July 16, 2012 Tags: ANALYTIC functions, ASCII (Character set), EQUATIONS, FUNCTIONS, MATHEMATICS
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In this paper, we determine some stability results concerning the general mixed additive-cubic equation f(kx + y) + f(kx – y) = kf(x + y) + kf(x – y) + 2f(fx) – 2kf(x) in F-spaces, and generalized related results in reference in different aspects. [ABSTRACT FROM AUTHOR]
Read MoreJuly 14, 2012 Tags: ADDITIVE functions, CAUCHY problem, Cubic, EQUATIONS, GENERALIZATION, HOMOMORPHISMS (Mathematics), STABILITY, VECTOR spaces
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Using the fixed point method, we prove the Hypers-Ul am stability of the orthogonally additive-quadratic functional equation 2f (x + y/2) + 2f (x – y/2) = 3/2f(x) – 1/2f(-x) + 1/2f(y) + 1/2f(-y) (0.1) for all x, y with x ⊥ y, in non-Archimedean Banach spaces. Here ⊥ is the orthogonality in the sense of Rätz. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BANACH spaces, CAUCHY problem, EQUATIONS, FIXED point theory, INEQUALITIES (Mathematics), ORTHOGONALIZATION methods, Quadratic, STABILITY
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Using the fixed point method, we prove the Hyers-Ulam stability of the following generalized Jensen quadratic funtional equation f ( x + y / r + sz ) + f ( x + y / r – sz ) + f ( x – y / r + sz ) + f (x – y / r – sz ) = 4 / r² f (x) + 4 / r² f (y) + 4s² f (z) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BANACH spaces, EQUATIONS, FIXED point theory, FUNCTIONAL equations, FUNCTIONS of complex variables, FUZZY sets, GENERALIZATION, Quadratic
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Eshaghi Gordji and Bodaghi [2] proved the Hyers-Ulam stability of quadratic double centralizers on Banach algebras for the system of the functional equations f(kx + y) + f(kx – y) = 2k² f(x) + 2f(y) & f(xy) = f(x)y for a fixed integer k greater than 1. One can easily show that all the quadratic double centralizers (L, R) in the results are (0,0). The results are trivial. In this paper, we correct the results. Using the direct method, we prove the Hyers-Ulam stability of quadratic double centralizers on Banach algebras for the system of the functional equations f(kx + y) + f(kx – y) = 2k² f(x) + 2f(y) & f(xy) = f(x)y² for a fixed integer k greater than 1. [ABSTRACT FROM AUTHOR]
Read MoreJuly 9, 2012 Tags: BANACH algebras, EQUATIONS, FUNCTION algebras, FUNCTIONAL equations, MATHEMATICAL proofs, Natural, NUMBERS, NUMERICAL analysis, Quadratic
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Recently M.W.Müller [9] gave the Gamma quasi-interpolants and obtained approximation equivalence theorems with Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. In this paper we obtain characterizations on simultaneous approximation for left. Gamma quasi-interpolants with Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. [ABSTRACT FROM AUTHOR]
Read MoreJuly 9, 2012 Tags: APPROXIMATION theory, EQUATIONS, EQUATIONS -- Numerical solutions, EQUIVALENCE classes (Set theory), GAMMA functions, GRAPH theory, MATHEMATICAL models, Simultaneous
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In this paper, using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation: Af (x+y+z/b) + af (x-y+z/b) + af (x+y-z/b) + af (-x+y+z/b) = cf(x)+cf(y)+cf(z) where a, b and c are positive real numbers, in random normed spaces. [ABSTRACT FROM AUTHOR]
Read MoreJuly 8, 2012 Tags: APPROXIMATION theory, EQUATIONS, FIXED point theory, FUNCTION algebras, MATHEMATICAL proofs, NUMBERS, POSITIVE systems, Quadratic, Real
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This paper studies the state feedback stabilization of discrete singular large-scale control systems by using Lyapunov matrix equation, generalized Lyapunov function method and matrix theory. There gives some sufficient conditions for determining the asymptotical stability and instability of the corresponding singular closed-loop large-scale systems while the subsystems are regular, causal and R-controllable. At last, an example is given to show the application of main result. [ABSTRACT FROM AUTHOR]
Read MoreMay 31, 2012 Tags: ASYMPTOTIC distribution (Probability theory), DIFFERENTIAL equations, EQUATIONS, LYAPUNOV functions, MATRICES
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The complex Ginzburg–Landau equation (CGLE), probably the most celebrated nonlinear equation in physics, describes generically the dynamics of oscillating, spatially extended systems close to the onset of oscillations. Using symmetry arguments, this article gives an easy access to this equation and an introduction into the rich spatio-temporal behaviour it describes. Starting out from the familiar linear oscillator, we first show how the generic model for an individual nonlinear oscillator, the so-called Stuart–Landau equation, can be derived from symmetry arguments. Then, we extend our symmetry considerations to spatially extended systems, arriving at the CGLE. A comparison of diffusively coupled linear and nonlinear oscillators makes apparent the source of instability in the latter systems. A concise survey of the most typical patterns in 1D and 2D is given. Finally, more recent extensions of the CGLE are discussed that comprise external, time-periodic forcing as well as nonlocal and global spatial coupling. [ABSTRACT FROM AUTHOR]
Read MoreApril 1, 2012 Tags: ELECTROMOTIVE force, EQUATIONS, NONLINEAR theories, OSCILLATIONS, PHYSICS
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Abstract: We investigate two solvable models for Bose–Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of both models, as we vary some parameters of the Hamiltonian, suggests a connection between the behavior of the roots of the Bethe ansatz equations and the physical behavior of the models. Then, by the use of standard techniques for approaching quantum phase transition – gap, entanglement and fidelity – we find that the change in the scenery in the roots of the Bethe ansatz equations is directly related to a quantum phase transition, thus providing an alternative method for its detection. [Copyright &y& Elsevier]
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