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  • On implicational bases of closure system with unique critical sets 
    Adaricheva, Kira; Nation, J.B. (2013)
    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 ...
  • On K-means algorithm with the use of Mahalanobis distances 
    Melnykov, Igor; Melnykov, Volodymyr (Statistics & Probability Letters, 2014-01-01)
    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 ...
  • On scattered convex geometries 
    Adaricheva, Kira; Pouzet, Maurice (2015)
    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 ...
  • On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load 
    Elgindi, Mohamed B. M.; Wei, Dongming; Soukiassian, Yeran; Liu, Yu (World Journal of Engineering and Technology, 2014)
    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 ...
  • On the Global Solvability of a Class of Fourth- Order Nonlinear Boundary Value Problems 
    Elgindi, Mohamed B. M.; Wei, Dongming (Mathematics Faculty Publications, 2012)
    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 ...
  • On the QR decomposition of backslashfancyscript H -matrices 
    Benner, Peter; Mach, Thomas (Computing (Vienna/New York), 2010-06-09)
    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 ...
  • On the solvability of euler graphene beam subject to axial compressive load 
    Elgindi, Mohamed B. M.; Wei, Dongming; Elgindi, T.M. (arXiv.org, 2014)
    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 ...
  • On the solvability of the Brinkman-forchheimer-extended darcy Equation 
    Skrzypacz, Piotr; Wei, Dongming (arXiv.org, 2016)
    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 ...
  • On the theory of function-valued mappings and its application to the processing of hyperspectral images 
    Otero, Daniel; La Torre, Davide; Michailovich, Oleg; Vrscay, Edward R. (Signal Processing, 2017-05-01)
    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 ...
  • Optimal Design of Helical Springs of Power Law Materials 
    Wei, Dongming; Fyrillas, Marios; Otemissov, Adilet; Bekishev, Rustam (arXiv.org, 2016)
    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 ...
  • Optimum basis of finite convex geometry 
    Adaricheva, Kira (2016)
    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 ...
  • Ordered direct implication basis of a finite closure system 
    Adaricheva, Kira; Nation, J.B.; Rand, R. (2012)
    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 ...
  • Penalty finite element approximations of the stationary power- law Stokes problem 
    Lefton, Lew; Wei, Dongming (Journal of Numerical Mathematics, 2003)
    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 ...
  • Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device 
    Wei, D.; Kadyrov, S.; Kazbek, Z. (Applied and Computational Mechanics, 2017)
    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 ...
  • Positive entropy invariant measures on the space of lattices with escape of mass 
    Kadyrov, Shirali (2010)
    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
  • Positive undecidable numberings in the Ershov hierarchy 
    Mustafa, M.; Sorbi, Andrea (2012)
    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 ...
  • Realization of abstract convex geometries by point configurations. Part I 
    Adaricheva, Kira; Wild, Marcel (2007)
    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 ...
  • Representing finite convex geometries by relatively convex sets 
    Adaricheva, Kira (2011)
    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 ...
  • Rogers semilattices of families of two embedded sets in the Ershov hierarchy 
    Badaev, Serikzhan A.; Mustafa, M. (2012)
    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, ...
  • Roots of Polynomials: on twisted QR methods for companion matrices and pencils 
    Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S. (arXiv, 2016-11-08)
    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 ...