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...

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...

For k a field of arbitrary characteristic, and R a k-algebra, we show that the PI degree of an iterated skew polynomial ring R[x1; τ1, δ1] · · · [xn; τn, δn] agrees with the PI degree of R[x1; τ1] · · · [xn; τn] when each (τi, δi) satisfies a qi-skew relation for qi ∈ k and extends to a higher qi-skew τi-derivation. We confirm the quantum Gel’fand-Kirillov conjecture for various quantized coord...

in this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. also, we represent several theorems for constructing each generalized skew t-normal distribution. next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, nickel and vanadium, associated with crude oil in shadgan wetland in the south-...

Let A be an arbitrary symmetrizable Cartan matrix of rank r, and n = n+ be the standard maximal nilpotent subalgebra in the Kac-Moody algebra associated with A (thus, n is generated by E1, . . . , Er subject to the Serre relations). Let Ûq(n) be the completion (with respect to the natural grading) of the quantized enveloping algebra of n. For a sequence i = (i1, . . . , im) with 1 ≤ ik ≤ r, let...

High-speed links which employ source synchronous clocking architectures have the ability to track correlated jitter between clock and data channels up to high frequencies. However, system timing margins are degraded by channel skew between clock and data signals and high-frequency loss. This paper describes how these key channel effects impact the jitter performance and influence the clocking a...

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple identities showing that skew functions are semi-invariant up to translation and rotation $\pi$ angle diagram. It follows that, in some special cases, coefficients with respect basis monomial polynomials nonnegative integer coefficients.