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1
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Some remarks on the stability of the multi-Jensen equation

100%
Schwaiger J.
Open Mathematics
|
2013
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tom 11
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nr 5
966-971
EN
First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in terms of stability requirements for multi-Jensen functions is presented.
2
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Superstability of functional equations related to spherical functions

100%
Székelyhidi L.
Open Mathematics
|
2017
|
tom 15
|
nr 1
427-432
EN
In this paper we prove stability-type theorems for functional equations related to spherical functions. Our proofs are based on superstability-type methods and on the method of invariant means.
3
Content available remote

Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

80%
Biçer C., Özbek L., Erbay H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
934-945
EN
In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable. The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.
4
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The BV solution of the parabolic equation with degeneracy on the boundary

80%
Zhan H., Chen S.
Open Mathematics
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2016
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tom 14
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nr 1
272-282
EN
Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.
5
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Inverse Problems for Parabolic Equation with Discontinuous Coefficients

80%
Dinakar V., Balan N. B., Balachandran K.
Nonautonomous Dynamical Systems
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2017
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tom 4
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nr 1
40-51
EN
We consider the reaction-diffusion equation with discontinuities in the diffusion coefficient and the potential term. We start by deriving the Carleman estimate for the discontinuous reaction-diffusion operator which is deployed in the inverse problems of finding the stability result of the two discontinuous coefficients from the internal observations of the given parabolic equation.
6
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Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X-1A=L

80%
Adam M., Assimakis N.
Open Mathematics
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2015
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tom 13
|
nr 1
EN
In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the proposed algorithm is based on the solution of the matrix equation X + A*X-1A=L, where A is a singular matrix and L a positive definite matrix.
7
Content available remote

On stability and robust stability of positive linear Volterra equations in Banach lattices

70%
Murakami S., Ngoc P.
Open Mathematics
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2010
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tom 8
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nr 5
966-984
EN
We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
8
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A finite difference approach for the initial-boundary value problem of the fractional Klein-Kramers equation in phase space

70%
Gao G.-h., Sun Z.-z.
Open Mathematics
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2012
|
tom 10
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nr 1
101-115
EN
Considering the features of the fractional Klein-Kramers equation (FKKE) in phase space, only the unilateral boundary condition in position direction is needed, which is different from the bilateral boundary conditions in [Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers equation, Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583]. In the paper, a finite difference scheme is constructed, where temporal fractional derivatives are approximated using L1 discretization. The advantages of the scheme are: for every temporal level it can be dealt with from one side to the other one in position direction, and for any fixed position only a tri-diagonal system of linear algebraic equations needs to be solved. The computational amount reduces compared with the ADI scheme in [Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and the five-point scheme in [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers equation, Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583]. The stability and convergence are proved and two examples are included to show the accuracy and effectiveness of the method.
9
Content available remote

Richardson Extrapolation combined with the sequential splitting procedure and the θ-method

70%
Zlatev Z., Faragó I., Havasi Á.
Open Mathematics
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2012
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tom 10
|
nr 1
159-172
EN
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
10
Content available remote

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

61%
Raffoul Y., Rai H.
Nonautonomous Dynamical Systems
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2016
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tom 3
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nr 1
14-23
EN
In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]
11
Content available remote

Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections

51%
Keller J., Tønnesen-Friedman C.
Open Mathematics
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2012
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tom 10
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nr 5
1673-1687
EN
We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.
12
Content available remote

On the Normal Stability of Functional Equations

41%
Moszner Z.
Annales Mathematicae Silesianae
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2016
|
tom 30
|
nr 1
111-128
EN
In the paper two types of stability and of b-stability of functional equations are distinguished.
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