We consider a surjective morphism f : X → Y from a smooth projective variety X onto a smooth projective variety Y with connected fibers, henceforth called a fibration for short. Typically, if a certain geometric object on X like a cohomology class has a certain property, then its restriction to a smooth fiber of f trivially satisfies the same property. The converse question is of more interest:...

A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues λn, a complete asymptotic expansion for large n is obtained, and the coefficients of this expansion are expressed in terms of the heat invariants. A sequence of trace formulas is obtained, expressing regularised sums of integer powers of eigenvalues ...

Abstract. This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator x′′ + h(t)x′ + ωx = 0 is uniformly asymptotically stable, where h : [0,∞) → [0,∞) is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h. The obtained sufficient conditi...

A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues λn, a complete asymptotic expansion for large n is obtained, and the coefficients of this expansion are expressed in terms of the heat invariants. A sequence of trace formulas is obtained, expressing regularised sums of integer powers of eigenvalues ...

where Aj = −d/dx + fj(x) are first order differential operators. A Darboux chain is called periodic if Lj+r = Lj for some r and for all j = 1, 2, . . . . Number r is called the period of a Darboux chain. The operator L+ α2 appears to be the harmonic oscillator in the particular case r = 1. Periodic Darboux chains lead to integrable systems of differential equations for functions fj, which are e...

In this paper, we propose a methodology for analyzing the near-field coupling between two surface mount device (SMD) inductors using 3-dimensional electromagnetic (3D-EM) model. To develop 3D-EM model, first constitute equivalent circuit of SMD inductor from measured impedance and derive loss tangent parameters. Secondly, damped harmonic oscillator model is introduced to extract effective perme...

The goal of this research is to improve the linearity of integrated oscillator based on switched-capacitor band-pass filter with a low Q-factor in order to achieve a feasible integration. With the minimum addition control digital control circuit, high linearity can be achieved by suppressing 3rd harmonic which requires high Q of filter in traditional way. Description. The aim of this research i...

Embedding results of Sobolev type are proved for the Dunkl harmonic oscillator on the line.