Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.

A planar harmonic mapping in a simply connected domain D ⊂ C is a complex-valued function f u iv defined in D for which both u and v are real harmonic in D, that is, Δf 4fzz 0, where Δ represents the Laplacian operator. The mapping f can be written as a sum of an analytic and antianalytic functions, that is, f h g. We refer to 1 and the book of Duren 2 for many interesting results on planar har...

the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...

in the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. the basic assumption is that the class of functions that we investigate here, except the verification of dirichlet's principles, is concurrently able to be expanded in taylor's representation, over a particular interval o...

Based on the linear prediction property of sinusoidal signals, a closed form unbiased frequency estimator for a real sinusoid in white noise is proposed. The frequency estimate derives from minimizin g a constrained least squares cost function and it is simple to implemen t either in batch or recursive mode. The relationship of the proposed method with the well-known Pisarenko harmonic decompos...

In this paper we show that harmonic compact operator-valued functions are characterized by having harmonic diagonal matrix coefficients in any choice of basis. We also give an example which shows that an operator-valued function with values outside the compact operators can have harmonic diagonal matrix coefficients in any choice of basis without being a harmonic operator-valued function. We us...

this paper presents a new control methodology for active power filters that provide an adaptive online harmonic estimation with partial and selective harmonic reduction schemes, which has been implemented within an integrated controller. the proposed approach is to provide partial and selective reduction of those individual harmonics which exceed the recommended levels as set by regulatory bodi...