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...

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Abstract We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates curvilinear by making use a convolution function with Dirac delta functions whose arguments are determined between two systems. By integrating out an original function, we replace new in systematic way. A recursive allows successively. After replacing every into coordinate, find t...

In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this on the unit disk, obtained one-dimensional heat equation. It is well-known that can be solved taking into account boundary condition for general solution circle. paper, boundary-value problem using method called separation of variables. As result, to terms Fourier series...

We have investigated the diversity and repertoire of human TCR delta chain variable gene segments in the human peripheral blood CD4- CD8- (double-negative) population, using rearrangement and expression studies and sequence analyses. 20 TCR delta DNA clones were derived from the RNA of bulk-cultured double-negative T cells and their nucleotide sequences determined. These clones can be classifie...

Identification of simultaneous speech sounds, such as pairs of steady-state vowels (double vowels), is more accurate when there is a difference in fundamental frequency (F0). Accuracy of identification for double vowels increases with increasing F0 difference (delta F0) asymptoting above 1 semitone. The experiment described here attempts to distinguish two mechanisms underlying this effect: fir...

Let $R$ be a ring and $Z(R)$ the center of $R.$ The aim this paper is to define notions centrally extended Jordan derivations $\ast$-derivations, prove some results involving these mappings. Precisely, we that if $2$-torsion free noncommutative prime admits derivation (resp. $\ast$-derivation) $\delta:R\to R$ such that\[[\delta(x),x]\in Z(R)~~(resp.~~[\delta(x),x^{\ast}]\in Z(R))\text{ for all ...