moment
T-X family
The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed, and reversed-J shaped, and can have increasing, decreasing, bathtub, and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy, and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fréchet distribution, and illustrate its importance by means of two applications to real data sets.
2017-01-09T05:52:03Z
2017-01-09T05:52:03Z
2016-12-16
Article
Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., & Zubair, M. (2016). The logistic-X family of distributions and its applications. Communications in Statistics - Theory and Methods, 45(24), 7326-7349. DOI: 10.1080/03610926.2014.980516
http://nur.nu.edu.kz/handle/123456789/2220
en
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Communications in Statistics - Theory and Methods
oai:nur.nu.edu.kz:123456789/22222018-08-15T03:50:01Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Variations on Barbalat's lemma
Farkas, Bálint
Wegner, Sven Ake
lemma
control theory
It is not hard to prove that a uniformly continuous real function, whose integral up to infinity exists, vanishes at infinity, and it is probably little known that this statement runs under the name "Barbalat's lemma." In fact, the latter name is frequently used in control theory, where the lemma is used to obtain Lyapunov-like stability theorems for nonlinear and nonautonomous systems. Barbalat's lemma is qualitative in the sense that it asserts that a function has certain properties, here convergence to zero. Such qualitative statements can typically be proved by "soft analysis," such as indirect proofs. Indeed, in the original 1959 paper by Barbalat, the lemma was proved by contradiction, and this proof prevails in the control theory textbooks. In this short note, we first give a direct, "hard analyis" proof of the lemma, yielding quantitative results, i.e., rates of convergence to zero. This proof allows also for immediate generalizations. Finally, we unify three different versions that recently appeared and discuss their relation to the original lemma.
2017-01-09T06:00:14Z
2017-01-09T06:00:14Z
2016-10-01
Article
Farkas, B., & Wegner, S. A. (2016). Variations on Barbalat's lemma. American Mathematical Monthly, 123(8), 825-830. DOI: 10.4169/amer.math.monthly.123.08.825
http://nur.nu.edu.kz/handle/123456789/2222
en
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American Mathematical Monthly
oai:nur.nu.edu.kz:123456789/22242018-08-15T03:50:06Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum
Benner, Peter
Börm, Steffen
Mach, Thomas
Reimer, Knut
slicing the spectrum
symmetric generalized eigenproblem
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.
2017-01-09T07:20:30Z
2017-01-09T07:20:30Z
2015-03-04
Article
Benner, P., Börm, S., Mach, T., & Reimer, K. (2015). Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum. Computing and Visualization in Science. DOI: 10.1007/s00791-015-0238-y
http://nur.nu.edu.kz/handle/123456789/2224
en
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Computing and Visualization in Science
oai:nur.nu.edu.kz:123456789/22252018-08-15T03:50:07Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Fast and backward stable computation of roots of polynomials
Aurentz, Jared L.
Mach, Thomas
Vandebril, Raf
Watkins, David S.
companion matrix
eigenvalue
polynomial
QR algorithm
root
rootfinding
rotators
A stable algorithm to compute the roots of polynomials is presented. The roots are found by computing the eigenvalues of the associated companion matrix by Francis's implicitly shifted QR algorithm. A companion matrix is an upper Hessenberg matrix that is unitary-plus-rankone, that is, it is the sum of a unitary matrix and a rank-one matrix. These properties are preserved by iterations of Francis's algorithm, and it is these properties that are exploited here. The matrix is represented as a product of 3n - 1 Givens rotators plus the rank-one part, so only O(n) storage space is required. In fact, the information about the rank-one part is also encoded in the rotators, so it is not necessary to store the rank-one part explicitly. Francis's algorithm implemented on this representation requires only O(n) flops per iteration and thus O(n2) flops overall. The algorithm is described, normwise backward stability is proved, and an extensive set of numerical experiments is presented. The algorithm is shown to be about as accurate as the (slow) Francis QR algorithm applied to the companion matrix without exploiting the structure. It is faster than other fast methods that have been proposed, and its accuracy is comparable or better.
2017-01-09T07:33:23Z
2017-01-09T07:33:23Z
2015
Article
Aurentz, J. L., Mach, T., Vandebril, R., & Watkins, D. S. (2015). Fast and backward stable computation of roots of polynomials. SIAM Journal on Matrix Analysis and Applications, 36(3), 942-973. DOI: 10.1137/140983434
http://nur.nu.edu.kz/handle/123456789/2225
en
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SIAM Journal on Matrix Analysis and Applications
oai:nur.nu.edu.kz:123456789/22262018-08-15T03:50:06Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Fast and stable unitary QR algorithm
Aurentz, Jared L.
Mach, Thomas
Vandebril, Raf
Watkins, David S.
core transformations rotators
eigenvalue
Francis's QR algorithm
unitary matrix
A fast Fortran implementation of a variant of Gragg's unitary Hessenberg QR algorithm is presented. It is proved, moreover, that all QR- And QZ-like algorithms for the unitary eigenvalue problems are equivalent. The algorithm is backward stable. Numerical experiments are presented that confirm the backward stability and compare the speed and accuracy of this algorithm with other methods.
2017-01-09T10:28:50Z
2017-01-09T10:28:50Z
2015
Article
Aurentz, J. L., Mach, T., Vandebril, R., & Watkins, D. S. (2015). Fast and stable unitary QR algorithm. Electronic Transactions on Numerical Analysis, 44, 327-341.
http://nur.nu.edu.kz/handle/123456789/2226
en
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Electronic Transactions on Numerical Analysis
oai:nur.nu.edu.kz:123456789/22282018-08-15T03:50:06Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices
Mach, Thomas
Pranić, Miroslav S.
Vandebril, Raf
extended Krylov
Iterative methods
Krylov
rational Krylov
rotations
similarity transformations
It has been shown that approximate extended Krylov subspaces can be computed, under certain assumptions, without any explicit inversion or system solves. Instead, the vectors spanning the extended Krylov space are retrieved in an implicit way, via unitary similarity transformations, from an enlarged Krylov subspace. In this paper this approach is generalized to rational Krylov subspaces, which aside from poles at infinity and zero, also contain finite non-zero poles. Furthermore, the algorithms are generalized to deal with block rational Krylov subspaces and techniques to exploit the symmetry when working with Hermitian matrices are also presented. For each variant of the algorithm numerical experiments illustrate the power of the new approach. The experiments involve matrix functions, Ritz-value computations, and the solutions of matrix equations.
2017-01-09T11:00:15Z
2017-01-09T11:00:15Z
2014
Article
Mach, T., Pranić, M. S., & Vandebril, R. (2014). Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices. Electronic Transactions on Numerical Analysis, 43, 100-124.
http://nur.nu.edu.kz/handle/123456789/2228
en
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Electronic Transactions on Numerical Analysis
oai:nur.nu.edu.kz:123456789/22302018-08-15T03:50:09Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices
Mach, Thomas
Van Barel, Marc
Vandebril, Raf
data sparse factorizations
extended Hessenberg matrix
inverse eigenvalue problem
rational Arnoldi
rational nonsymmetric Lanczos
In inverse eigenvalue problems one tries to reconstruct a matrix, satisfying some constraints, given some spectral information. Here, two inverse eigenvalue problems are solved. First, given the eigenvalues and the first components of the associated eigenvectors (called the weight vector) an extended Hessenberg matrix with prescribed poles is computed possessing these eigenvalues and satisfying the eigenvector constraints. The extended Hessenberg matrix is retrieved by executing particularly designed unitary similarity transformations on the diagonal matrix containing the eigenvalues. This inverse problem closely links to orthogonal rational functions: the extended Hessenberg matrix contains the recurrence coefficients given the nodes (eigenvalues), poles (poles of the extended Hessenberg matrix), and a weight vector (first eigenvector components) determining the discrete inner product. Moreover, it is also sort of the inverse of the (rational) Arnoldi algorithm: instead of using the (rational) Arnoldi method to compute a Krylov basis to approximate the spectrum, we will reconstruct the orthogonal Krylov basis given the spectral info. In the second inverse eigenvalue problem, we do the same, but refrain from unitarity. As a result we execute possibly non-unitary similarity transformations on the diagonal matrix of eigenvalues to retrieve a (non)-symmetric extended tridiagonal matrix. The algorithm will be less stable, but it will be faster, as the extended tridiagonal matrix admits a low cost factorization of O(n) (n equals the number of eigenvalues), whereas the extended Hessenberg matrix does not. Again there is a close link with orthogonal function theory, the extended tridiagonal matrix captures the recurrence coefficients of bi-orthogonal rational functions. Moreover, it is again sort of inverse of the nonsymmetric Lanczos algorithm: given spectral properties, we reconstruct the two basis Krylov matrices linked to the nonsymmetric Lanczos algorithm. © 2014 Elsevier B.V. All rights reserved.
2017-01-10T10:36:03Z
2017-01-10T10:36:03Z
2014-12-15
Article
Mach, T., Van Barel, M., & Vandebril, R. (2014). Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices. Journal of Computational and Applied Mathematics, 272, 377-398. DOI: 10.1016/j.cam.2014.03.015
http://nur.nu.edu.kz/handle/123456789/2230
en
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Journal of Computational and Applied Mathematics
oai:nur.nu.edu.kz:123456789/22322018-08-15T03:50:01Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On deflations in extended QR algorithms
Mach, Thomas
Vandebril, Raf
aggressive early deflations
deflation
extended Hessenberg matrices
extended QR algorithms
middle deflations
perturbation bounds
rotations
In this paper we discuss the deflation criterion used in the extended QR algorithm based on the chasing of rotations. We provide absolute and relative perturbation bounds for this deflation criterion. Further, we present a generalization of aggressive early deflation to the extended QR algorithms. Aggressive early deflation is the key technique for the identification and deflation of already converged, but hidden, eigenvalues. Often these possibilities for deflation are not detected by the standard technique. We present numerical results underpinning the power of aggressive early deflation also in the context of extended QR algorithms. We further generalize these ideas by the transcription of middle deflations. © 2014 Society for Industrial and Applied Mathematics.
2017-01-11T03:46:37Z
2017-01-11T03:46:37Z
2014
Article
Mach, T., & Vandebril, R. (2014). On deflations in extended QR algorithms. SIAM Journal on Matrix Analysis and Applications, 35(2), 559-579. DOI: 10.1137/130935665
http://nur.nu.edu.kz/handle/123456789/2232
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
SIAM Journal on Matrix Analysis and Applications
oai:nur.nu.edu.kz:123456789/22352018-08-15T03:50:03Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Bornological projective limits of inductive limits of normed spaces
Bonet, José
Wegner, Sven Ake
Bornological spaces
inductive limits
locally convex spaces
projective limits
weighted spaces of continuous functions
We establish a criterion to decide when a countable projective limit of countable inductive limits of normed spaces is bornological. We compare the conditions occurring within our criterion with well-known abstract conditions from the context of homological algebra and with conditions arising within the investigation of weighted PLB-spaces of continuous functions.
2017-01-11T04:13:58Z
2017-01-11T04:13:58Z
2011
Article
Bonet, J., & Wegner, S. A. (2011). Bornological projective limits of inductive limits of normed spaces. Functiones et Approximatio, Commentarii Mathematici, 44(2), 227-242.
http://nur.nu.edu.kz/handle/123456789/2235
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Functiones et Approximatio, Commentarii Mathematici
oai:nur.nu.edu.kz:123456789/22362018-08-15T03:50:04Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On the QR decomposition of backslashfancyscript H -matrices
Benner, Peter
Mach, Thomas
decomposition
linear algebra
boundary value problems
The hierarchical ( backslashfancyscriptH -) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix--matrix and matrix--vector products, matrix inversion and LU decomposition can be implemented efficiently using the backslashfancyscriptH -matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of backslashfancyscriptH -matrices. In the past, two different approaches for this task have been suggested in Bebendorf (Hierarchical matrices: a means to efficiently solve elliptic boundary value problems. Lecture notes in computational science and engineering (LNCSE), vol 63. Springer, Berlin, 2008) and Lintner (Dissertation, Fakultät für Mathematik, TU München. http://tumb1.biblio.tu-muenchen.de/publ/diss/ma/2002/lintner.pdf , 2002). We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an backslashfancyscriptH -matrix. Like other backslashfancyscriptH -arithmetic operations, the backslashfancyscriptH QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach.
2017-01-11T04:24:03Z
2017-01-11T04:24:03Z
2010-06-09
Article
Benner, P., & Mach, T. (2010). On the QR decomposition of backslashfancyscript H -matrices. Computing (Vienna/New York), 88(3), 111-129. DOI: 10.1007/s00607-010-0087-y
http://nur.nu.edu.kz/handle/123456789/2236
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Computing (Vienna/New York)
oai:nur.nu.edu.kz:123456789/27572018-08-15T03:50:14Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport
Kominis, Yannis
Bountis, Tassos
Flach, Sergej
asymmetric active coupler
nonlinear supermodes
We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.
2017-11-08T10:56:48Z
2017-11-08T10:56:48Z
2016-09-19
Article
Kominis Yannis et al.(>2), 2016(September 19), The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport, Scientific Reports
DOI: 10.1038/srep33699
http://nur.nu.edu.kz/handle/123456789/2757
en
Open Access - the content is available to the general public
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Scientific Reports
oai:nur.nu.edu.kz:123456789/27892018-08-15T03:50:15Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device
Wei, D.
Kadyrov, S.
Kazbek, Z.
lumped-mass model
nonlinear spring
graphene
electrostatic pull-in stability
periodic solutions
Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear
electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear
model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined
2017-11-13T06:14:43Z
2017-11-13T06:14:43Z
2017
Article
Wei D. et al.(>2), 2017, Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device, Applied and Computational Mechanics, pp. 81–90
https://doi.org/10.24132/acm.2017.322
http://nur.nu.edu.kz/handle/123456789/2789
en
Open Access - the content is available to the general public
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Applied and Computational Mechanics
oai:nur.nu.edu.kz:123456789/27922018-08-15T03:50:16Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Nonlinear Waves in Rods and Beams of Power-Law Materials
Wei, Dongming
Skrzypacz, Piotr
Yu, Xijun
Some novel traveling waves and special solutions to the 1D nonlinear dynamic equations of rod and beam of power-law materials are found in closed forms. The traveling solutions represent waves of high elevation that propagates without change of forms in time. These waves resemble the usual kink waves except that they do not possess bounded elevations. The special solutions satisfying certain boundary and initial conditions are presented to demonstrate the nonlinear behavior of the materials. This note demonstrates the apparent distinctions between linear elastic and nonlinear plastic waves.
2017-11-13T08:26:36Z
2017-11-13T08:26:36Z
2017-07-13
Article
Wei Dongming et al.(>2), 2017(July 13), Nonlinear Waves in Rods and Beams of Power-Law Materials, Journal of Applied Mathematics Volume 2017, 6 pages
https://doi.org/10.1155/2017/2095425
http://nur.nu.edu.kz/handle/123456789/2792
en
Open Access - the content is available to the general public
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Journal of Applied Mathematics
oai:nur.nu.edu.kz:123456789/28012018-08-15T03:50:15Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Controllable asymmetric phase-locked states of the fundamental active photonic dimer
Kominis, Yannis
Kovanis, Vassilios
Bountis, Tassos
photonic
phase-locked states
semiconductor lasers
photonic dimer
Research Subject Categories::MATHEMATICS
Coupled semiconductor lasers are systems possessing complex dynamics that are interesting for numerous applications in photonics. In this work, we investigate the existence and the stability of asymmetric phase-locked states of the fundamental active photonic dimer consisting of two coupled lasers.We showthat stable phase-locked
states of arbitrary asymmetry exist for extended regions of the parameter space of the system and that their field amplitude ratio and phase difference can be dynamically controlled by appropriate current injection. The model includes the important role of carrier density dynamics and shows that the phase-locked state asymmetry is related to operation conditions providing, respectively, gain and loss in the two lasers.
2017-11-14T05:35:53Z
2017-11-14T05:35:53Z
2017-10-16
Article
Kominis Yannis et al.(>2), 2017(October 16), Controllable asymmetric phase-locked states of the fundamental active photonic dimer, Physical Review
2469-9926
DOI: 10.1103/PhysRevA.96.043836
http://nur.nu.edu.kz/handle/123456789/2801
en
Open Access - the content is available to the general public
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Physical Review
oai:nur.nu.edu.kz:123456789/28022018-08-15T03:50:14Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer
Kominis, Yannis
Kovanis, Vassilios
Bountis, Tassos
The fundamental active photonic dimer consisting of two coupled quantum well lasers is inves-tigated in the context of the rate equation model. Spectral transition properties and exceptional points are shown to occur under general conditions, not restricted by PT-symmetry as in coupled mode models, suggesting a paradigm shift in the field of non-Hermitian photonics. The optical spectral signatures of system bifurcations and exceptional points are manifested in terms of self-termination effects and observable drastic variations of the spectral line shape that can be controlled in terms of optical detuning and inhomogeneous pumping.
2017-11-14T06:10:18Z
2017-11-14T06:10:18Z
2017-10-04
Article
Kominis Yannis et al.(>2), 2017(October 4), Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer, ArXiv
arXiv:1710.01687v1 [physics.optics] 4 Oct 2017
http://nur.nu.edu.kz/handle/123456789/2802
en
Open Access - the content is available to the general public
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
ArXiv
oai:nur.nu.edu.kz:123456789/28032018-08-15T03:50:15Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers
Kominis, Yannis
Bountis, Tassos
Flach, Sergej
We analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT) symmetry point the coupler is unstable. Suitable symmetry breakings lead to an asymmetric coupler, which hosts nonlinear supermodes. A subset of these broken symmetry cases finally yields nonlinear supermodes which are stable against modulational perturbations. The lack of symmetry requirements is expected to facilitate experimental implementations and relevant photonics applications.
2017-11-14T06:10:34Z
2017-11-14T06:10:34Z
2017-06-23
Article
Kominis Yannis et al.(>2), 2017(June 23), Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers, ArXiv
arXiv:1702.04980v2 [nlin.PS] 23 Jun 2017
http://nur.nu.edu.kz/handle/123456789/2803
en
Open Access - the content is available to the general public
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
ArXiv
oai:nur.nu.edu.kz:123456789/28872018-08-15T03:50:17Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On K-means algorithm with the use of Mahalanobis distances
Igor, Melnykov
Melnykov, Igor
Melnykov, Volodymyr
K-means algorithm
Mahalanobis distance
Initialization
Abstract The K-means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can be complicated. We propose a novel approach for initializing covariance matrices.
2017-12-14T04:51:53Z
2017-12-14T04:51:53Z
2014-01-01
Article
DOI:10.1016/j.spl.2013.09.026
Igor Melnykov, Volodymyr Melnykov, On K-means algorithm with the use of Mahalanobis distances, In Statistics & Probability Letters, Volume 84, 2014, Pages 88-95
01677152
https://www.sciencedirect.com/science/article/pii/S0167715213003246
http://nur.nu.edu.kz/handle/123456789/2887
en
Statistics & Probability Letters
Copyright © 2013 Elsevier B.V. All rights reserved.
Statistics & Probability Letters
oai:nur.nu.edu.kz:123456789/29292018-08-15T03:50:18Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
The heart of the Banach spaces
Sven-Ake, Wegner
Wegner, Sven-Ake
Abstract Consider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beĭlinson, Bernstein and Deligne consider in this setting a t-structure on the derived category and remark that its heart can be described as a category of formal quotients. They further point out that the category of Banach spaces is an example, and that here a similar category of formal quotients was studied by Waelbroeck already in 1962. In the current article, we give a direct and rigorous construction of the latter category by considering first the monomorphism category. Then we localize with respect to a multiplicative system. Our approach gives rise to a heart-like category not only for the Banach spaces. In particular, the main results apply to categories in which the set of all kernel–cokernel pairs does not form an exact structure. Such categories arise frequently in functional analysis.
2017-12-15T04:58:24Z
2017-12-15T04:58:24Z
2017-11-01
Article
DOI:10.1016/j.jpaa.2017.02.006
Sven-Ake Wegner, The heart of the Banach spaces, In Journal of Pure and Applied Algebra, Volume 221, Issue 11, 2017, Pages 2880-2909
00224049
https://www.sciencedirect.com/science/article/pii/S0022404917300312
http://nur.nu.edu.kz/handle/123456789/2929
en
Journal of Pure and Applied Algebra
© 2017 Elsevier B.V. All rights reserved.
Journal of Pure and Applied Algebra
oai:nur.nu.edu.kz:123456789/29362018-08-15T03:50:19Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
A note on the convexity of the Moore–Penrose inverse
Kenneth, Nordström
Nordström, Kenneth
Generalized inverse
Jensen convexity
Loewner ordering
Midpoint convexity
Abstract This note is a sequel to an earlier study (Nordström [7]) on convexity properties of the inverse and Moore–Penrose inverse, in which the following question was raised. Given nonnegative definite matrices A and B with Moore–Penrose inverses A+ and B+, respectively, can one show that(λA+λ‾B)+⩽λA++λ‾B+ holding for a single λ∈]0,1[ is enough to guarantee its validity for all λ∈]0,1[? (The ordering above is the partial ordering, induced by the convex cone of nonnegative definite matrices, and λ‾:=1−λ.) In this note an affirmative answer is provided to this question.
2017-12-15T05:47:14Z
2017-12-15T05:47:14Z
2018-02-01
Article
DOI:10.1016/j.laa.2017.10.016
Kenneth Nordström, A note on the convexity of the Moore–Penrose inverse, In Linear Algebra and its Applications, Volume 538, 2018, Pages 143-148
00243795
https://www.sciencedirect.com/science/article/pii/S0024379517305955
http://nur.nu.edu.kz/handle/123456789/2936
en
Linear Algebra and its Applications
© 2017 Elsevier Inc. All rights reserved.
Linear Algebra and its Applications
oai:nur.nu.edu.kz:123456789/29702018-08-15T03:50:19Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
On the theory of function-valued mappings and its application to the processing of hyperspectral images
Daniel, Otero
Otero, Daniel
La Torre, Davide
Michailovich, Oleg
Vrscay, Edward R.
Function-valued functions
Image processing
Banach spaces
Fourier transform
And fractal transform
Abstract The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well.
2017-12-20T09:19:03Z
2017-12-20T09:19:03Z
2017-05-01
Article
DOI:10.1016/j.sigpro.2016.12.014
Daniel Otero, Davide La Torre, Oleg Michailovich, Edward R. Vrscay, On the theory of function-valued mappings and its application to the processing of hyperspectral images, In Signal Processing, Volume 134, 2017, Pages 185-196
01651684
https://www.sciencedirect.com/science/article/pii/S0165168416303565
http://nur.nu.edu.kz/handle/123456789/2970
en
Signal Processing
© 2016 Elsevier B.V. All rights reserved.
Signal Processing
oai:nur.nu.edu.kz:123456789/30122018-08-15T03:50:21Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces
Jorge J., Betancor
Betancor, Jorge J.
Castro, Alejandro J.
Fariña, Juan C.
Rodríguez-Mesa, L.
Conical square functions
Vector-valued harmonic analysis
UMD Banach spaces
Bessel
Laguerre
Schrödinger
Abstract In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hytönen, van Neerven and Portal [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces Lp((0,∞),B) and Lp(Rn,B), 1<p<∞, in terms of our square functions, provided that B is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.
2017-12-22T03:12:34Z
2017-12-22T03:12:34Z
2017-03-01
Article
DOI:10.1016/j.jmaa.2016.10.006
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña, L. Rodríguez-Mesa, Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces, In Journal of Mathematical Analysis and Applications, Volume 447, Issue 1, 2017, Pages 32-75
0022247X
https://www.sciencedirect.com/science/article/pii/S0022247X16305923
http://nur.nu.edu.kz/handle/123456789/3012
en
Journal of Mathematical Analysis and Applications
© 2016 Elsevier Inc. All rights reserved.
Journal of Mathematical Analysis and Applications
oai:nur.nu.edu.kz:123456789/30212018-08-15T03:50:21Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Fractal attractors and singular invariant measures in two-sector growth models with random factor shares
Davide, La Torre
La Torre, Davide
Marsiglio, Simone
Mendivil, Franklin
Privileggi, Fabio
Two-sector growth model
Stochastic factor shares
Fractal attractors
Singular measures
Abstract We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler–Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley’s fern attractor.
2017-12-22T03:44:17Z
2017-12-22T03:44:17Z
2018-05-01
Article
DOI:10.1016/j.cnsns.2017.07.008
Davide La Torre, Simone Marsiglio, Franklin Mendivil, Fabio Privileggi, Fractal attractors and singular invariant measures in two-sector growth models with random factor shares, In Communications in Nonlinear Science and Numerical Simulation, Volume 58, 2018, Pages 185-201
10075704
https://www.sciencedirect.com/science/article/pii/S1007570417302514
http://nur.nu.edu.kz/handle/123456789/3021
en
Communications in Nonlinear Science and Numerical Simulation
© 2017 Elsevier B.V. All rights reserved.
Communications in Nonlinear Science and Numerical Simulation
oai:nur.nu.edu.kz:123456789/30642018-08-15T03:50:22Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics
Chris G., Antonopoulos
Antonopoulos, Chris G.
Skokos, Charalampos
Bountis, Tassos
Flach, Sergej
Klein–Gordon
Wave packet spreading
Chaotic dynamics
Quasi-periodic motion
Subdiffusive regime
q-Gaussian
q-statistics
Tsallis entropy
Abstract In the study of subdiffusive wave-packet spreading in disordered Klein–Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG particle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q−Gaussian probability distribution functions of sums of position observables with q > 1 always approach pure Gaussians (q=1) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonicity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this system in the subdiffusive energy domain using q-statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t=109.
2017-12-26T09:43:43Z
2017-12-26T09:43:43Z
2017-11-01
Article
DOI:10.1016/j.chaos.2017.08.005
Chris G. Antonopoulos, Charalampos Skokos, Tassos Bountis, Sergej Flach, Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics, In Chaos, Solitons & Fractals, Volume 104, 2017, Pages 129-134
09600779
https://www.sciencedirect.com/science/article/pii/S0960077917303259
http://nur.nu.edu.kz/handle/123456789/3064
en
Chaos, Solitons & Fractals
© 2017 Elsevier Ltd. All rights reserved.
Chaos, Solitons & Fractals
oai:nur.nu.edu.kz:123456789/30702018-08-15T03:50:20Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_904
Lotka–Volterra systems satisfying a strong Painlevé property
Tassos, Bountis
Bountis, Tassos
Vanhaecke, Pol
Integrable Lotka Volterra systems
Strong Painlevé property
Abstract We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj,i≠j, and require that all variables diverge as t−1. We also require that the leading terms depend on n−2 free parameters. We thus discover a cocycle relation among the coefficients aij of the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixi is added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.
2017-12-26T10:12:55Z
2017-12-26T10:12:55Z
2016-12-09
Article
DOI:10.1016/j.physleta.2016.09.034
Tassos Bountis, Pol Vanhaecke, Lotka–Volterra systems satisfying a strong Painlevé property, In Physics Letters A, Volume 380, Issue 47, 2016, Pages 3977-3982
03759601
https://www.sciencedirect.com/science/article/pii/S0375960116309963
http://nur.nu.edu.kz/handle/123456789/3070
en
Physics Letters A
© 2016 Elsevier B.V. All rights reserved.
Physics Letters A
oai:nur.nu.edu.kz:123456789/31972019-12-26T09:05:49Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Actuarial Applications of a two-parameter generalized Logistic model
Alekberova, Nargiz
rate-state equation
gompertz models
logistic models
This project presents a generalization of the classical logistic and the Gompertz model by using two parameter power law exponent. The suggested generalized with two parameters models was shown by numerical example to be potentially a better choice for fitting a certain data. The solutions of these models are used in terms of force of mortality function in actuarial math as insurance contingency models or as hazard function for quality control in science and engineering. The complexity of solution is presented in the form of hypergeometric function and corresponding to it nonlinear implicit regression analysis. Due to the mentioned complexity we develop the approximation of the actual solution and consider only its special cases.
2018-05-28T08:45:51Z
2018-05-28T08:45:51Z
2018-05-10
Capstone Project
Alekberova, Nargiz. (2018) Actuarial Applications of a two-parameter generalized Logistic model. Nazarbayev University School of Science and Technology
http://nur.nu.edu.kz/handle/123456789/3197
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai:nur.nu.edu.kz:123456789/31982019-12-26T09:14:44Zcom_123456789_511com_123456789_70com_123456789_67col_123456789_1701
Estimation and application of best ARIMA model for forecasting the uranium price.
Amangeldi, Medeu
Autoregressive Integrated Moving Average (ARIMA)
uranium price
This paper presents the application of an iterative approach for prediction of uranium price by model identification, parameter estimation and diagnostic checking which are designed by Box and Jenkins. In particular, the autoregressive integrated moving average model is used to predict the future values of monthly uranium price. As the analysis of structural dependence in observations is one of the key features of time series analysis, the past values, which were taken as monthly values from January 2000 to June 2017, are used for forecasting. As a result, ARIMA (2,1,0) became one that met all the criteria and predicted the increase of uranium price over time within 95% confidence.
2018-05-28T08:49:51Z
2018-05-28T08:49:51Z
2018-05-13
Capstone Project
Amangeldi, Medeu. (2018) Estimation and application of best ARIMA model for forecasting the uranium price. Nazarbayev University School of Science and Technology
http://nur.nu.edu.kz/handle/123456789/3198
en
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Nazarbayev University School of Science and Technology
oai_dc///com_123456789_511/100