Abstract We study the lines of constant phase corresponding to ratio formed by building blocks Titchmarsh counterexample, that is two Dirichlet L-functions whose characters are complex conjugate each other. This on critical line sensitive zeros off line.

The limited usefulness of the maximum power transfer theorem in practice is argued. Inappropriately, the utility and value of the maximum power transfer theorem are often elevated to be religious icons of electrical engineering. While the theorem appears to be useful, often in real circuits the load impedance is not set equal to the complex conjugate of the equivalent impedance of the connectin...

We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian with Hermitian projection matrices allows an accessible introduction of the geometric concepts required for an intrinsic conjugate gradient method. In particula...

The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an...

Let M n (IK) denote the set of all n n matrices with elements in IK, where IK represents the eld IR of real numbers, the eld 0 C of complex numbers or the (noncommutative) eld IH of quaternion numbers. We call a subset T of M n (IK) a *-subalgebra of M n (IK) over the eld IR (or simply a *-subalgebra) if (i) T forms a subring of M n (IK) with the usual addition A + B and multiplication AB of ma...

An implementation of a parallel ScaLAPACK-style solver for the general Sylvester equation, op(A)X−Xop(B) = C, where op(A) denotes A or its transpose A , is presented. The parallel algorithm is based on explicit blocking of the Bartels-Stewart method. An initial transformation of the coefficient matrices A and B to Schur form leads to a reduced triangular matrix equation. We use different matrix...

In this note we extend a theorem of Bartle, Dunford, and Schwartz [ l ] which states that for every countably additive measure denned on a (T-algebra there exists a positive "control measure" v such that v{E)—>0 if and only if ||/z||(.E) —»0, where ||/x|| is the semivariation of JJL. In this paper, ju, which is defined on a ring S, is assumed to be finitely additive and strongly bounded (^-boun...

Many mathematicians have studied Euler numbers and Euler polynomials( see [1-11]). Euler polynomials posses many interesting properties and arising in many areas of mathematics and physics. In this paper we introduce the generalized q-Euler numbers and polynomials with weak weight α. Throughout this paper we use the following notations. By Zp we denote the ring of p-adic rational integers, Q de...

background: active immunization with gonadotropin releasing hormone conjugate (gnrh-bsa) manipulates the fertility axis and thus alters the reproductive cyclicity serum estradiol and progesterone levels. while the application of kamdhenu ark increases the efficacy of gnrh-bsa. objective: this experimental investigation is aimed to evaluate the modulatory effects on estrous cycle serum estradiol...