in this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{t}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. we use a strong convolution technique and derive inclusion results. a radius problem and some other interesting properties of these classes are discussed.

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest of which remains the Pollard rho algorithm with r-adding walks. For the first time, we rigorously analyze the Pollard rho method with r-addin...

We study the effects of strong Coulomb disorder on transverse magnetoresistance in Weyl semimetals at low temperatures. Using diagrammatic technique and Keldysh model to sum up leading terms expansion, we find that linear exhibits a renormalization due long-range nature interaction ${\ensuremath{\rho}}_{xx}\ensuremath{\propto}H\phantom{\rule{0.16em}{0ex}}ln(eH\ensuremath{\hbar}{v}^{2}/c{T}_{\ma...

AIMS To compare the International Consultation on Incontinence Questionnaire-Urinary Incontinence Short Form (ICIQ-UI SF) with the Incontinence Severity Index (ISI), and to propose intervals for four severity levels of ICIQ-UI SF. METHODS Cross-sectional, Internet-based study of 1,812 women responding to a general health questionnaire. Four severity levels for the ICIQ-UI SF scores were const...

Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...