DSpace Collection: 2018 Volume 29
http://hdl.handle.net/10525/3587
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New Reductions of a Matrix Generalized Heisenberg Ferromagnet Equation
http://hdl.handle.net/10525/3605
Title: New Reductions of a Matrix Generalized Heisenberg Ferromagnet Equation<br/><br/>Authors: Valchev, Tihomir; Yanovski, Alexandar<br/><br/>Abstract: In this report, we shall present a new 1 + 1 dimensional nonlinear partial differential equation integrable through inverse scattering transform. The integrable system under consideration is a pseudo-Hermitian reduction of a matrix generalization of classical 1 + 1 dimensional Heisenberg ferromagnet equation. We derive recursion operators and describe the integrable hierarchy related to that matrix equation. 2010 Mathematics Subject Classification: 17B80, 35G50, 37K10, 37K15.<br/><br/>Description: [Valchev Tihomir; Вълчев Тихомир]; [Yanovski Alexandar; Яновски Александър]On the Common Points of Two Families of N-Spheres in the flat N + 1 Dimensional Space, Each of which Passes through the Vertexes of a Given N-Simplex
http://hdl.handle.net/10525/3604
Title: On the Common Points of Two Families of N-Spheres in the flat N + 1 Dimensional Space, Each of which Passes through the Vertexes of a Given N-Simplex<br/><br/>Authors: Tinchev, Vassil K.<br/><br/>Abstract: 2010 Mathematics Subject Classification: 51F99.<br/><br/>Description: [Tinchev Vassil K.; Тинчев Васил К.]A Fractional Inequality on Compact Manifolds and Lie Groups
http://hdl.handle.net/10525/3603
Title: A Fractional Inequality on Compact Manifolds and Lie Groups<br/><br/>Authors: Tarulli, Mirko; Venkov, George<br/><br/>Abstract: 2010 Mathematics Subject Classification: 35B45, 53B20.<br/><br/>Description: [Venkov George; Венков Георги]Local Activity in Memristor-Based Chaotic System Model
http://hdl.handle.net/10525/3602
Title: Local Activity in Memristor-Based Chaotic System Model<br/><br/>Authors: Slavova, Angela; Tetzlaff, Ronald; Markova, Maya<br/><br/>Abstract: In this paper a memristor-based chaotic system model will be studied. Dynamics of such model will be investigated. Local activity theory will be applied in order to determine the edge of chaos domain of the parameter set in which the model under consideration can exhibit complexity. Simulations and applications will be provided. 2010 Mathematics Subject Classification: 92B20, 34C55, 34C28.<br/><br/>Description: [Slavova Angela; Славова Анжела]; [Markova Maya; Маркова Мая]Edge of Chaos in Reaction-Diffusion CNN Models
http://hdl.handle.net/10525/3601
Title: Edge of Chaos in Reaction-Diffusion CNN Models<br/><br/>Authors: Slavova, Angela; Bobeva, Galina<br/><br/>Abstract: In this paper different reaction-diffusion Cellular Nonlinear Networks (RDCNN) models will be presented. Dynamics of Oregonator RD-CNN model will be studied. Local activity theory will be applied in order to determine the edge of chaos domain of the parameter set in which the model under consideration can exhibit complexity. Simulations and applications will be provided. 2010 Mathematics Subject Classification: 92B20, 34C28, 35K57.<br/><br/>Description: [Slavova Angela; Славова Анжела]; [Bobeva Galina; Бобева Галина]Effects of Time Rescaling for the Gas Dynamics Equations
http://hdl.handle.net/10525/3600
Title: Effects of Time Rescaling for the Gas Dynamics Equations<br/><br/>Authors: Rozanova, Olga<br/><br/>Abstract: We show that a special change of time variable allows to obtain splitting by physical processes in the barotropic gas dynamics equations. Namely, on the first time step the gas dynamics can be reduced to nonlinear heat equation, whereas on the second step the same system can be reduced to the pressureless gas dynamics equations with a friction term. We discuss also how the Cauchy data can be used on every step. Further, we show that in several cases there exists analytical representation of solution. 2010 Mathematics Subject Classification: 76N99.Vibration of Dry Ice Placed on a Metallic Structure
http://hdl.handle.net/10525/3599
Title: Vibration of Dry Ice Placed on a Metallic Structure<br/><br/>Authors: Mochimaru, Yoshihiro<br/><br/>Abstract: Vibration of a dry ice block placed on a metallic beam structure is analyzed under two steps, i.e. a sublimation step under high heat flux using one-dimensional linearized heat conduction equation neglecting gaseous flow and the following jump stage of solid dry ice due to high gas pressure. Eigenfrequency of the metallic structure can be detected experimentally due to crashing by the dry ice block. 2010 Mathematics Subject Classification: 34B40, 35K05, 35K45.Partial Regularity of Hopf Weak Solutions of the Navier-Stokes Equations, which Satisfy a Suitable Extra-Condition
http://hdl.handle.net/10525/3598
Title: Partial Regularity of Hopf Weak Solutions of the Navier-Stokes Equations, which Satisfy a Suitable Extra-Condition<br/><br/>Authors: Mauro, Jimmy Alfonso<br/><br/>Abstract: We estimate the Hausdorff dimension of the set S of the possible singular points, associated to a Hopf weak solution which satisfies a suitable extracondition. According to what is known at the moment, the extra-conditions which we consider doesn’t assure the regularity of the Hopf weak solution. 2010 Mathematics Subject Classification: 76D05, 35Q30, 76D03.Dynamic Fracture of a Nano-Crack in Finite Exponentially Inhomogeneous Piezoelectric Solid
http://hdl.handle.net/10525/3597
Title: Dynamic Fracture of a Nano-Crack in Finite Exponentially Inhomogeneous Piezoelectric Solid<br/><br/>Authors: Marinov, Marin; Rangelov, Tsviatko; Dineva, Petia<br/><br/>Abstract: Aim of the study is to propose, develop, verify and apply in intensive simulations an efficient non-hypersingular traction boundary integral equation method (BIEM) for solution of anti-plane dynamic problem of a finite exponentially inhomogeneous piezoelectric solid with a nano-crack. The modelling approach is in the frame of continuum mechanics, wave propagation theory, the Gurtin and Murdoch surface elasticity theory and linear fracture mechanics. The simulations reveal the dependence of the stress concentration field on the electromechanical coupling, on the type and characteristics of the dynamic load, on the position-dependent material parameters, on the surface elasticity, on the size effect and on the wave-nanocrack-material gradient interaction. 2010 Mathematics Subject Classification: 35Q74, 74S15, 74H35.<br/><br/>Description: [Marinov Marin; Маринов Марин]; [Rangelov Tsviatko; Рангелов Цвятко]; [Dineva Petia; Динева Петя]A Family of Recurrence Generated Parametric Functions Based on Volmer-Weber-Kaishew Activation Function
http://hdl.handle.net/10525/3596
Title: A Family of Recurrence Generated Parametric Functions Based on Volmer-Weber-Kaishew Activation Function<br/><br/>Authors: Kyurkchiev, Nikolay<br/><br/>Abstract: The Volmer theory is correct in predicting a dependence of critical supersaturation on contact angle in heterogeneous nucleation. In this paper we consider dependence of supersaturation on contact angle by a family of recurrence generated parametric functions based on the Volmer–Weber–Kaishew activation function (VWKAF). 2010 Mathematics Subject Classification: 41A46.<br/><br/>Description: [Kyurkchiev Nikolay; Кюркчиев Николай]Necessary and Sufficient Condition for Finite Time Blow up of the Solutions to Sixth Order Double Dispersive Equations
http://hdl.handle.net/10525/3595
Title: Necessary and Sufficient Condition for Finite Time Blow up of the Solutions to Sixth Order Double Dispersive Equations<br/><br/>Authors: Kutev, N.; Kolkovska, N.; Dimova, M.<br/><br/>Abstract: The nonlinear double dispersive equation of sixth order with linear restoring force is investigated. Necessary and sufficient condition for finite time blow up of the solution with arbitrary positive energy is obtained. New very general sufficient conditions for blow up of the solution are proved. Explicit choice of initial data with arbitrary positive initial energy, satisfying all conditions of the theorems, are given. 2010 Mathematics Subject Classification: 35B44, 35L75.<br/><br/>Description: [Kutev N.; Kutev Nikolai; Кутев Николай]; [Kolkovska N.; Кольковска Н.]; [Dimova M.; Димова М.]Singular Infinite Horizon Linear-Quadratic Optimal Control Problem for Systems with Known Disturbances: a Regularization Approach
http://hdl.handle.net/10525/3594
Title: Singular Infinite Horizon Linear-Quadratic Optimal Control Problem for Systems with Known Disturbances: a Regularization Approach<br/><br/>Authors: Glizer, Valery Y.; Kelis, Oleg<br/><br/>Abstract: We consider an infinite horizon linear-quadratic optimal control problem for a system with known additive disturbance. A weight matrix of the control cost in the cost functional of this problem is singular, meaning that the problem itself is singular. Using a regularization method, we obtain the infimum of the cost functional and a minimizing sequence of state-feedback controls in this problem. 2010 Mathematics Subject Classification: 49N10, 49K40, 49N60, 49N35, 49N25, 93C73.Maximum Principle for Weakly Coupled Linear Non-Cooperative Systems
http://hdl.handle.net/10525/3593
Title: Maximum Principle for Weakly Coupled Linear Non-Cooperative Systems<br/><br/>Authors: Boyadzhiev, G.; Kutev, N.<br/><br/>Abstract: In this article is considered the validity of the maximum principle for noncooperative linear parabolic systems. Unlike the cooperative ones, when cooperativeness is a sufficient condition for maximum principle, simple examples show that for non-cooperative systems there is no general validity of the maximum principle. In this work are given some conditions for global on time variable validity of the maximum principle, as well as some local on time sufficient conditions for it. 2010 Mathematics Subject Classification: 35J47, 35J57.<br/><br/>Description: [Boyadzhiev G.; Бояджиев Г.]; [Kutev N.; Кутев Н.]Semilinear Differential Inclusions in Banach Spaces
http://hdl.handle.net/10525/3592
Title: Semilinear Differential Inclusions in Banach Spaces<br/><br/>Authors: Bilal, S.; Donchev, T.; Haider, K.; Kitanov, N.; Kolev, D.<br/><br/>Abstract: We define limit solutions for semilinear differential inclusions in arbitrary Banach space. The main properties of the limit solution set is then studied. In particular it is shown that the limit solution set is Rδ. 2010 Mathematics Subject Classification: 34A60, 35R70.<br/><br/>Description: [Donchev T.; Дончев Т.]; [Kitanov N.; Китанов Н.]; [Kolev D.; Колев Д.]Adaptive Computing by Memristor Circuits
http://hdl.handle.net/10525/3591
Title: Adaptive Computing by Memristor Circuits<br/><br/>Authors: Tetzlaff, Ronald; Ascoli, Alon; Baumann, Dominik; Hild, Manfred; Chua, Leon O.<br/><br/>Abstract: Neuromorphic circuits will be considered for energy efficient computing based on biological principles in future electronic systems. Thereby, memristors are assumed in neuron models and for synapses in several recent investigations in order to overcome the limits of conventional von Neumann architectures by taking these devices as memory elements and as well as devices for computation also in bioinspired artificial neural networks. Cellular Neural Networks (CNN) are universal high-speed computing systems with stored programmability and are already based on the principle of distributed computing with memory. The dynamical behavior of these spatiotemporal systems will be exploited to solve multidimensional signal processing and classification problems. For example, reaction-diffusion systems can be represented by state equations of socalled reaction-diffusion CNN showing the emergence of complex behavior (e.g. pattern formation) based on local activity and especially on a parameter subset called the edge of chaos. A first approach to the principle of combined sensing and computing will be presented in this contribution. A memristor enhanced control system for a humanoid robot called Myon [1,2] will be shown. For different memristor models new bio-inspired movement control paradigms will be introduced and the performance in achieving a fast energy efficient movement control evaluated for different cases. It will be demonstrated that memristors endow the control system of Myon with the adaptability to changes in its topology. 2010 Mathematics Subject Classification: 92B20, 68U10, 34C28, 35K57.Critical Points of Dirac Functional with Broken Symmetry
http://hdl.handle.net/10525/3590
Title: Critical Points of Dirac Functional with Broken Symmetry<br/><br/>Authors: Georgiev, Vladimir; Maiale, Francesco Paolo<br/><br/>Abstract: In this paper, we prove the existence of a radially symmetric critical point of the Dirac functional with broken symmetry. 2010 Mathematics Subject Classification: 35J50, 35Q40, 35J45.<br/><br/>Description: [Georgiev Vladimir; Георгиев Владимир]