منابع مشابه
Tube Formulas for Self-Similar Fractals
Tube formulas (by which we mean an explicit formula for the volume of an (inner) ε-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of Euclidean space, this includes Weyl’s celebrated results on spectral asymptotics, and the subsequent relation between curvature and spectrum. Additionally, a tube f...
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Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.
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There are a number of so-called factorization theorems for rook polynomials that have appeared in the literature. For example, Goldman, Joichi and White [6] showed that for any Ferrers board B = F (b1, b2, . . . , bn), n
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Nonlinear versions of the Lie-Trotter product formula exp[t(A + B)] = \im„^x[exp((t/n)A)exp((t/n)B)}" and related formulas are given in this paper. The convergence rates are optimal. The results are applicable to some nonlinear partial differential equations. 0. Introduction. The Lie-Trotter product formula states that (0.1) exp(^)exp(^)exp(^C e,(A + B+c) asn^oo. (The exponent n indicates itera...
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This article is based on a talk presented at a conference “Quantum Annealing and Other Optimization Methods” held at Kolkata, India on March 2–5, 2005. It will be published in the proceedings “Quantum Annealing and Other Optimization Methods” (Springer, Heidelberg) pp. 39–70. In the present article, we review the progress in the last two decades of the work on the Suzuki-Trotter decomposition, ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1989
ISSN: 0019-2082
DOI: 10.1215/ijm/1255988811