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...

Let HC ( ? ) and c denote the classes of sense-preserving harmonic mappings f = h + g ¯ in D with dilation ? z ? for | < 1 such that is Ma–Minda type convex function respect to conjugate points respectively. Here, : ? ? , called function, analytic univalent has positive real part, symmetric axis, starlike 0 > . The are derived from work Sun et al. (2016) on class M ? We study growth theorems fu...

The bipartite Gaussian state, corresponding to an anisotropic harmonic oscillator in a noncommutative space (NCS), is investigated with the help of Simon’s separability condition (generalized Peres-Horodecki criterion). It turns out that, exhibit entanglement between co-ordinates, parameters (mass and frequency) have satisfy unique constraint equation. We considered most general form NCS, both ...

conclusions vaccine based on the conjugation of p. aeruginosa pao-1 lps with dt increased anti-lps antibodies and had a significant potential to protect against pseudomonas infections. background treatment of pseudomonas aeruginosa pao-1 infections through immunological means has been proved to be efficient and protective. objectives the purpose of this study was to produce a conjugate vaccine ...

This paper describes a simplified mathematical model and the relevant numerical algorithm that simulates a draped cloth over a virtual human body. The proposed algorithm incorporates an elliptical, or non-consecutive, method to simulate the cloth wrinkles on moving bodies without having to reference the results of past drape simulation time steps. A global–local analysis technique was employed ...

miRNAs as one of the potential therapeutic agents have been recently considered for cancer treatment. AS1411 (aptNCL) is a DNA aptamer specifically binding to nucleolin protein on the cancer cell surface with antiproliferative effect. The aim of the study was to develop a conjugate consisted of aptNCL (as targeted delivery of therapeutic agent) and miRNA let-7d (as a tumor suppressor) using two...

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

Complex-conjugate-resolved Fourier-domain optical coherence tomography, where the quadrature components of the interferogram are obtained by simultaneous acquisition of the first and second harmonics of the phase-modulated interferogram, is applied to multisurface test targets and biological samples. The method provides efficient suppression of the complex-conjugate, dc, and autocorrelation art...