We present a general framework for balancing expressions (terms) in form of so called tree straight-line programs. The latter can be seen as circuits over the free term algebra extended by contexts (terms with a hole) and the operations which insert terms/contexts into contexts. It is shown that for every term one can compute in DLOGTIME-uniform TC$^0$ a tree straight-line program of logarithmi...

Abstract Let $${\mathcal {C}} \subset {\mathbb {N}}^p$$ C ⊂ N p be a finitely generated integer cone and $$S\subset {\mathcal {C}}$$ S an affine semigroup such that the real cones by S are equal. ...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...

The Agabus bipustulatus complex includes one of Europe's most widely distributed and common diving beetles. This complex, which is known for its large morphological variation, has a complex demographic and altitudinal variation in elytral reticulation. The various depth of the reticulation imprint, both in smaller and larger meshes, results in both mat and shiny individuals, as well as intermed...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field‎. ‎Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...