منابع مشابه
Integral Representations of Positive Definite Matrix-valued Distributions on Cylinders
The notion of a <7-continuous matrix-valued positive definite distribution on 5/v(2a) x RM x G is introduced, where G is an abelian separable locally compact group and where Sp/(2a) is an open ball around zero in RA' with radius la > 0 . This notion generalizes that one of strongly continuous positive definite operator-valued functions. For these objects, a Bochner-type theorem gives a suitable...
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We adopt the following rules: r, x, y are real numbers, i, j are natural numbers, and p is a finite sequence of elements of R. The following proposition is true (1) For every closed-interval subset A of R and for every x holds x ∈ A iff inf A ¬ x and x ¬ supA. Let I1 be a finite sequence of elements of R. We say that I1 is non-decreasing if and only if the condition (Def. 1) is satisfied. (Def....
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We present a verifiable symbolic definite integral table look-up: a system which matches a query, comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. Our system is able to obtain correct answers in ...
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As a generalization of the famous four square theorem of Lagrange, Ramanujan and Willerding found all positive definite integral quaternary quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary quadratic forms that represent all positive definite integral binary quadratic forms. We also discuss recent results on positive definite int...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1950
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1950-0043273-6