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1
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On continuous solutions of a functional equation

100%
Dankiewicz K.
Annales Polonici Mathematici
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1996-1997
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tom 65
|
nr 2
151-156
EN
This paper discusses continuous solutions of the functional equation φ[f(x)] = g(x,φ(x)) in topological spaces.
2
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An extension of the Cayley-Hamilton theorem for nonlinear time-varying systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 1
141-145
EN
The classical Cayley-Hamilton theorem is extended to nonlinear time-varying systems with square and rectangular system matrices. It is shown that in both cases system matrices satisfy many equations with coefficients being the coefficients of characteristic polynomials of suitable square matrices. The proposed theorems are illustrated with numerical examples.
3
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Versatile asymmetrical tight extensions

100%
Otafudu O. O., Mushaandja Z.
Topological Algebra and its Applications
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2017
|
tom 5
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nr 1
6-12
EN
We show that the image of a q-hyperconvex quasi-metric space under a retraction is q-hyperconvex. Furthermore, we establish that quasi-tightness and quasi-essentiality of an extension of a T0-quasi-metric space are equivalent.
4
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Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique

88%
Zeriahi A.
Annales Polonici Mathematici
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1996
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tom 63
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nr 1
35-50
EN
We first give a general growth version of the theorem of Bernstein-Walsh-Siciak concerning the rate of convergence of the best polynomial approximation of holomorphic functions on a polynomially convex compact subset of an affine algebraic manifold. This can be considered as a quantitative version of the well known approximation theorem of Oka-Weil. Then we give two applications of this theorem. The first one is a generalization to several variables of Winiarski's theorem relating the growth of an entire function to the rate of convergence of its best polynomial approximation; the second application concerns the extension with growth of an entire function from an algebraic submanifold to the whole space.
5
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Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
|
nr 2
231-234
EN
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.
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