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...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

In this paper, statistical analysis of watermarking schemes based on correlation detection is presented. Statistical properties of watermark sequences generated by piecewise-linear Markov maps are exploited, resulting in superior watermark detection reliability. Correlation/spectral properties of such sequences are easily controllable, a fact that reflects on the watermarking system performance...

Let k be an algebraically closed field of characteristic 0, let N ∈ N, let g : P−→P be a non-constant morphism, and let A : A−→A be a linear transformation defined over k(P), i.e., for a Zariski open dense subset U ⊂ P, we have that for x ∈ U(k), the specialization A(x) is an N -by-N matrix with entries in k. We let f : P×A99KP×A be the rational endomorphism given by (x, y) 7→ (g(x), A(x)y). We...

We consider compact Lie groups extensions of expanding maps of the circle, essentially restricting to U(1) and SU(2) extensions. The central object of the paper is the associated Ruelle transfer (or pull-back) operator F̂ . Harmonic analysis yields a natural decomposition F̂ = ⊕F̂α, where α indexes the irreducible representation spaces. Using Semiclassical techniques we extend a previous result by...

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 we prove that if a Grassmann space Δ = GrA(m,h,K) of the h–subspaces of an affine space A = AG(m,K) has an embedding e into a projective space PG(n,K′) over a skew–field K′, and e satisfies two suitable conditions (α) and (β), then K and K′ are isomorphic fields and Δ is, up to projections, an affine Grassmannian. Mathematics Subject Classification (2000). 51A45; 51M35.

General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, appropriate to the situation under study. In the context of spin-12 particles, these guidelines are used starting with the Dirac equation. The spinor theory just constructed is used to obtain the transfer maps for normal and skew magnetic quadrup...

the ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, linton and banaschewski with nelson defined and studied the tensor product in an equational category and in a general (concrete) category k, respectively, using bimorphisms, that is, defined via the hom-functor on k. also, the so-called sesquilinear, or on...