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991.
We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available. 相似文献
992.
Katerina Saneva 《Journal of Mathematical Analysis and Applications》2010,370(2):543-554
We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S0(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients. 相似文献
993.
The operator of F. Bergeron, Garsia, Haiman and Tesler [F. Bergeron, A. Garsia, M. Haiman, G. Tesler, Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions, Methods Appl. Anal. 6 (1999) 363–420] acting on the k-Schur functions [L. Lapointe, A. Lascoux, J. Morse, Tableaux atoms and a new Macdonald positivity conjecture, Duke Math. J. 116 (2003) 103–146; L. Lapointe, J. Morse, Schur functions analogs for a filtration of the symmetric functions space, J. Combin. Theory Ser. A 101 (2003) 191–224; L. Lapointe, J. Morse, Tableaux on k+1-cores, reduced words for affine permutations and k-Schur expansion, J. Combin. Theory Ser. A 112 (2005) 44–81] indexed by a single column has a coefficient in the expansion which is an analogue of the (q,t)-Catalan number with a level k. When k divides n we conjecture a representation theoretical model in this case such that the graded dimensions of the module are the coefficients of the (q,t)-Catalan polynomials of level k. When the parameter t is set to 1, the Catalan numbers of level k are shown to count the number of Dyck paths that lie below a certain Dyck path with q counting the area of the path. 相似文献
994.
Úlfar F. Stefánsson 《Journal of Computational and Applied Mathematics》2010,233(6):1601-1606
We establish asymptotics for Christoffel functions of Müntz systems at the endpoints x=0 and x=1 of [0,1], assuming that there exists a ρ>0, such that the Müntz exponents {λk} satisfy
995.
Mehrdad Lakestani 《Journal of Computational and Applied Mathematics》2010,235(3):669-1804
A numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. The method is derived by expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem can be reduced to a set of algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use. 相似文献
996.
Let T:D⊂X→X be an iteration function in a complete metric space X. In this paper we present some new general complete convergence theorems for the Picard iteration xn+1=Txn with order of convergence at least r≥1. Each of these theorems contains a priori and a posteriori error estimates as well as some other estimates. A central role in the new theory is played by the notions of a function of initial conditions of T and a convergence function of T. We study the convergence of the Picard iteration associated to T with respect to a function of initial conditions E:D→X. The initial conditions in our convergence results utilize only information at the starting point x0. More precisely, the initial conditions are given in the form E(x0)∈J, where J is an interval on R+ containing 0. The new convergence theory is applied to the Newton iteration in Banach spaces. We establish three complete ω-versions of the famous semilocal Newton–Kantorovich theorem as well as a complete version of the famous semilocal α-theorem of Smale for analytic functions. 相似文献
997.
Rational compacts and exposed quadratic irrationalities 总被引:1,自引:1,他引:0
998.
Let be the usual Sobolev class of functions on the unit ball in , and be the subclass of all radial functions in . We show that for the classes and , the orders of best approximation by polynomials in coincide. We also obtain exact orders of best approximation in of the classes by ridge functions and, as an immediate consequence, we obtain the same orders in for the usual Sobolev classes . 相似文献
999.
Yiorgos-Sokratis Smyrlis 《Journal of Approximation Theory》2009,161(2):617-633
In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by linear combinations of translates of fundamental solutions of the underlying partial differential operator. The singularities of the fundamental solutions lie outside of . The domains under consideration may possess holes and they are required to satisfy a rather mild boundary regularity requirement, namely the segment condition. We study approximations with respect to the norms of the spaces and the spaces of uniformly Hölder continuous functions , and we establish density and non-density results for elliptic operators with constant coefficients. We also provide applications of our density results related to the method of fundamental solutions and to the theory of universal series. 相似文献
1000.
Yaryong Heo 《Journal of Mathematical Analysis and Applications》2009,351(1):152-162
For and m>0 we consider the maximal operator given by