Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions Abstract We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose–Einstein statistics) this distributio...

Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions Abstract We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose–Einstein statistics) this distributio...

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

in this research, a two-phase algorithm based on the artificial neural network (ann) and a harmony search (hs) algorithm has been developed with the aim of assessing the reliability of structures with implicit limit state functions. the proposed method involves the generation of datasets to be used specifically for training by finite element analysis, to establish an ann model using a proven an...

capacity of a road facility as an important characteristic in transportation and traffic studies is defined as the maximum rate of flow that could be held by that facility, which has been supposed to have a constant and certain value. this assumption, although necessary for most traffic studies, has also caused some problems, like that of demand exceeding capacity in many road facilities. resea...

We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p(N, d), defined as the number of decompositions of N into integer summands, with each summand appearing at most d times in a given decomposition. The derivation involves mapping to an equivalent physical problem concerning the aver...

[03.1] For a bounded sequence of complex numbers c n , prove that ∞ n=0 c n z n z n + 1 converges to a holomorphic function on |z| < 1. Each summand is holomorphic on |z| < 1, because of the quotient rule, and that the numerator and denominator are polynomials, hence holomorphic. To prove that the sum n f n of a sequence of holomorphic functions on |z| < 1 is itself holomorphic, it suffices to ...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...