Abstract. In this paper, a family of skew-slash distributions is defined and investigated. We define the new family by the scale mixture of a skew-elliptically distributed random variable with the power of a uniform random variable. This family of distributions contains slash-elliptical and skew-slash distributions. We obtain the moments and some distributional properties of the new family of d...

In this paper, we study skew cyclic and skew constacyclic codes over the ring R = Fq + uFq + vFq + uvFq where q = p^m; p is an odd prime, u^2 = u; v^2 = v; uv = vu. We show that Gray image of a skew cyclic code of length n is a skew quasi-cyclic code of length 4n over Fq of index 4. We also study the structural properties of skew cyclic and skew constacyclic codes over R. Further, generating po...

let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such tha...

In 1968, M. Artin proved that any formal power series solution of a system of analytic equations may be approximated by convergent power series solutions. Motivated by this result and a similar result of Płoski, he conjectured that this remains true when we replace the ring of convergent power series by a more general ring. This paper presents the state of the art on this problem, aimed at non-...

We define and study a notion of ring of formal power series with exponents in a cyclically ordered group. Such a ring is a quotient of various subrings of classical formal power series rings. It carries a two variable valuation function. In the particular case where the cyclically ordered group is actually totally ordered, our notion of formal power series is equivalent to the classical one in ...

In this paper, skew cyclic and skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv=vu=0 are studied. We show that Gray image of a skew cyclic code of length n over R is a skew quasi-cyclic code of length 3n over F_q of index 3. Structural properties of skew cyclic and skew constacyclic over R are obtained. Further, gener...

Clock skew variations adversely affect timing margins, limiting performance, reducing yield, and may also lead to functional faults. Non-tree clock distribution networks, such as meshes and crosslinks, are employed to reduce skew and also to mitigate skew variations. These networks, however, increase the dissipated power while consuming significant metal resources. Several methods have been pro...

The aim of this work is to study some noncommutative differential operators. We take an algorithmic approach as well as further developing the mathematics, and design and analyse algorithms to solve fundamental problems. We also give applications to differential equations. First we consider how to factor skew polynomials. These are polynomials in a differential or difference operator. Using the...