Search results for "Subharmonic"

The effect of MPEG audio compression on multidimensional set of voice parameters

2002

The MPEG-1 Layer 3 compression schema of audio signal, or commonly known as mp3, has caused a great impact in recent years as it has reached high compression rates while also conserving a high sound quality. Previous listening tests have shown that music and speech samples compressed at high bitrates are virtually indistinguishable from the original samples, but very little is known about how compression acoustically affects the voice signal. In Experiment 1 the spectral composition of original and compressed speech signals were analyzed by means of the Long-Term Average Spectrum using the Computerized Speech Laboratory (Kay Elemetrics Corp. (Pine Brook, NJ, USA)). In Experiment 2 a set of …

Positivity, complex FIOs, and Toeplitz operators

2018

International audience; We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz operators on the Bargmann space is implied by the boundedness of their Weyl symbols.

Approximation of plurisubharmonic functions

2015

We extend a result by Fornaaess and Wiegerinck [Ark. Mat. 1989;27:257-272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.

Superharmonic functions are locally renormalized solutions

2011

Abstract We show that different notions of solutions to measure data problems involving p-Laplace type operators and nonnegative source measures are locally essentially equivalent. As an application we characterize singular solutions of multidimensional Riccati type partial differential equations.

Polar Sets in a Nonlinear Potential Theory

1988

In this lecture we discuss nonlinear potential theory based on “A-super-harmonic functions”; the theory can be viewed as a (nonlinear) extension of the classical study of superharmonic functions in ℝn.

Improved Bounds for Hermite–Hadamard Inequalities in Higher Dimensions

2019

Let $\Omega \subset \mathbb{R}^n$ be a convex domain and let $f:\Omega \rightarrow \mathbb{R}$ be a positive, subharmonic function (i.e. $\Delta f \geq 0$). Then $$ \frac{1}{|\Omega|} \int_{\Omega}{f dx} \leq \frac{c_n}{ |\partial \Omega| } \int_{\partial \Omega}{ f d\sigma},$$ where $c_n \leq 2n^{3/2}$. This inequality was previously only known for convex functions with a much larger constant. We also show that the optimal constant satisfies $c_n \geq n-1$. As a byproduct, we establish a sharp geometric inequality for two convex domains where one contains the other $ \Omega_2 \subset \Omega_1 \subset \mathbb{R}^n$: $$ \frac{|\partial \Omega_1|}{|\Omega_1|} \frac{| \Omega_2|}{|\partial \Ome…

Functions of One Variable

2019

A classical result of Fatou gives that every bounded holomorphic function on the disc has radial limits for almost every point in the torus, and the limit function belongs to the Hardy space H_\infty of the torus. This property is no longer true when we consider vector-valued functions. The Banach spaces X for which this property is satisfied are said to have the analytic Radon-Nikodym property (ARNP). Some important equivalent reformulations of ARNP are studied in this chapter. Among others, X has ARNP if and only if each X-valued H_p- function f on the disc has radial limits almost everywhere on the torus (and not only H_\infty-functions). Even more, in this case each such f has non-tange…

A-superharmonic functions and supersolutions of degenerate elliptic equations

1988

Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials

2019

We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…

Forced oscillations in a self-oscillating surface reaction model

2004

A microscopic lattice gas model for the catalytic CO + O2 reaction on Pt(110) subject to external periodic forcing is studied by means of cellular automaton simulations. Harmonic resonance, subharmonic and superharmonic entrainment, quasiperiodic as well as chaotic behavior are among the observed phenomena in this model when the gas phase concentration of CO as an external control parameter is periodically varied and interacts with the self-oscillating reaction system.