منابع مشابه
On a Multiplicative Partition Function
Let D(s) = ∑∞ m=1 amm −s be the Dirichlet series generated by the infinite product ∏∞ k=2(1− k−s). The value of am for squarefree integers m with n prime factors depends only on the number n, and we let f(n) denote this value. We prove an asymptotic estimate for f(n) which allows us to solve several problems raised in a recent paper by M. V. Subbarao and A. Verma.
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Markov Random Fields (MRFs) have proven very powerful both as density estimators and feature extractors for classification. However, their use is often limited by an inability to estimate the partition function Z. In this paper, we exploit the gradient descent training procedure of restricted Boltzmann machines (a type of MRF) to track the log partition function during learning. Our method reli...
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Stanley defined a partition function t(n) as the number of partitions λ of n such that the number of odd parts of λ is congruent to the number of odd parts of the conjugate partition λ modulo 4. We show that t(n) equals the number of partitions of n with an even number of hooks of even length. We derive a closed-form formula for the generating function for the numbers p(n)− t(n). As a consequen...
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chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولOn Congruence Properties of the Partition Function
Some congruence properties of the partition function are proved.
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ژورنال
عنوان ژورنال: Researches in Mathematics and Mechanics
سال: 2018
ISSN: 2519-206X
DOI: 10.18524/2519-206x.2018.1(31).134626