Laan in (Ph.D Thesis, Tartu. 1999) introduced the principal weak form of Condition $(P)$ as Condition $(PWP)$ and gave some characterization of monoids by this condition of their acts. In this paper first we introduce Condition (G-PWP), a generalization of Condition $(PWP)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. We also ...

laan in (ph.d thesis, tartu. 1999) introduced the principal weak form of condition $(p)$ as condition $(pwp)$ and gave some characterization of monoids by this condition of their acts. in this paper first we introduce condition (g-pwp), a generalization of condition $(pwp)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. we also ...

This paper presents a theorem on universality on orthogonal polynomials/random matrices under a weak local condition on the weight function w. With a new inequality for polynomials and with the use of fast decreasing polynomials, it is shown that an approach of D. S. Lubinsky is applicable. The proof works at all points which are Lebesgue-points both for the weight function w and for logw.

this paper is devoted to the study of products of classes of right $s$-posets possessing one of the flatness properties and preservation of such properties under products. specifically, we characterize a pomonoid $s$ over which its nonempty products as right $s$-posets satisfy some known flatness properties. generalizing this results, we investigate products of right $s$-posets satisfying condi...

Constructing S-boxes with low differential uniformity and high nonlinearity is of cardinal significance in cryptography. In the present paper, we show that numerous differentially 4-uniform permutations over F22k can be constructed by composing the inverse function and cycles over F22k . Two sufficient conditions are given, which ensure that the differential uniformity of the corresponding comp...

The complex measure condition was introduced by Itô (1965) as a sufficient condition on the potential term in a one-dimensional Schrödinger equation and/or corresponding linear diffusion equation to obtain a FeynmanKac path integral formula. In this paper we provide an alternative probabilistic derivation of this condition and extend it to include any other lower order terms, i.e. drift and for...