two digraphs of same order are said to be skew-equienergetic if theirskew energies are equal. one of the open problems proposed by li andlian was to construct non-cospectral skew-equienergetic digraphs onn vertices. recently this problem was solved by ramane et al. inthis paper, we give some new methods to construct new skew-equienergeticdigraphs.

Let α be a polynomial Poisson bivector on a finite-dimensional vector space V over C. Then Kontsevich [K97] gives a formula for a quantization f ⋆ g of the algebra S(V )∗. We give a construction of an algebra with the PBW property defined from α by generators and relations. Namely, we define an algebra as the quotient of the free tensor algebra T (V ∗) by relations xi ⊗ xj − xj ⊗ xi = Rij(~) wh...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

In this paper, some properties of $alpha$-skew Armendariz and central Armendariz rings have been studied by variety of others. We generalize the notions to central $alpha$-skew Armendariz rings and investigate their properties. Also, we show that if $alpha(e)=e$ for each idempotent $e^{2}=e in R$ and $R$ is $alpha$-skew Armendariz, then $R$ is abelian. Moreover, if $R$ is central $alpha$-skew A...

In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Exti (M,N) is provided when N is a centralizing bimodule. Mathematics Subject Classifications (2000): 16Z05, 16E30.

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, standardized marginal distributions are standard normal. The copula itself depends on familiar skewing construction based normal function. This concerned with two topics. First, number extensions Notably these include case in Student’s t, different degrees freedom allowed for each margin. I...

We show that over algebraically closed fields of characteristic zero a Hopf algebra with central Hopf algebra coradical has a PBW basis after some localization of the coradical.

In proton beam writing (PBW) a focused MeV proton beam is scanned in a predetermined pattern over a resist (e.g. PMMA, SU-8 or HSQ), which is subsequently chemically developed. In e-beam writing as well as p-beam writing the energy loss of the primary beam is dominated by energy transfer to substrate electrons. Unlike the high energy secondary electrons generated during e-beam writing the secon...