This study constitutes the continuation of innovative research in Discrete Mathematics introduced in earlier papers on algebras in general, regarding the use of graphs to study the particular case of graphicable algeb...
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This study constitutes the continuation of innovative research in Discrete Mathematics introduced in earlier papers on algebras in general, regarding the use of graphs to study the particular case of graphicable algebras, which form a subset of evolution algebras. evolution algebras are particularly interesting since they are intrinsically linked with other mathematical fields, such as group theory, stochastics processes, and dynamical systems, for instance. Our advances in this study are obtained by setting a natural correspondence between evolution algebras and direct graphs, in order to translate the general concepts of graphicable algebras: subalgebra, ideal, centralizer, normalizer ... to the language of graphs. These translations will enable advances in the application of these algebras to various branches of Mathematics. (C) 2012 Elsevier Inc. All rights reserved.
The notion of the evolution of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear evolution operator is studied. Viewing these sources as possibly sta...
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The notion of the evolution of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear evolution operator is studied. Viewing these sources as possibly stable dynamical systems it is proved that all random sources with finite evolution dimension are asymptotically mean stationary, which implies that such random sources have ergodic properties and a well-defined entropy rate. It is shown that the class of random sources with finite evolution dimension properly generalizes the well-studied class of finitary stochastic processes, which includes (hidden) Markov sources as special cases.
The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transv...
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The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transverse-field Ising model and the XY model, it is demonstrated that when the gate error is decreased by approximately an order of magnitude relative to typical modern values, higher-order Trotterization becomes advantageous. This form of Trotterization yields a global minimum of the overall simulation error, comprising both the mathematical error of Trotterization and the physical error arising from gate execution.
Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by {1, 2,, n} and, similarly, that the male types are indexed by {1, 2,..., v}. Recently an evo...
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Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by {1, 2,, n} and, similarly, that the male types are indexed by {1, 2,..., v}. Recently an evolution algebra of bisexual population was introduced by identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. In this paper we study constrained evolution algebra of bisexual population in which type "1" of females and males have preference. For such algebras sets of idempotent and absolute nilpotent elements are known. We consider two particular cases of this algebra, giving more constraints on the structural constants of the algebra. By the first our constraint we obtain an n + nu-dimensional algebra with a matrix of structural constants containing only 0 and 1. In the second case we consider n = nu = 2 but with general constraints. In both cases we study dynamical systems generated by the quadratic evolution operators of corresponding constrained algebras. We find all fixed points, limit points and some 2-periodic points of the dynamical systems. Moreover we study several properties of the constrained algebras connecting them to the dynamical systems. We give some biological interpretation of our results. (C) 2016 Elsevier Inc. All rights reserved.
In this article, we consider the second-order nonautonomous integro-differential system with finite delay and noninstantaneous impulse. The aim of this paper is to establish the approximate controllability result for ...
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In this article, we consider the second-order nonautonomous integro-differential system with finite delay and noninstantaneous impulse. The aim of this paper is to establish the approximate controllability result for the proposed control problem. We use the evolution operator and Schauder's fixed-point approach for proving our main result. Also, we provide an example to illustrate our main result.
The paper proposes a second-order accurate finite volume local evolution Galerkin (FVLEG) method for two-dimensional special relativistic hydrodynamical (RHD) equations. Instead of using the dimensional splitting meth...
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The paper proposes a second-order accurate finite volume local evolution Galerkin (FVLEG) method for two-dimensional special relativistic hydrodynamical (RHD) equations. Instead of using the dimensional splitting method or solving one-dimensional local Riemann problem in the direction normal to cell interface, the FVLEG method couples a finite volume formulation with the (genuinely) multi-dimensional approximate local evolution operator, which is derived by evolving the solutions of corresponding locally linearized RHD equations along all bicharacteristic directions. Several numerical examples are given to demonstrate the accuracy and the performance of the proposed FVLEG method. (C) 2013 Elsevier Inc. All rights reserved.
A propagation method for the time dependent Schrodinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in syst...
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A propagation method for the time dependent Schrodinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u(t)-G(u) = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schrodinger equation with time-dependent potential and to non-linear Schrodinger equation will be presented.
Models of the quantum oscillator, based on Al-Salam-Chihara orthogonal q-polynomials, are constructed. The position and momentum operators have the continuous simple spectra, covering a finite interval. Eigenfunctions...
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Models of the quantum oscillator, based on Al-Salam-Chihara orthogonal q-polynomials, are constructed. The position and momentum operators have the continuous simple spectra, covering a finite interval. Eigenfunctions of these operators are explicitly defined. The evolution operator is an integral operator with a kernel, whose explicit form is also derived. (c) 2007 Elsevier B.V. All rights reserved.
This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild soluti...
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This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild solutions for these systems by using the measure of non-compactness and a fixed-point theorem wth the properties of Clarke subdifferential. Then, the existence of time optimal control of governed by stochastic control systems is also obtained. We do not assume that the evolution operator and the values of multi-valued map are compact. Finally, an example is given to illustrate the effectiveness of the results.
In this paper we consider the controllability of certain class of non-autonomous impulsive neutral evolution stochastic functional differential equations, with time varying delays, driven by a Rosenblatt process, in a...
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In this paper we consider the controllability of certain class of non-autonomous impulsive neutral evolution stochastic functional differential equations, with time varying delays, driven by a Rosenblatt process, in a Hilbert space. Sufficient conditions for controllability are obtained by employing a fixed point approach. A practical example is provided to illustrate the viability of the abstract result of this work.
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