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Quasi-bipartite synchronization for delayed coupled inertial neural networks having cooperative and competitive communication via pinning control strategy

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IET CONTROL THEORY AND APPLICATIONS 2025年第1期19卷

作者： Chenthamarakshan, Chesintha Ganesan, Soundararajan Sivakumar, Kathiresan Kashkynbayev, Ardak Rathinam Coll Arts & Sci Dept Math Coimbatore Tamil Nadu India Nazarbayev Univ Dept Math Astana 020000 Kazakhstan Inst Math & Math Modeling Almaty Alma Ata Kazakhstan

This study concentrates on achieving quasi-bipartite synchronization within signed coupled inertial neural networks featuring time-varying delays. The pinning controller technique addresses this problem within a structure incorporating cooperative and competitive interaction among the nodes. With the structurally balanced networks, some linear matrix inequality based sufficient conditions are derived for both reduced and non-reduced order methods with the help of Lyapunov-Krasovskii functional to achieve the quasi-bipartite pinning synchronization criterion. Further, the error bound is derived analytically for the leader-follower representation of the signed coupled inertial neural network model. At last, a numerical simulation result is provided to verify the correctness of the established theoretical results.

关键词： linear matrix inequality Lyapunov-Krasovskii functional pinning control signed inertial neural networks synchronization

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Eigenvalue variations of the Neumann Laplace operator due to perturbed boundary conditions

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RESEARCH IN THE mathEMATICAL SCIENCES 2025年第1期12卷 1-27页

作者： Nursultanov, Medet Trad, William Tzou, Justin Tzou, Leo Univ Helsinki Dept Math & Stat Helsinki Finland Inst Math & Math Modeling Almaty Alma Ata Kazakhstan Univ Sydney Sch Math & Stat Sydney Australia Macquarie Univ Sch Math & Phys Sci Sydney Australia Univ Amsterdam Amsterdam Netherlands

This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold (M,g,partial derivative M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M,g,\partial M)$$\end{document} under a singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions on a small portion of the boundary. We derive an asymptotic expansion of the perturbed eigenvalues as the Dirichlet part shrinks to a point x & lowast;is an element of partial derivative M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x<^>*\in \partial M$$\end{document} in terms of the spectral parameters of the unperturbed system. This asymptotic expansion demonstrates the impact of the geometric properties of the manifold at a specific point x & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x<^>*$$\end{document}. Furthermore, it becomes evident that the shape of the Dirichlet region holds significance as it impacts the first terms of the asymptotic expansion. A crucial part of this work is the construction of the singularity structure of the restricted Neumann Green's function which may be of independent interest. We employ a fusion of layer potential techniques and pseudo-differential operators during this work.

关键词： Eigenvalues Neumann Laplacian Singular perturbation

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Numerical Simulation and Experimental Analysis of Mare's Milk Sublimation Drying

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PROCESSES 2025年第1期13卷

作者： Rakhmatulina, Ayaulym Altybay, Arshyn Imanbayeva, Nurbibi Bagitova, Saltanat Baikonys, Anuar U Joldasbekov Inst Mech & Engn Dept Mech Engn & Robot Shevchenko Str 28 Alma Ata 050010 Kazakhstan Univ Illinois Global Educ & Training Int Studies Champaign IL 61820 USA Al Farabi Kazakh Natl Univ Dept Comp Sci Alma Ata 050040 Kazakhstan Inst Math & Math Modeling 125 Pushkin Str Alma Ata 050010 Kazakhstan Satbayev Univ Dept Mech Engn Alma Ata 050000 Kazakhstan Almaty Technol Univ Dept Automat & Robot Tole Bi Str Alma Ata 050000 Kazakhstan Abai Kazakh Natl Pedag Univ Dept Math & Math Modeling Alma Ata 050010 Kazakhstan

This study presents a combined numerical and experimental analysis of heat and mass transfer in mare's milk during vacuum sublimation drying, which is a process essential for producing high-quality powdered products. The numerical model was developed using two-dimensional simulations and validated against experimental data obtained for varying sample thicknesses (3 mm, 5 mm, and 7 mm). Results demonstrated a strong agreement between the model and experimental temperature data, with a coefficient of determination (R2) of 95% during the sublimation process. The findings revealed that thinner samples (3 mm) exhibited a 20% faster drying rate than thicker samples (7 mm), highlighting the critical role of sample thickness in sublimation dynamics. Additionally, the effects of heat flux distribution and mass loss due to sublimation were analyzed to understand the drying dynamics. This study highlights the importance of optimizing process parameters such as chamber pressure, shelf temperature, and sample thickness to enhance drying efficiency and reduce processing time. The findings provide valuable insights for scaling vacuum sublimation drying of mare's milk for industrial applications.

关键词： numerical simulation heat and mass transfer vacuum freeze-drying sublimation

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Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary

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ADVANCES IN OPERATOR THEORY 2025年第3期10卷 1-41页

作者： Cardona, Duvan Kumar, Vishvesh Ruzhansky, Michael Tokmagambetov, Niyaz Univ Ghent Dept Math Anal Log & Discrete Math Ghent Belgium Queen Mary Univ London Sch Math Sci London England Ctr Recerca Matemat Campus Bellaterra Edif C Barcelona 08193 Spain Inst Math & Math Modeling 28 Schevchenko str Alma Ata 050010 Kazakhstan AL Farabi Kazakh Natl Univ 71 Almaty Ave Al Farabi 050040 Kazakhstan

Given a smooth manifold M (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed, using the global pseudo-differential calculus on manifolds (with or without boundary) developed in Ruzhansky and Tokmagambetov (Int math Res Not IMRN 12:3548-3615, 2016), the Calder & oacute;n-Vaillancourt Theorem and the global functional calculus in Cardona et al. (Adv Oper Theory arXiv:2101.02519, 2020), we determine the singularity orders in the regularisation of traces and the sharp regularity orders for the Dixmier traceability of the global H & ouml;rmander classes. Our analysis (free of coordinate systems) allows us to obtain non-harmonic analogues of several classical results arising from the microlocal analysis of regularised traces for pseudo-differential operators with symbols defined by localisations.

关键词： Manifolds with boundary Pseudo-differential operators Dixmier traces Regularised traces

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The Absolute Stability of Program Manifold of Control Systems with Rigid and Tachometric Feedbacks

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LOBACHEVSKII JOURNAL OF mathEMATICS 2022年第11期43卷 3344-3351页

作者： Zhumatov, S. S. Vassilina, G. K. Inst Math & Math Modeling Alma Ata Kazakhstan Almaty Univ Power Engn & Telecommun Alma Ata Kazakhstan

The absolute stability of a program manifold of control systems with rigid and tachometric feedbacks is considered. Stability conditions of the feedback control systems with constant and variables coefficients are investigated in the neighborhood of a given program manifold. Nonlinearities satisfy to the conditions of local quadratic connections and they are differentiable in all variables. Sufficient conditions of the absolute stability of the program manifold with respect to the given vector functions are obtained by constructing the Lyapunov function. Sufficient conditions of the absolute stability of the program manifold of non autonomous feedback control system with stationary feedbacks are established.

关键词： program manifold absolute stability stationary nonlinearity Lyapunov functions local quadratic connection

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Optimal Control Problem of Stochastic Systems

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LOBACHEVSKII JOURNAL OF mathEMATICS 2021年第3期42卷 641-648页

作者： Vassilina, G. K. Inst Math & Math Modeling Alma Ata Kazakhstan Almaty Univ Power Engn & Telecommun Alma Ata Kazakhstan

Problems of optimal control of linear and nonlinear stochastic systems with quadratic criterion qualities are studied. For such problems the existence of optimal control in feedback control form is proved by method of dynamic programming. The work consists of two parts. The first part deals with the linear problem. In the first part, the existence of a solution to the Cauchy problem for the generalized Riccati equation is proved by a method based on the idea of the Bellman linearization scheme. The proof consists in the direct application of existence theorems for ordinary differential equations to the generalized Riccati equation. The main part of the article is its second part, which concerns the study of a nonlinear problem. Meaningful result is obtained only when the control is included with a small parameter in the stochastic part. Existence for small epsilon of the solution of the Bellman equation corresponding to the nonlinear problem are proved using the abstract implicit function theorem.

关键词： optimal control feedback Bellman function Riccati equation Wiener process stochastic system

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Hardy-Sobolev-Rellich, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg Inequalities on General Lie Groups

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JOURNAL OF GEOMETRIC ANALYSIS 2024年第7期34卷 1-28页

作者： Ruzhansky, Michael Yessirkegenov, Nurgissa Univ Ghent Dept Math Anal Log & Discrete Math Ghent Belgium Queen Mary Univ London Sch Math Sci London England SDU Univ Kaskelen 040900 Kazakhstan Inst Math & Math Modeling Almaty Alma Ata Kazakhstan

In this paper, we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequalities and their critical versions for an ample class of sub-elliptic differential operators on general connected Lie groups, which include both unimodular and non-unimodular cases in compact and noncompact settings. We also obtain the corresponding uncertainty type principles.

关键词： Sobolev spaces Sobolev embeddings Hardy inequality Rellich inequality Hardy-Littlewood-Sobolev inequality Caffarelli-Kohn-Nirenberg inequality Lie groups

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On Asymptotics of Attractors of the Navier-Stokes System in Anisotropic Medium with Small Periodic Obstacles

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DOKLADY mathEMATICS 2023年第1期108卷 277-281页

作者： Bekmaganbetov, K. A. Toleubay, A. M. Chechkin, G. A. Lomonosov Moscow State Univ Kazakhstan Branch Astana Kazakhstan Inst Math & Math Modeling Almaty Alma Ata Kazakhstan Gumilyov Eurasian Natl Univ Astana Kazakhstan Lomonosov Moscow State Univ Fac Mech & Math Moscow Russia Russian Acad Sci Inst Math Comp Ctr Div Ufa Fed Res Ctr Ufa Russia

The two-dimensional system of Navier-Stokes equations in a medium with anisotropic variable viscosity and periodic small obstacles is considered. It is proved that the trajectory attractors of the system tend in a certain weak topology to the trajectory attractors of the homogenized system of Navier-Stokes equations with an additional potential in a medium without obstacles.

关键词： attractors homogenization system of Navier-Stokes equations nonlinear equations weak convergence perforated domain rapidly oscillating terms anisotropic medium

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Stochastic Helmholtz Problem with Constraints Linearly Depending on Velocities

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LOBACHEVSKII JOURNAL OF mathEMATICS 2022年第11期43卷 3292-3297页

作者： Tleubergenov, M. I. Vassilina, G. K. Kulakhmetova, D. S. Inst Math & Math Modeling Alma Ata Kazakhstan Al Farabi Kazakh Natl Univ Alma Ata Kazakhstan Almaty Univ Power Engn & Telecommun Gumarbek Dauke Alma Ata Kazakhstan

In this paper based on a given stochastic system, an equivalent almost sure Lagrangian structure equation is constructed in direct and indirect representation, assuming that nonholonomic relations are imposed on the o... 详细信息

关键词： stochastic equations inverse problems Helmholtz problem almost sure equivalence

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mathematical model of thermal phenomena of closure electrical contact with Joule heat source and nonlinear thermal coefficients

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INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2024年 158卷

作者： Bollati, Julieta Briozzo, Adriana C. Kharin, Stanislav N. Nauryz, Targyn A. Univ Austral FCE Dept Matemat Paraguay 1950 RA-2000 Rosario Argentina Consejo Nacl Invest Cient & Tecn Buenos Aires Argentina Kazakh British Tech Univ Alma Ata Kazakhstan Inst Math & Math Modeling Almaty Alma Ata Kazakhstan Narxoz Univ Alma Ata Kazakhstan

The mathematical model describing the dynamics of closed contact heating which involves vaporization of the metal when instantaneous explosion of micro-asperity occurs is presented through a Stefan type problem. The temperature field for metallic vaporization zone is introduced as heat resistance that decreases linearity. Temperature fields for liquid and solid phases of the metal described by spherical heat equations with nonlinear thermal coefficients and Joule heat source have to be determined as well as the free boundaries. Joule heating component depends on space and time variable when alternating current is considered. Solution method of the problem based on similarity variable transformation is applied which enables us to reduce the problem to an ordinary differential equations and nonlinear integral equations. Existence and uniqueness of the integral equations are proved by using fixed point theorem in Banach space.

关键词： Stefan problem Nonlinear thermal coefficients Joule heat source

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