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Item Open Access On the TASEP with Second Class Particles(National Academy of Science of Ukraine, 2018-01-18) Lee, EunghyunIn this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and N−1 second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at x and it is still the leftmost particle at time t. In particular, we show that this probability is expressed by the determinant of an N×N matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487-502].Item Open Access Manual vs Automatic Bitext Extraction(Nazarbayev University School of Sciences and Humanities, 2018-05-12) Myrzakhmetov, Bagdat; Assylbekov, Zhenisbek; Makazhanov, AibekWe compare manual and automatic approaches to the problem of extracting bitexts from the Web in the framework of a case study on building a Russian-Kazakh parallel corpus. Our findings suggest that targeted, site-specific crawling results in cleaner bitexts with a higher ratio of parallel sentences. We also find that general crawlers combined with boilerplate removal tools tend to retrieve shorter texts, as some content gets cleaned out with the markup. When it comes to sentence splitting and alignment we show that investing some effort in data pre- and post-processing as well as fiddling with off-the-shelf solutions pays a noticeable dividend. Overall we observe that, depending on the source, automatic bitext extraction methods may lack severely in coverage (retrieve fewer sentence pairs) and on average are fewer precise (retrieve less parallel sentence pairs). We conclude that if one aims at extracting high-quality bitexts for a small number of language pairs, automatic methods best be avoided, or at least used with caution.Item Open Access Weighted L^{p}-Hardy and L^{p}-Rellich inequalities with boundary terms on stratified Lie groups(Springer, 2018-06-29) Ruzhansky, Michael; Sabitbek, Bolys; Suragan, DurvudkhanIn this paper, generalised weighted Lp-Hardy, Lp-Caffarelli–Kohn–Nirenberg, and Lp-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg–Pauli–Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted L2-Rellich type inequality with the boundary term is obtained.Item Open Access Efficient and secure business model for content centric network using elliptic curve cryptography(International Journal of Communication Systems, 2018-10-25) Adhikari, Sharmistha; Ray, Sangram; Biswas, Gosta P.; Obaidat, Mohammad S.Initially, Internet has evolved as a resource sharing model where resources are identified by IP addresses. However, with rapid technological advancement, resources/hardware has become cheap and thus, the need of sharing hardware over Internet is reduced. Moreover, people are using Internet mainly for information exchange and hence, Internet has gradually shifted from resource sharing to information sharing model. To meet the recent growing demand of information exchange, Content Centric Network (CCN) is envisaged as a clean‐slate future network architecture which is specially destined for smooth content distribution over Internet. In CCN, content is easily made available using network caching mechanism which is misaligned with the existing business policy of content providers/publishers in IP‐based Internet. Hence, the transition from contemporary IP‐based Internet to CCN demands attention for redesigning the business policy of the content publishers/providers. In this paper, we have proposed efficient and secure communication protocols for flexible CCN business model to protect the existing business policies of the content publisher while maintaining the salient CCN features like in‐network content caching and Interest packet aggregation. To enhance the efficiency and security, the Elliptic Curve Cryptography (ECC) is used. The proposed ECC‐based scheme is analyzed to show that it is resilient to relevant existing cryptographic attacks. The performance analysis in terms of less computation and communication overheads and increased efficiency is given. Moreover, a formal security verification of the proposed scheme is done using widely used AVISPA simulator and BAN logic that shows our scheme is well secured.Item Open Access Analytical and numerical investigations of thecollapse of blood vessels with nonlinear wallmaterial embedded in nonlinear soft tissues(Alexandria Engineering Journal, 2018-11-22) Ghazy, Mohammed; Elgindi, Mohamed B.; Wei, DongmingIn this paper, shapes of nonlinear blood vessels, surrounded by nonlinear soft tissues,and buckled due to radial pressure are solved for analytically and numerically. The blood flow ratesthrough the bucked shapes are then computed numerically. A Fung-type isotropic hyperelasticstress-strain constitutive equation is used to establish a nonlinear mathematical model for radialbuckling of blood vessels...Item Open Access COMPLEX DYNAMICS AND STATISTICS OF 1-D HAMILTONIAN LATTICES: LONG RANGE INTERACTIONS AND SUPRATRANSMISSION(Nonlinear Phenomena in Complex Systems, 2019) Bountis, AnastasiosIn this paper, I review a number of results that my co-workers and I have obtained in the field of 1–Dimensional (1D) Hamiltonian lattices. This field has grown in recent years, due to its importance in revealing many phenomena that concern the occurrence of chaotic behavior in conservative physical systems with a high number of degrees of freedom. After the establishment of the Kolomogorov–Arnol’d–Moser (KAM) theory in the 1960s, a wealth of results were obtained about such systems as small perturbations of completely integrable N degree-of-freedom Hamiltonians, where ordered motion is dominant in the form of invariant tori. Since the 1980s, however, and particularly in the last two decades, there has been great progress in understanding the properties of Hamiltonian 1D lattices far from the KAM regime, where "weak" and "strong" forms of chaos begin to play an increasingly significant role. It is the purpose of this review to address and highlight some of these advances, in which the author has made several contributions concerning the dynamics and statistics of these latticesItem Open Access FOURIER NEURAL NETWORKS: A COMPARATIVE STUDY(arxiv, 2019) Zhumekenov, Abylay; Uteuliyeva, Malika; Takhanov, Rustem; Assylbekov, Zhenisbek; Castro, Alejandro J.We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks. These networks are empirically evaluated in synthetic and real-world tasks. Neither of them outperforms the standard neural network with sigmoid activation function in the real-world tasks. All neural networks, both Fourier and the standard one, empirically demonstrate lower approximation error than the truncated Fourier series when it comes to approximation of a known function of multiple variables.Item Open Access Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays(SpringerOpen, 2019) Kashkynbayev, Ardak; Cao, Jinde; Damiyev, ZhaksybekWe consider fuzzy shunting inhibitory cellular neural networks (FSICNNs) with time-varying coefficients and constant delays. By virtue of continuation theorem of coincidence degree theory and Cauchy–Schwartz inequality, we prove the existence of periodic solutions for FSICNNs. Furthermore, by employing a suitable Lyapunov functional we establish sufficient criteria which ensure global exponential stability of the periodic solutions. Numerical simulations that support the theoretical discussions are depicted.Item Open Access CRITICAL HARDY INEQUALITIES(SUOMALAINEN TIEDEAKATEMIA, 2019) Ruzhansky, Michael; Suragan, DurvudkhanWe prove a range of critical Hardy inequalities and uncertainty type principles on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. Moreover, we establish a new type of critical Hardy inequality and prove Hardy-Sobolev type inequalities. Most of the obtained estimates are new already for the case of R-n. For example, for any f is an element of C-0(infinity) (R-n \ { 0 }) we obtain the range of critical Hardy inequalities of the formItem Open Access GLOBAL ANALYTIC SOLUTIONS FOR THE NONLINEAR SCHRODINGER EQUATION(arxiv, 2019) BIYAR, MAGZHAN; DA SILVA, DANIEL OLIVEIRAWe prove the existence of global analytic solutions to the nonlinear Schr¨odinger equation in one dimension for a certain type of analytic initial data in L2Item Open Access Weighted L-p-Hardy and L-p-Rellich inequalities with boundary terms on stratified Lie groups(SPRINGER-VERLAG ITALIA SRL, 2019-01) Ruzhansky, Michael; Suragan, Durvudkhan; Sabitbek, BolysIn this paper, generalised weighted Lp-Hardy, Lp-Caffarelli-Kohn-Nirenberg, and Lp-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg-Pauli-Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted L2-Rellich type inequality with the boundary term is obtained.Item Open Access Dead-Core Solutions to Simple Catalytic Reaction Problems in Chemical Engineering(The Institute of Combustion Problems, 2019-02-20) Sabit, F.; Shakipov, Mansur; Skrzypacz, Piotr; Golman, BorisThe catalytic chemical reaction is usually carried out in a pellet where the catalyst is distributed throughout its porous structure. The selectivity, yield and productivity of the catalytic reactor often depend on the rates of chemical reactions and the rates of diffusion of species involved in the reactions in the pellet porous space. In such systems, the fast reaction can lead to the consumption of reactants close to the external pellet surface and creation of the dead core where no reaction occurs. This will result in an inefficient use of expensive catalyst. In the discussed simplified diffusion-reaction problems a nonlinear reaction term is of power-law type with a small positive reaction exponent. Such reaction term represents the kinetics of catalytic reaction accompanied by a strong adsorption of the reactant. The ways to calculate the exact solutions possessing dead cores are presented. It was also proved analytically that the exact solution of the nonlinear two-point boundary value problem satisfies physical a-priori bounds. Furthermore, the approximate solutions were obtained using the orthogonal collocation method for pellets of planar, spherical and cylindrical geometries. Numerical results confirmed that the length of the dead core increases for the more active catalysts due to the larger values of the reaction rate constant. The dead core length also depends on the pellet geometry.Item Open Access L-P-CAFFARELLI-KOHN-NIRENBERG TYPE INEQUALITIES ON HOMOGENEOUS GROUPS(OXFORD UNIV PRESS, 2019-03) Ozawa, Tohru; Ruzhansky, Michael; Suragan, DurvudkhanWe prove L-P-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the Abelian cases of isotropic or anisotropic R-n, our results provide new conclusions in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.Item Open Access Adaptive numerical homogenization for upscaling single phase flow and transport(ELSEVIER, 2019-03-05) Amanbek, Yerlan; Singh, Gurpreet; Wheeler, Mary F.; Duijn, HansvanWe propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.Item Open Access Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials(Mathematics in Engineering, 2019-04-03) Mac´ıas-D´ıaz, Jorge E.; Bountis, Anastasios; Christodoulidi, HelenWe consider a family of 1-dimensional Hamiltonian systems consisting of a large number of particles with on-site potentials and global (long range) interactions. The particles are initially at rest at the equilibrium position, and are perturbed sinusoidally at one end using Dirichlet data, while at the other end we place an absorbing boundary to simulate a semi-infinite medium. Using such a lattice with quadratic particle interactions and Klein-Gordon type on-site potential, we use a parameter 0 ≤ α < ∞as a measure of the “length” of interactions, and show that there is a sharp threshold above which energy is transmitted in the form of large amplitude nonlinear modes, as long as driving frequencies Ω lie in the forbidden band-gap of the system. This process is called nonlinear supratransmission and is investigated here numerically to show that it occurs at higher amplitudes the longer the range of interactions, reaching a maximum at a value α = αmax . 1.5 that depends on Ω. Below this αmax supratransmission thresholds decrease sharply to values lower than the nearest neighbor α = ∞ limit. We give a plausible argument for this phenomenon and conjecture that similar results are present in related systems such as the sine-Gordon, the nonlinear Klein-Gordon and the double sine-Gordon type.Item Open Access Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids(Elsevier, 2019-04-20) Wei, Dongming; Al-Ashhab, SamerThe reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.Item Open Access Traveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids(Nazarbayev University School of Sciences and Humanities, 2019-09) Wei, Dongming; Shu, YupengWe present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of solutions to the equations. We also provide numerical estimates of the shock thickness as well as the maximum stress associated with the traveling waves.Item Open Access Context Vectors Are Reflections of Word Vectors in Half the Dimensions(AI ACCESS FOUNDATION, 2019-09) Assylbekov, Zhenisbek; Takhanov, RustemThis paper takes a step towards theoretical analysis of the relationship between word embeddings and context embeddings in models such as word2vec. We start from basic probabilistic assumptions on the nature of word vectors, context vectors, and text generation. These assumptions are supported either empirically or theoretically by the existing literature. Next, we show that under these assumptions the widely-used word-word PMI matrix is approximately a random symmetric Gaussian ensemble. This, in turn, implies that context vectors are reflections of word vectors in approximately half the dimensions. As a direct application of our result, we suggest a theoretically grounded way of tying weights in the SGNS model.Item Open Access Soliton surface associated with the WDVV equation for n = 3 case(IOP Publishing, 2019-11-01) Zhadyranova, A.A.; Myrzakul, Zhanbotahis paper describes the soliton surfaces approach to the Witten-Dijkgraaf-E.Verlinde-H. Verlinde (WDVV) equation. We constructed the surface associated with the WDVV equations using Sym-Tafel formula, which gives a connection between the classical geometry of manifolds immersed in R m and the theory of solitons. The so-called Sym-Tafel formula simplifies the explicit reconstruction of the surface from the knowledge of its fundamental forms, unifies various integrable nonlinearities and enables one to apply powerful methods of the soliton theory to geometrical problems. The soliton surfaces approach is very useful in construction of the so-called integrable geometries. Indeed, any class of soliton surfaces is integrable. Geometrical objects associated with soliton surfaces (tangent vectors, normal vectors, foliations by curves etc.) usually can be identified with solutions to some nonlinear models (spins, chiral models, strings, vortices etc.) [1], [2]. We consider the geometry of surfaces immersed in Euclidean spaces. Such soliton surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η11 = 0 are considered, and first and second fundamental forms of soliton surfaces are found for this case. Also, we study an area of surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η11 = 0.Item Open Access A priori error analysis for transient problems using Enhanced Velocity approach in the discrete-time setting(ELSEVIER SCIENCE BV, 2019-12) Amanbek, Yerlan; Wheeler, Mary F.Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for transient problems with the Dirichlet boundary condition. Enhanced Velocity Mixed FEM as domain decomposition method is used in the space discretization and the backward Euler method and the Crank–Nicolson method are considered in the discrete-time setting. Enhanced Velocity scheme was used in the adaptive mesh refinement dealing with heterogeneous porous media for single phase flow and transport and demonstrated as mass conservative and efficient method. Numerical tests validating the backward Euler theory are presented. These error estimates are useful in the determining of time step size and the space discretization size.