Single crystals of nonlinear optical material bis (guanidinium) hydrogen phosphate monohydrate (G2HP) belonging to non centrosymmetric space group P 21c were successfully grown by the slow evaporation method. Optical transmittance and second harmonic generation of the grown crystals have been studied by UV-vis-NIR spectrum and Kurtz powder technique respectively. The transmittance of G2HP cryst...

Recommended by Narendra Kumar Govil We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions their boundaries are determined explicitly and the proofs rely on Schw...

where E(x, y) > 0. The parametric curves x = const. and y = const. form an isothermal net on 1. It is well known that h(x, y) = c, where h is a harmonic function of (x, y), that is, h satisfies the Laplace equation, hA, + h,, = 0, defines an isothermal family of curves on Z. The constant c is called the isothermal parameter. The converse of the preceding statement is not valid. That is, if g(x,...

for any φ ∈ C 0 (Ω). Such functions are locally C 1,α for some α ∈ (0, 1). In the case p = N , the function u is called N -harmonic. The N -harmonic functions play an important role as a natural extension of classical harmonic functions. They also appear in the theory of bounded distortion mappings [8]. One of the main properties of the class of N -harmonic functions is its invariance by confor...

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...

The general expression for magnetic induction in the z axis direction is derived from magnetic scalar potential, and magnetic induction for biplanar shimming coils (BSCs) is also derived from magnetic vector potentials and Green functions, which simultaneously include Sin and Cos harmonic fields. The relationship between these expressions is discussed, and we show they are partially consistent....

By the degree elevation-based method of approximating rational curves and surfaces using polynomial curves and surfaces, a new effective approach to construct rational Bézier harmonic surfaces over rectangular or triangular domain is presented. First, rational Bézier curves, given as the boundaries, are transferred into some approximate polynomial curves, according to which a polynomial harmoni...

Ship noise received by passive sonar is multiple harmonic sources, from which the recognition features of ship can be extracted. Based on the multiple signal classification estimation theory, a joint estimation method of harmonic sources number, harmonic orders and fundamental frequencies is developed in this paper. The observed signal vector is decomposed into multiple harmonics vector and noi...