In the context of the ring Q[x,y], of polynomials in 2n variables x = x1, . . . , xn and y = y1, . . . , yn, we introduce the notion of diagonally quasisymmetric polynomials. These, also called diagonal Temperley-Lieb invariants, make possible the further introduction of the space of diagonal Temperley-Lieb harmonics and diagonal Temperley-Lieb coinvariant space. We present new results and conj...

Abstract. Let u(x, t) be the solution to the free time-dependent Schrödinger equation at the point (x, t) in space-time Rn+1 with initial data f . We characterize the size of u in terms Lp(Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Ḣs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interp...

Let u(x; t) be the solution to the free time-dependent Schrr odinger equation at the point (x; t) in space-time R n+1 with initial data f. We characterize the size of u in terms L p (L q)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces _ H s (R n). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interpo...

We present analysis of coherence properties of odd harmonics radiated from a SASE FEL with planar undulator. Nonlinear mechanism of harmonic generation is under study. Temporal and space correlation functions, coherence time and degree of transverse coherence are calculated by means of numerical simulations with the code FAST. Similarity techniques have been used to derive general coherence pro...

The mustache bat emits a three-harmonic echolocation pulse. At the external ear, large interaural intensity differences are generated only when a sound originates within a limited area of two-dimensional space, and this area is different for each pulse harmonic. As a consequence, the external ear generates pronounced binaural spectral cues containing two-dimensional spatial information. This in...

In this paper, we propose a novel descriptor for shapes. The proposed descriptor is obtained from 3D spherical harmonics. The inadequacy of 2D spherical harmonics is addressed and the method to obtain 3D spherical harmonics is described. 3D spherical harmonics requires construction of a 3D model which implicitly represents rich features of objects. Spherical harmonics are used to obtain descrip...

Results are presented on the generation of high harmonics through the scattering of relativistic electrons from high-intensity laser light. The characteristic signatures of this process are found to be the emission of evenorder harmonics, linear dependence on the electron density, significant amount of harmonics with circular polarization, and small spatial extent of the source. The harmonics a...

In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a...

A generalised formulation of SHE-PWM technique applicable for high power voltage source cascaded multilevel inverter used in constant frequency utility applications has been discussed in this paper. The SHE-PWM scheme features a broad solution space. This paper aims at to eliminate low order dominant harmonics and at the same time maintaining fundamental also. Since SHE equations are non-linear...

Wind energy conversion systems are now occupying important space in the research of renewable energy sources with microgrid. The main challenge in wind power generation is power quality problem and their connection with the distribution network in microgrid. The main factor behind poor power quality is the impact of harmonics in current and voltage in power network. In microgrid the converter a...