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Item Open Access A class of infinite convex geometries(2015) Adaricheva, Kira; Nation, J.B.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 givenItem Open Access A free/open-source hybrid morphological disambiguation tool for Kazakh(DOI: 10.13140/RG.2.2.12467.43045, 2016-04) Assylbekov, Zhenisbek; Washington, Jonathan; Tyers, Francis; Nurkas, Assulan; Sundetova, Aida; Karibayeva, Aidana; Abduali, Balzhan; Amirova, DinaThis 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.Item Open Access A Lumped-Parameter Model for Nonlinear Waves in Graphene(2015) Wei, Dongming; Hazim, Hamad; Elgindi, Mohamed; Soukiassian, YeranA 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.Item Open Access A Lumped-Parameter Model for Nonlinear Waves in Graphene(World Journal of Engineering and Technology, 2015) Hazim, Hamad; Wei, Dongming; Elgindi, Mohamed B. M.; Soukiassian, YeranA 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 applicationsItem Open Access A New Weibull–Pareto Distribution: Properties and Applications(Communications in Statistics: Simulation and Computation, 2016-11-25) Tahir, M. H.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.; Zubair, M.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.Item Open Access A Penalty Method for Approximations of the Stationary Power-Law Stokes Problem(Electronic journal of differential equations, 2001) Lefton, Lew; Wei, DongmingWe 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.Item Open Access A Short Note On Solving 1-D Porous Medium Equation by Finite Element Methods(Nazarbayev University School of Science and Technology, 2016-05-20) Matayev, ChingisPorous 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.Item Open Access Actuarial Applications of a two-parameter generalized Logistic model(Nazarbayev University School of Science and Technology, 2018-05-10) Alekberova, NargizThis 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.Item Open Access Adaptive cross approximation for ill-posed problems(Journal of Computational and Applied Mathematics, 2016-09-01) Mach, Thomas; Reichel, Lothar; Van Barel, Marc; Vandebril, R.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.Item Open Access Algebraic convex geometries revisited(2014) Adaricheva, KiraRepresentation 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 earlierItem Open Access Algebraic numbers, hyperbolicity, and density modulo one(2011) Kadyrov, Shirali; Gorodnik, A.Item Open Access Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension(2012) Kadyrov, Shirali; Pohl, A.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.Item Open Access An extended Hessenberg form for Hamiltonian matrices(Calcolo, 2016-06-01) Ferranti, Micol; Iannazzo, Bruno; Mach, Thomas; Vandebril, RafA 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.Item Open Access Analysis of Dynamic Pull-in for a Graphene-based MEMS Model(Nazarbayev University School of Science and Technology, 2018) Omarov, DaniyarA novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic solutions and non-periodic solutions in the pull-in analysis of a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there is no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the periodic solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions. Also, Low Order Fourier Approximation is used to find the solution for the linear spring case. Comparison with the highly accurate Runge-Kutta method is done to verify derived values from the new numerical approximation.Item Open Access Analytic Solutions for a Nonlinear Transport Equation(Nazarbayev University School of Science and Technology, 2019-08-07) Biyar, Magzhan; da Silva, Daniel Oliveira; Castro Castilla, Alejandro JavierWe prove that the Cauchy problem for a transport equation with algebraic nonlinearity of degree p with initial data in Gevrey spaces is locally well-posed. In particular, we show that the analyticity of solutions persists for a short time and we derive a sufficient condition for solutions to be analytic for all times.Item Open Access Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using q-Statistics(arXiv, 2018-03-19) Antonopoulos, Chris G.; Skokos, Charalampos; Bountis, Tassos; Flach, SergejIn 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 distribu- tion 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 sys- tem 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 = 10Item Metadata only Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics(Chaos, Solitons & Fractals, 2017-11-01) Antonopoulos, Chris G.; Skokos, Charalampos; Bountis, Tassos; Flach, Sergej; Chris G., AntonopoulosAbstract 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.Item Open Access The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport(Scientific Reports, 2016-09-19) Kominis, Yannis; Bountis, Tassos; Flach, SergejWe 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.Item Open Access Bernstein-walsh inequalities in higherdimensions over exponential curves(2011) Kadyrov, Shirali; Lawrence, MarkLet 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.Item Open Access Bornological projective limits of inductive limits of normed spaces(Functiones et Approximatio, Commentarii Mathematici, 2011) Bonet, José; Wegner, Sven AkeWe 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.