In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

This paper analyzes and characterizes the nature of interactions between countries West African Economic Monetary Union (WAEMU) over period 1995–2015. The analysis uses sigma-convergence on one hand Dendrinos-Sonis spatial competition model estimated by SUR method other hand. results show a lack convergence living standards support idea income polarization in space; these also very poorly integ...

Magnetic fields grow quickly even at early cosmological times, suggesting the action of a small-scale dynamo (SSD) in interstellar medium galaxies. Many studies have focused on idealized turbulent driving SSD. Here we simulate more realistic supernova-driven turbulence to determine whether it can drive an field growth occurring our models appears inconsistent with simple tangling magnetic field...

‎a ring $r$ is strongly clean provided that every element‎ ‎in $r$ is the sum of an idempotent and a unit that commutate‎. ‎let‎ ‎$t_n(r,sigma)$ be the skew triangular matrix ring over a local‎ ‎ring $r$ where $sigma$ is an endomorphism of $r$‎. ‎we show that‎ ‎$t_2(r,sigma)$ is strongly clean if and only if for any $ain‎ ‎1+j(r)‎, ‎bin j(r)$‎, ‎$l_a-r_{sigma(b)}‎: ‎rto r$ is surjective‎. ‎furt...

‎In this paper‎, ‎algebraic investigations on sup-$Sigma$-algebras are presented‎. ‎A representation theorem for‎ ‎sup-$Sigma$-algebras in terms of nuclei and quotients is obtained‎. ‎Consequently‎, ‎the relationship between‎ ‎the congruence lattice of a sup-$Sigma$-algebra and the lattice of its nuclei is fully developed.

in this paper, we define the common minimal common neighborhooddominating signed graph (or common minimal $cn$-dominating signedgraph) of a given signed graph and offer a structuralcharacterization of common minimal $cn$-dominating signed graphs.in the sequel, we also obtained switching equivalencecharacterization: $overline{sigma} sim cmcn(sigma)$, where$overline{sigma}$ and $cmcn(sigma)$ are ...

In this article, we present and assess the labor productivity changes that have occurred in Poland’s rural sectors since country became a member of European Union. The study is linked with concept convergence, which one key goals integration. Convergence when two or more things, ideas, processes become similar. an economic sense, convergence reduction development disparities between countries, ...

We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and dominated theorem are established; analogues classical ${\mathcal L}^1$- ${\mathrm L}^1$-spaces investigated. results extend earlier work by Wright specialise those for Lebesgue when ...