scholarly journals POLYNOMIAL APPROXIMATION, LOCAL POLYNOMIAL CONVEXITY, AND DEGENERATE CR SINGULARITIES — II

2011 ◽  
Vol 22 (12) ◽  
pp. 1721-1733 ◽  
Author(s):  
GAUTAM BHARALI
Keyword(s):  
Approximation Theorem ◽  
Sufficient Conditions ◽  
Hölder Continuous ◽  
Polynomial Convexity ◽  
Closed Disk ◽  
Local Polynomial ◽  
Polynomially Convex ◽  
Polynomial Hull ◽  
Weierstrass Approximation Theorem ◽  
Almost All

We provide some conditions for the graph of a Hölder-continuous function on [Formula: see text], where [Formula: see text] is a closed disk in ℂ, to be polynomially convex. Almost all sufficient conditions known to date — provided the function (say F) is smooth — arise from versions of the Weierstrass Approximation Theorem on [Formula: see text]. These conditions often fail to yield any conclusion if rank ℝDF is not maximal on a sufficiently large subset of [Formula: see text]. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in ℂ2 at an isolated complex tangency.

scholarly journals On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Time Delay ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Algorithm ◽  
Directed Network ◽  
Consensus Protocol ◽  
Special Cases ◽  
Coupling Time ◽  
Almost All ◽  
Double Integrator

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

scholarly journals Boundary behavior of the Bergman metric

2002 ◽  
Vol 168 ◽  
pp. 27-40 ◽  
Author(s):  
Bo-Yong Chen
Keyword(s):  
Green Function ◽  
Pseudoconvex Domain ◽  
Boundary Point ◽  
Boundary Behavior ◽  
Sufficient Conditions ◽  
Bergman Metric ◽  
Hölder Continuous ◽  
Pluricomplex Green Function ◽  
Peak Function

AbstractLet Ω be a bounded pseudoconvex domain in Cn. We give sufficient conditions for the Bergman metric to go to infinity uniformly at some boundary point, which is stated by the existence of a Hölder continuous plurisubharmonic peak function at this point or the verification of property (P) (in the sense of Coman) which is characterized by the pluricomplex Green function.

Hyponormal and essentially normal operators

1979 ◽  
Vol 83 (1-2) ◽  
pp. 123-132
Author(s):  
C. R. Putnam
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Principal Result ◽  
Hyponormal Operator ◽  
Essentially Normal ◽  
Normal Operators ◽  
Result Theorem ◽  
Almost All ◽  
Spectral Family

SynopsisLet T be a hyponormal operator on a Hilbert space, so that T*T – TT*≧ 0. Let T have the Cartesian representation T = H + iJ where H has the spectral family {Et} and suppose that EtJ − JEt is compact for almost all t on a Borei set α satisfying E(α) = I. The principal result (Theorem 3) is that under these hypotheses T must be normal. In case T is hyponormal and essentially normal some sufficient conditions are given assuring that, for a fixed t, EtJ − JEt is compact.

Embeddings of weighted Sobolev spaces into spaces of continuous functions

1992 ◽  
Vol 439 (1906) ◽  
pp. 279-296 ◽  
Keyword(s):  
Weighted Sobolev Spaces ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Hölder Continuous ◽  
Compact Embeddings ◽  
Spaces Of Continuous Functions ◽  
Hölder Continuous Functions ◽  
Continuous And Compact Embeddings ◽  
Necessary And Sufficient ◽  
Theoretical Results

We give sufficient conditions and necessary conditions (which in some cases are both necessary and sufficient) for continuous and compact embeddings of the weighted Sobolev space W 1,p ( Ω ;v 0 v 1 )into spaces of weighted continuous and Holder continuous functions. The theoretical results are illustrated by several examples.

Bernstein Power Series

1964 ◽  
Vol 16 ◽  
pp. 241-252 ◽  
Author(s):  
E. W. Cheney ◽  
A. Sharma
Keyword(s):  
Power Series ◽  
Infinite Series ◽  
Approximation Theorem ◽  
Bernstein Polynomials ◽  
Starting Point ◽  
Image Position ◽  
Weierstrass Approximation Theorem

In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomialsare constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared. It is our purpose here to consider several generalizations in the form of infinite series and to establish some of their properties.

scholarly journals Regular and Irregular Performance Variation of Module String and Occurred Conditions for Potential Induced Degradation-Affected Crystalline Silicon Photovoltaic Power Plants

Energies ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 4230 ◽  
Author(s):  
Jingsheng Huang ◽  
Yaojie Sun ◽  
He Wang ◽  
Junjun Zhang
Keyword(s):  
Power Plants ◽  
Crystalline Silicon ◽  
Sufficient Conditions ◽  
Ethyl Vinyl ◽  
Climate Conditions ◽  
Photovoltaic Power ◽  
Performance Variation ◽  
Current Voltage ◽  
Almost All ◽  
Necessary And Sufficient

Potential induced degradation (PID) leads to power degradation, and reduces durability and reliability of solar modules. However, this problem has not been thoroughly solved so far. The results from interlaboratory and field study show contradictory fault phenomenon for PID. In this paper, PID of crystalline silicon photovoltaic power plants distributed in various climate conditions was investigated. These photovoltaic power plants consist of two types of crystalline silicon solar modules, which cover almost all kinds of front glass, ethyl vinyl acetate (EVA) and backsheet available commercially. It was found that only a few of power plants were affected by PID. By measuring current voltage characteristics of PID-affected solar modules, the real faults phenomenon was uncovered and classified into regular and irregular power degradation in a module string. The results obtained in this work show that the negative potential caused by high system voltage and stacking faults are necessary and sufficient conditions for PID occurrence for the first time. The anomalous power degradation is related to the stacking fault, which appears randomly during the crystal growth.

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