Theses and Dissertations
http://nur.nu.edu.kz:80/handle/123456789/4179
Wed, 06 Dec 2023 00:30:20 GMT2023-12-06T00:30:20ZMODELING AND NUMERICAL ANALYSIS OF GRAPHENE MICROBEAM RESONATOR
http://nur.nu.edu.kz:80/handle/123456789/7373
MODELING AND NUMERICAL ANALYSIS OF GRAPHENE MICROBEAM RESONATOR
Yessetov, Yerkebulan
Microelectromechanical systems (MEMS) have emerged as a revolutionary technology,
enabling the development of miniaturized devices with diverse functionalities and
superior performance. Among the essential components of MEMS, microresonators
hold significant importance as they find applications in various fields, including mass
and force sensing, molecular detection, and nanoscale imaging. The quest to improve
the sensitivity and performance of microresonators has led researchers to explore novel
materials and innovative designs.
This thesis delves into the static and dynamic behavior of graphene cantilever
beam resonators under electrostatic actuation at their free tips. A rigorous analysis
of the system’s response was performed. The constitutive nonlinear equation of the
system was derived using the Energy method and Hamilton’s principle. An analytical
solution to the nonlinear static problem was obtained.
A lumped mass model was developed to study the essential dynamics of the
graphene cantilever beam. The generalized stiffness coefficient for the beam under
load at its tip was calculated, enabling a comprehensive analysis of its dynamic behavior.
A key focus was on investigating the dynamic pull-in conditions of the system
under both constant and harmonic excitation. Analytical predictions were validated
through numerical simulations. We observed that the system exhibited periodic solutions
when the excitation parameters 𝛼 and 𝜆 were below a certain separatix curve,
leading to sustained oscillations. On the other hand, if these parameters exceeded the
separatix curve, the system experienced pull-in instability, causing the beam to collapse.
Furthermore, we explored the impact of excitation frequency on the dynamic
response of the graphene cantilever beam under harmonic load. The simulations revealed
that choosing the excitation frequency near the beam’s resonant frequency
could lead to structural collapse under certain parameter conditions.
Sat, 01 Jul 2023 00:00:00 GMThttp://nur.nu.edu.kz:80/handle/123456789/73732023-07-01T00:00:00ZMULTIVARIATE MITTAG-LEFFLER FUNCTION
http://nur.nu.edu.kz:80/handle/123456789/7246
MULTIVARIATE MITTAG-LEFFLER FUNCTION
Abilassan, Akmarzhan
This thesis presents an exploration of a variant of the multivariate Mittag-Leffler
function, with a focus on its properties and applications in the context of solving
differential equations. The work includes several theorems related to the convergence,
Laplace transform, and integral representation of the function, as well as an analysis
of its usefulness as a tool for constructing solutions to certain classes of fractional
differential equations with constant coefficients. Notably, the methods discussed are
not limited to fractional derivative operators, but can also be applied to high-order
ordinary differential equations.
Sun, 01 Jan 2023 00:00:00 GMThttp://nur.nu.edu.kz:80/handle/123456789/72462023-01-01T00:00:00ZVARIETY OF BICOMMUTATIVE ALGEBRAS DEFINED BY IDENTITY Γ[(AB)C − 2(BA)C + (CA)B] + Δ[C(BA) − 2C(AB) + B(AC)] = 0
http://nur.nu.edu.kz:80/handle/123456789/6153
VARIETY OF BICOMMUTATIVE ALGEBRAS DEFINED BY IDENTITY Γ[(AB)C − 2(BA)C + (CA)B] + Δ[C(BA) − 2C(AB) + B(AC)] = 0
Bakirova, Altynay
One of the important problem of the theory of polynomial identi tites in algebra is describe all varieties of algebras with given system of
identities. Our aim is to classify all subvarieties of the variety of bicom mutative algebras. Classifying is usually done in the language of lattices.
Of course this problem is equivalent to describing of T-ideals. In order
to construct a lattice of subvarieties of given variety of algebras, we need
to define the following 1) determine the module structure of Pn(M) over
the symmetric group; 2) find for each irreducible Sn-module in Pn(M)
a consequence in Pn+1(M).
Sun, 01 May 2022 00:00:00 GMThttp://nur.nu.edu.kz:80/handle/123456789/61532022-05-01T00:00:00ZEXISTENCE OF A TRAVELING WAVE SOLUTION TO GLIOBLASTOMA MULTIFORME MODEL WITH MODIFIED GOMPERTZ GROWTH FUNCTION
http://nur.nu.edu.kz:80/handle/123456789/6143
EXISTENCE OF A TRAVELING WAVE SOLUTION TO GLIOBLASTOMA MULTIFORME MODEL WITH MODIFIED GOMPERTZ GROWTH FUNCTION
Zhuman, Gulnissa
This thesis explores a model for aggressive brain cancer - glioblastoma multiforme,
with modified gompertzian growth function. Density-dependent diffusion term, taxis,
and growth functions are included in the model that considers the glioblastoma mul tiforme properties. The experimental data of Stein et al. [58] has been used in this
work. The given model is solved both analytically and numerically by using the Mat lab program. The analytical method finds the condition for existing a traveling wave
solution of the given glioblastoma model and numerical computations are done by
using the Nelder-Mead simplex algorithm that minimizes the function through which
it finds the optimal parameters of the model. The simulation results confirm the
analytical predictions.
Sun, 01 May 2022 00:00:00 GMThttp://nur.nu.edu.kz:80/handle/123456789/61432022-05-01T00:00:00ZA PRIORI ESTIMATE FOR A HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION IN NEGATIVE SOBOLEV SPACES
http://nur.nu.edu.kz:80/handle/123456789/6142
A PRIORI ESTIMATE FOR A HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION IN NEGATIVE SOBOLEV SPACES
Tobakhanov, Nurdaulet
The higer order Nonlinear Schrödinger equation is one of the general
examples of dispersive nonlinear partial differential equations. We study a priori
bounds for higher-order nonlinear Schrödinger in the Sobolev space. The equation
models propagation of light pulses in optical fibers. We show that the solution
of the Cauchy problem associated with this equation solution satisfies a priori
upper bound which depends only on the time. The result is weak than the global
well-posedness. We obtain a priori bound on range −1/8 < s < 0. The main
methodology comes from recent work of Christ, Holmer and Tataru
Sun, 01 May 2022 00:00:00 GMThttp://nur.nu.edu.kz:80/handle/123456789/61422022-05-01T00:00:00ZTHE REDISCOVERY HYPOTHESIS: LANGUAGE MODELS NEED TO MEET LINGUISTICS
http://nur.nu.edu.kz:80/handle/123456789/6141
THE REDISCOVERY HYPOTHESIS: LANGUAGE MODELS NEED TO MEET LINGUISTICS
Maxat, Tezekbayev
There is an ongoing debate in the NLP community whether modern language models
contain linguistic knowledge, recovered through so-called probes. This work examines
whether linguistic knowledge is a necessary condition for the good performance of
modern language models, which we call the rediscovery hypothesis.
In the first place, we show that language models that are significantly compressed
but perform well on their pretraining objectives retain good scores when probed for
linguistic structures. This result supports the rediscovery hypothesis and leads to
an information-theoretic framework that relates language modeling objectives with
linguistic information. This framework also provides a metric to measure the impact of
linguistic information on the word prediction task. We reinforce our analytical results
with various experiments, both on synthetic and on real NLP tasks in English.
Sun, 01 May 2022 00:00:00 GMThttp://nur.nu.edu.kz:80/handle/123456789/61412022-05-01T00:00:00Z