Existence and uniqueness of band-limited, positive semidefinite extrapolations

1990 ◽  
Vol 38 (3) ◽  
pp. 547-549 ◽  
Author(s):  
K.S. Arun ◽  
L.C. Potter
Keyword(s):  
Existence And Uniqueness ◽  
Positive Semidefinite ◽  
Band Limited

scholarly journals Application of Localization to the Multivariate Moment Problem

2014 ◽  
Vol 115 (2) ◽  
pp. 269 ◽  
Author(s):  
Murray Marshall
Keyword(s):  
Hilbert Space ◽  
Moment Problem ◽  
Existence And Uniqueness ◽  
Positive Semidefinite ◽  
Linear Functionals ◽  
Localization Technique ◽  
Adjoint Operators

It is explained how the localization technique introduced by the author in [19] leads to a useful reformulation of the multivariate moment problem in terms of extension of positive semidefinite linear functionals to positive semidefinite linear functionals on the localization of $\mathsf{R}[\underline{x}]$ at $p = \prod_{i=1}^n(1+x_i^2)$ or $p' = \prod_{i=1}^{n-1}(1+x_i^2)$. It is explained how this reformulation can be exploited to prove new results concerning existence and uniqueness of the measure $\mu$ and density of $\mathsf{C}[\underline{x}]$ in $\mathscr{L}^s(\mu)$ and, at the same time, to give new proofs of old results of Fuglede [11], Nussbaum [21], Petersen [22] and Schmüdgen [27], results which were proved previously using the theory of strongly commuting self-adjoint operators on Hilbert space.

scholarly journals Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel

2012 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Timir Karmakar ◽  
Meraj Alam ◽  
G. P. Raja Sekhar
Keyword(s):  
Porous Medium ◽  
Approximate Solution ◽  
Existence And Uniqueness ◽  
Perturbation Expansion ◽  
Positive Semidefinite ◽  
Darcy Number ◽  
Momentum Equation ◽  
Matched Asymptotic Expansion ◽  
Regular Perturbation ◽  
Uniqueness Results

<p style='text-indent:20px;'>We present asymptotic analysis of Couette flow through a channel packed with porous medium. We assume that the porous medium is anisotropic and the permeability varies along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We developed existence and uniqueness results corresponding to the anisotropic Brinkman-Forchheimer extended Darcy's equation in case of fully developed flow using the Browder-Minty theorem. Complemented with the existence and uniqueness analysis, we present an asymptotic solution by taking Darcy number as the perturbed parameter. For a high Darcy number, the corresponding problem is dealt with regular perturbation expansion. For low Darcy number, the problem of interest is a singular perturbation. We use matched asymptotic expansion to treat this case. More generally, we obtained an approximate solution for the nonlinear problem, which is uniformly valid irrespective of the porous medium parameter values. The analysis presented serves a dual purpose by providing the existence and uniqueness of the anisotropic nonlinear Brinkman-Forchheimer extended Darcy's equation and provide an approximate solution that shows good agreement with the numerical solution.</p>

scholarly journals Existence and Uniqueness of the Positive Definite Solution for the Matrix EquationX=Q+A∗(X^−C)−1A

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Dongjie Gao
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Positive Semidefinite ◽  
Positive Definite ◽  
Nonlinear Matrix Equation ◽  
Block Diagonal Matrix ◽  
Positive Definite Solution ◽  
The Matrix ◽  
Nonlinear Matrix ◽  
Definite Solution

We consider the nonlinear matrix equationX=Q+A∗(X^−C)−1A, whereQis positive definite,Cis positive semidefinite, andX^is the block diagonal matrix defined byX^=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given.

Method of estimation of hidden correlation of narrowband noise signals

2019 ◽  
pp. 34-39 ◽  
Author(s):  
E.I. Chernov ◽  
N.E. Sobolev ◽  
A.A. Bondarchuk ◽  
L.E. Aristarhova
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
New Technology ◽  
Digital Signal ◽  
Measuring Instruments ◽  
Central Frequency ◽  
Pearson Criterion ◽  
Useful Signal ◽  
Band Limited ◽  
Narrowband Noise

The concept of hidden correlation of noise signals is introduced. The existence of a hidden correlation between narrowband noise signals isolated simultaneously from broadband band-limited noise is theoretically proved. A method for estimating the latent correlation of narrowband noise signals has been developed and experimentally investigated. As a result of the experiment, where a time frag ent of band-limited noise, the basis of which is shot noise, is used as the studied signal, it is established: when applying the Pearson criterion, there is practically no correlation between the signal at the Central frequency and the sum of signals at mirror frequencies; when applying the proposed method for the analysis of the same signals, a strong hidden correlation is found. The proposed method is useful for researchers, engineers and metrologists engaged in digital signal processing, as well as developers of measuring instruments using a new technology for isolating a useful signal from noise – the method of mirror noise images.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Sign in / Sign up

Export Citation Format

Share Document