We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and other one generalized type involving factorials in its coefficients. Using criteria due to Fejér Ozaki, we provide sufficient conditions for these functions be close-to-convex or starlike inside unit disk, thus univalent. our proofs assisted symbolic computat...

Let F be a finite field of characteristic ` > 0, F a number field, GF the absolute Galois group of F and let ρ̄ : GF → GLN (F) be an absolutely irreducible continuous representation. Suppose S is a finite set of places containing all places above ` and above ∞ and all those at which ρ̄ ramifies. Let O be a complete discrete valuation ring of characteristic zero with residue field F. In such a sit...

A sufficient condition for the convergence of a generalized formal power series solution to an algebraic q-difference equation is provided. The main result leans on geometric property related semi-group (complex) exponents such series. This corresponds situation in which small divisors phenomenon does not arise. Some examples illustrating cases where obtained can or cannot be applied are also d...

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...

The convergence sets of a multidimensional complete field are those having the property that all power series over it converge when substituting an element maximal ideal for variable. It is proved set lies in ring integers if and only contained some ring.

This paper deals with the simulation of a unified series-shunt compensator (USSC) aimed at examining its capability in improving power quality in a power distribution systems. The USSC simulation model comprises of two 12-pulse inverters which are connected in series and in shunt to the system. A generalized sinusoidal pulse width modulation switching technique is

This paper presents a novel, fast converging on-line rule for Generalized Eigendecomposition (GED) and its application in time series segmentation. We adopt the concepts of deflation and power method to iteratively estimate the generalized eigencomponents. The algorithm is guaranteed to produce stable results. In the second half of the paper, we discuss the application of GED to segment time se...

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...