In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

For an integer t ≥ 1 and a partition λ, we let Ht(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define aeven t (n) and aodd t (n) to be the number of partitions of n such that |Ht(λ)| is even or odd, respectively. In a recent paper, Han generalized the Nekrasov-Okounkov formula to obtain a generating function for at(n) = aeven t (n)− aodd t (n). We use this generating ...

We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi–classical computations, leading in particular to a closed formu...

Abstract Dirichlet series associated with the Poincaré attached to $$\mathrm{SL}(2,{{\mathbb {Z}}})$$ SL ( 2 , Z ) are introduced. Integral representations and transformation formulas given, which descr...

We calculate the form factor H[q], i.e. the generating function of the gyration radii, and the generating function G [q] of the end-to-end radii, to first order in the dimensionless second viral coefficient g, or in 03B5 = 4 2014 d, d being the space dimension. These functions are calculated in the asymptotic limit of Kuhnian chains, i.e. very long chains in a good solvent. They are used to det...

A bi-isotropic magneto-electric metamaterials is modeled by two independent reservoirs. The reservoirs contain a continuum of three dimensional harmonic oscillators, which describe polarizability and magnetizability of the medium. The paper aimed to investigate the effect of electromagnetic field on bi-isotropic. Starting with a total Lagrangian and using Euler-Lagrange equation, researcher cou...

Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results ...

Network reliability is one of the most important concepts in this modern era. Reliability characteristics, component significance measures, such as Birnbaum importance measure, critical risk growth factor and average factor, network stability communication system have been discussed paper to identify components network, also quantify impact failures. The study proposes an efficient algorithm co...