A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homog...

Ruscheweyh‘and She&Small proved the P6lya-Schoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that clos&o-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve...

This paper presents a harmonic+noise speech coder which uses an efficient spectral quantization technique and a novel voiced/unvoiced (V/UV) mixing model. The harmonic magnitudes are coded at 23 bits/frame using the magnitude response of a linear predictive coding (LPC) system. The difference between the harmonic magnitudes and the sampled magnitude response is minimized by the closed-loop appr...

‎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...

Modern wind turbines are commonly equipped with power electronics. The application of either a partial scale frequency converter or a full scale power converter will result in harmonic emission which is distinct from conventional harmonic sources: even harmonics and interharmonics appear with similar magnitudes as odd harmonics. Harmonic and interharmonic measurements on a few individual wind t...

1. The class Q of complex solutions of a linear partial differential equation. Any two real harmonic functions U(x, y), V(x, y)—that is, solutions of the Laplace equation—can be combined to form a complex harmonic function U+iV. The class of all complex harmonic functions is of no interest, because in effect it possesses no special properties not already possessed by real harmonic functions. Ho...

This paper presents an integrated approach feasible direction method and genetic algorithm (FDM+GA) to investigate the planning of large-scale passive harmonic filters. The optimal filter scheme can be obtained from a system under abundant harmonic current sources where harmonic amplification problems should be avoided. The constraints of harmonics with orders lower than the filter tuned-points...

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...

The projection on the base plane of a regular minimal surface S in R with isothermal parameters defines a complex-valued univalent harmonic function f = h(z) + g(z). The aim of this paper is to obtain the distortion inequalities for the Weierstrass-Enneper parameters of the minimal surface for the harmonic multivalent functions for which analytic part is an m-valent convex function. 2000 Mathem...