Results 181 to 190 of about 45,618 (222)

Chebyshev Expansion Applied to Dissipative Quantum Systems

The Journal of Physical Chemistry A, 2016
To determine the dynamics of a molecular aggregate under the influence of a strongly time-dependent perturbation within a dissipative environment is still, in general, a challenge. The time-dependent perturbation might be, for example, due to external fields or explicitly treated fluctuations within the environment. Methods to calculate the dynamics in
Popescu, B., Rahman, H., Kleinekathoefer, U.   +2 more
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Vandermonde systems on Gauss–Lobatto Chebyshev nodes

Applied Mathematics and Computation, 2005
Methods for factorization of the inverses of the Vandermonde matrices on Gauss-Lobatto Chebyshev nodes are presented and an algorithm for solving the primal and the dual system is given. Asymptotic estimates of the Frobenius norm of both the Vandermonde matrix and its inverse and an explicit formula for its determinant are derived. Results of numerical
Eisinberg A, FEDELE, Giuseppe
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p-Adic dynamical systems of Chebyshev polynomials

P-Adic Numbers, Ultrametric Analysis, and Applications, 2014
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Diarra, B., Sylla, D.
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Chebyshev and Descartes Systems

1995
A Chebyshev space is a finite-dimensional subspace of C(A) of dimension n + 1 that has the property that any element that vanishes at n + 1 points vanishes identically. Such spaces, whose prototype is the space P n of real algebraic polynomials of degree at most n, share with the polynomials many basic properties.
Peter Borwein, Tamás Erdélyi
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On sets admitting chebyshev vector systems

Mathematical Notes of the Academy of Sciences of the USSR, 1977
We study the topological properties of compacta on which exist vector (with values in space Rs) systems of Chebyshev functions or systems having a given Chebyshev rank. The lengths of the systems are assumed to be multiples of but not equal to the number s. A compactum on which a Chebyshev system exists is embedded into space Rs.
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Extended Chebyshev Systems on $( - \infty ,\infty )$

SIAM Journal on Mathematical Analysis, 1974
Let $0 \leqq t_0 < t_1 < \cdots < t_m $ be a sequence of integers. Necessary and sufficient conditions are obtained for $\{ x^{t_0 } ,x^{t_1 } , \cdots ,x^{t_m } \} $ to form an extended Chebyshev system of order $n + 1$ on $( - \infty ,\infty )$.
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A test for Chebyshev systems

Mathematical Notes of the Academy of Sciences of the USSR, 1986
A criterion for the existence of polynomials with a priori given roots (in that a sign is changed or not) depending on a number of functions contained in the system in question and its parity is given.
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Approximation Problems by Chebyshev Systems

1983
This chapter will be devoted to the study of the problem pairs (P) - (D) and (PA) - (DA) in a special but important case, namely when the moment generating functions a1, …,an form a so-called Chebyshev system. The most well-known instance of such a system is ar(s) = sr-1, r = 1,…,n, on a closed and bounded real interval.
Klaus Glashoff, Sven-Åke Gustafson
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On a System of Rational Chebyshev–Markov Fractions

Analysis Mathematica, 2018
The authors study Chebyshev-Markov rational fractions with complex conjugate poles at \(i\, a\) and \(-i\, a\) on the interval \([-1,1]\) defined by \[ M(x)= \cos\left(n\, \arccos\left(\frac{x\sqrt{1+a^2}}{\sqrt{1+a^2x^2}}\right)\right) \] or \[ M_n(x)=\frac{(x\sqrt{1+a^2}+i\sqrt{1-x^2})^n+ (x\sqrt{1+a^2}-\sqrt{1-x^2})^n}{2(\sqrt{1+a^2x^2)^n ...
Rouba, Y., Patseika, P., Smatrytski, K.
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Some classes of Chebyshev systems

Journal of Mathematical Sciences, 2007
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