• Title/Summary/Keyword: operator stability

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CHARACTERIZATION OF STRICTLY OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Choi, Gyeong-Suk
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.101-123
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    • 2001
  • For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

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RESOLVENT DYNAMICAL SYSTEMS FOR MIXED VARIATIONAL INEQUALITIES

  • Muhammad, Aslan-Noor
    • Journal of applied mathematics & informatics
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    • v.9 no.1
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    • pp.15-26
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    • 2002
  • In this paper, we suggest and analyze a class of resolvent dynamical systems associated with mixed variational inequalities. We study the globally asymptotic stability of the solution of the resolvent dynamical systems for the pseudomonotone operators. We also discuss some special cases, which can be obtained from our main results.

REMARKS ON GAUSSIAN OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Chae, Hong Chul;Choi, Gyeong Suk
    • Korean Journal of Mathematics
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    • v.8 no.2
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    • pp.111-119
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    • 2000
  • For a linear operator Q from $R^d$ into $R^d$. ${\alpha}$ > 0 and 0 < $b$ < 1, the Gaussian (Q, $b$, ${\alpha}$)-semi-stability of probability measures on $R^d$ is investigated.

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Characterization of Some Classes of Distributions Related to Operator Semi-stable Distributions

  • Joo, Sang Yeol;Yoo, Young Ho;Choi, Gyeong Suk
    • Communications for Statistical Applications and Methods
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    • v.10 no.1
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    • pp.177-189
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    • 2003
  • For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on R^d$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi-stability with exponent Q. Characterization of strictly operator na-semi-stable distributions among operator m-semi-stable distributions is given. Translation of strictly operator m-semi-stable distribution is discussed.

REPRESENTATION OF OPERATOR SEMI-STABLE DISTRIBUTIONS

  • Choi, Gyeong-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.135-152
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    • 2000
  • For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

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Characterization of some classes of distributions related to operator semi-stable distributions

  • Joo, Sang-Yeol;Choi, Gyeong-Suk
    • Proceedings of the Korean Statistical Society Conference
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    • pp.221-225
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    • 2002
  • For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on $R^{d}$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi- stability with exponent Q. Translation of strictly operator m-semi-stable distribution is discussed.

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A GENERALIZED ADDITIVE-QUARTIC FUNCTIONAL EQUATION AND ITS STABILITY

  • HENGKRAWIT, CHARINTHIP;THANYACHAROEN, ANURK
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1759-1776
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    • 2015
  • We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

STABILITY OF HAHN DIFFERENCE EQUATIONS IN BANACH ALGEBRAS

  • Abdelkhaliq, Marwa M.;Hamza, Alaa E.
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1141-1158
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    • 2018
  • Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

Consideration of Human Operators in Man-Machine Systems

  • Jin, Jae-Hyun;Ahn, Sung-Ho;Park, Byung-Suk;Yoon, Ji-Sup;Jung, Jae-Hoo
    • 제어로봇시스템학회:학술대회논문집
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    • pp.2471-2474
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    • 2003
  • This paper focuses on the stability and operability of a man-machine system considering a human operator. Some papers' main interest has been the stability only, but the operability such as fatigue is also the other main interest. In a man-machine system, feelings such as motional, visual, and kinesthetic are important since those enable operators to work easily or fatigue operators. A model of a man-machine system has been developed. Motional, visual, and kinesthetic feelings may be considered as feedbacked sensor signals. We also have quantified the degree of fatigue with respect to reference operation. This is a performance index to be optimized. Several methods are presented to optimize the degree of fatigue and the stability of the integrated system. Examples are presented to show that the usefulness of the proposed modeling method and fatigue mitigating algorithm.

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