Consider an entire (absolutely convergent in $\mathbb{C}$) Dirichlet series $F$ with the exponents $\lambda_n$, i.e., of form $F(s)=\sum_{n=0}^\infty a_ne^{s\lambda_n}$, and, for all $\sigma\in\mathbb{R}$, put $\mu(\sigma,F)=\max\{|a_n|e^{\sigma\lambda_n}:n\ge0\}$ and $M(\sigma,F)=\sup\{|F(s)|:\operatorname{Re}s=\sigma\}$. Previously, first authors M.M.~Sheremeta proved that if $\omega(\lambda)...

We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr 1981), but also over ∂-finite and holonomic summand expressions that are given by a linear recurrence. This approach implies new computer algebra tools implemented in Sigma to solve multi-summation problems efficien...

We analyse extensions $\Sigma$ of groupoids G by bundles A abelian groups. describe a pushout construction for such extensions, and use it to the extension group given groupoid bundle A. There is natural action Sigma on dual A, yielding corresponding transformation groupoid. The this map from fibre product with its Cartesian circle twist over resulting prove that full C*-algebra isomorphic $\Si...

A quantum-chemical model for non-adiabatic simulation of the energetic and radiative properties 2 Sigma + -X system OH radical is presented. The electronic structure parameters (potential energy functions matrix elements spin-orbit electron-rotation interactions) are obtained by means ab initio calculation. reliability performed calculations confirmed comparing estimates with experimental value...

Let $(A,\sigma)$ be a central simple algebra with an orthogonal involution. It is well-known that $O(A,\sigma)$ contains elements of reduced norm $-1$ if and only the Brauer class $A$ trivial. We generalize this statement to Azumaya algebras involution over semilocal rings, show "if" part fails one allows base ring arbitrary.

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.

For the symmetric space sigma model in the internal metric formalism we explicitly construct the lagrangian in terms of the axions and the dilatons of the solvable Lie algebra gauge and then we exactly derive the axion-dilaton field equations.

Combinatorial identities that were needed in [24] are proved, mostly with C. Schneider’s computer algebra package Sigma. The form of the Padé approximation of the logarithm of arbitrary order is stated as a conjecture.

background: the presence of rennin-angiotensin components in mammalian ovaries and their involvement in ovarian physiology have been established. in the present study, effects of angiotensin ii (ang ii) on sodium-potassium adenosine triphosphatase (na+/k+/atpase) expression and development of sheep embryos was evaluated. methods: the abattoir-derived cumulus oocyte complexes (coc) were randomly...

Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the N = 2 superconfor-mal models and contains generators of dimensions 1, 2 and 3 that close a linear algebra. Our construction can be carried out with one and two bosonic currents and th...