current researches have showed that n3, n5-diaryl-2, 6-dimethyl -1, 4-dihydropyrine-3, 5- dicarboxamide analogues demonstrate notable anti-tubercular activity. in this study, hantzsch condensation was used to design and synthesize new analogues of dihydropyridine (dhp). different diary carboxamides were inserted at positions 3 and 5 of the dhp ring. 4(5)-chloro-2-ethyl-5(4)-imidazolyl moiety wa...

Throughout the text, let R be a commutative ring with identity (often called a commutative unital ring) and with multiplicative group of units R∗. Likewise, let f(x) = a0x +a1x n−1+ · · ·+an−1x+an be a polynomial of the variable x over R such that a0 ∈ R∗. Traditionally, R[x] is the ring of all polynomials of x over R; thereby f(x) ∈ R[x]. For an arbitrary but fixed element α, suppose f(x) is t...

For a field F, let R(n,m) be the ring of invariant polynomials for the action of SL(n,F) × SL(n,F) on tuples of matrices – (A,C) ∈ SL(n,F)× SL(n,F) sends (B1, . . . , Bm) ∈ M(n,F) to (AB1C , . . . , ABmC ). In this paper we call R(n,m) the ring of matrix semi-invariants. Let β(R(n,m)) be the smallest D s.t. matrix semi-invariants of degree ≤ D generate R(n,m). Guided by the Procesi-Razmyslov-Fo...

1.1 By R we denote an integral domain; then R[[x]] is the ring of formal power series over R in the variables x = (x1, . . . , xn). We write a series f(x) ∈ R[[x]] as f(x) = ∑ ai1···inx i1 1 · · ·xin n = ∑ aνx ν where ν = (ν1, . . . , νn) is a multi-index and x = x1 1 · · ·xνn n . In the sequel R is usually the finite field Fp of p elements or the ring of p-adic integers Zp. One says that f(x) ...

Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

Switching of intramolecular energy transfer is a challenging subject [ l-3 1. The problem is: is it possible to use a photochromic molecule F as central part of a supermolecule D-F-A to allow or to hinder energy transfer from D (donor) to A (acceptor) by switching F with light of the appropriate wavelength from one of its photochromic configurations into the other one and back? Promising candid...

Let F be a field. We shall let W(F) denote the Wit t ring of equivalence classes of nondegenerate symmetric bilinear forms over F. There are many questions one migh t ask about the extent to which one can prescribe the Wit t ring of an extension field of F and the natural homomorphism between these Wit t rings induced by the field inclusion. In this note we consider a formally real field F and ...

The combinatorial architecture of cullin 1-RING ubiquitin ligases, in which multiple F-box containing substrate receptors compete for access to CUL1, poses special challenges to assembling cullin 1-RING ubiquitin ligase complexes through high affinity protein interactions while maintaining the flexibility to dynamically sample the entire F-box containing substrate receptor repertoire. Here, usi...

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve the equation of deformations in a polynomial frame. We consider also the deformations of the enveloping algebra of a rigid Lie algebra and we define valued de...