• Title/Summary/Keyword: compact perturbation

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A FIFTH ORDER NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.689-706
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    • 2008
  • In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

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GENERALIZED BROWDER, WEYL SPECTRA AND THE POLAROID PROPERTY UNDER COMPACT PERTURBATIONS

  • Duggal, Bhaggy P.;Kim, In Hyoun
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.281-302
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    • 2017
  • For a Banach space operator $A{\in}B(\mathcal{X})$, let ${\sigma}(A)$, ${\sigma}_a(A)$, ${\sigma}_w(A)$ and ${\sigma}_{aw}(A)$ denote, respectively, its spectrum, approximate point spectrum, Weyl spectrum and approximate Weyl spectrum. The operator A is polaroid (resp., left polaroid), if the points $iso{\sigma}(A)$ (resp., $iso{\sigma}_a(A)$) are poles (resp., left poles) of the resolvent of A. Perturbation by compact operators preserves neither SVEP, the single-valued extension property, nor the polaroid or left polaroid properties. Given an $A{\in}B(\mathcal{X})$, we prove that a sufficient condition for: (i) A+K to have SVEP on the complement of ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) for every compact operator $K{\in}B(\mathcal{X})$ is that ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) has no holes; (ii) A + K to be polaroid (resp., left polaroid) for every compact operator $K{\in}B(\mathcal{X})$ is that iso${\sigma}_w(A)$ = ∅ (resp., $iso{\sigma}_{aw}(A)$ = ∅). It is seen that these conditions are also necessary in the case in which the Banach space $\mathcal{X}$ is a Hilbert space.

Mass perturbation influence method for dynamic analysis of offshore structures

  • Cho, Kyu Nam
    • Structural Engineering and Mechanics
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    • v.13 no.4
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    • pp.429-436
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    • 2002
  • The current work presents an analysis algorithm for the modal analysis for the dynamic behaviors of offshore structures with concepts of mass perturbation influence term. The mass perturbation concept by using the term, presented in this paper offers an efficient solution procedure for dynamical response problems of offshore structures. The basis of the proposed method is the mass perturbation influence concepts associated with natural frequencies and mode shapes and mass properties of the given structure. The mathematical formulation of the mass perturbation influence method is described. New solution procedures for dynamics analysis are developed, followed by illustrative example problems, which deal with the effectiveness of the new solution procedures for the dynamic analysis of offshore structures. The solution procedures presented herein is compact and computationally simple.

LQG design under plant perturbation and uncertain noise covariance (패러미터와 잡음전력이 불확실한 시스템에 대한 LQG 제어기 설계)

  • 오원근;서병설
    • 제어로봇시스템학회:학술대회논문집
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    • 1991.10a
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    • pp.203-207
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    • 1991
  • In this paper, a linear stocastic dynamic system with norm - bounded plant perpurbations and norm - bounded noise covariarice is studied. Instead of Bellman-Gronwall inequality used in previous study, Lyapunov stability theorem is used to derive stability condition. The new condition is of more compact form than the previous result.

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A FIFTH ORDER NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH NEGATIVE SHIFT

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.441-452
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    • 2009
  • In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

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OPERATORS SIMILAR TO NORMALOID OPERATORS

  • Zhu, Sen;Li, Chun Guang
    • Journal of the Korean Mathematical Society
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    • v.48 no.6
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    • pp.1203-1223
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    • 2011
  • In this paper, the authors investigate the structure of operators similar to normaloid and transloid operators. In particular, we characterize the interior of the set of operators similar to normaloid (transloid, respectively) operators. This gives a concise spectral condition to determine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact perturbation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.

PERTURBATION OF NONHARMONIC FOURIER SERIES AND NONUNIFORM SAMPLING THEOREM

  • Park, Hee-Chul;Shin, Chang-Eon
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.351-358
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    • 2007
  • For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

A Reconfigurable Circularly Polarized Microstrip Antenna on a Cross-Shape Slotted Ground (십자형 접지면 슬롯을 이용한 재구성 가능한 원형 편파 마이크로스트립 안테나)

  • Yoon, Won-Sang;Han, Sang-Min;Lee, Dong-Hyo;Lee, Kyoung-Joo;Pyo, Seong-Min;Kim, Young-Sik
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.21 no.1
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    • pp.46-52
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    • 2010
  • A compact circular microstrip patch antenna with a switchable circular polarization(CP) is proposed at 2.4 GHz. An unequal cross-shaped slot on a ground plane is utilized as a perturbation. By switching pin diodes mounted on the slot, the CP sense of each antenna can be simply switched from left-handed(LH) CP to right-handed(RH) CP vice versa. Since the perturbation can be made on the ground plane and no bias circuit is required on the patch side, the bias circuit has not effect on the main beam radiation. From the experimental results, the impedance bandwidth and CP bandwidth of the proposed antenna have shown up to 150 MHz and 35 MHz, respectively. The peak gain of the proposed antenna is 1.7 dBi for both CP senses.

ON p-HYPONORMAL OPERATORS ON A HILBERT SPACE

  • Cha, Hyung-Koo
    • The Pure and Applied Mathematics
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    • v.5 no.2
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    • pp.109-114
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    • 1998
  • Let H be a separable complex H be a space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is said to be p-hyponormal if ($T^{\ast}T)^p - (TT^{\ast})^{p}\geq$ 0 for 0 < p < 1. If p = 1, T is hyponormal and if p = $\frac{1}{2}$, T is semi-hyponormal. In this paper, by using a technique introduced by S. K. Berberian, we show that the approximate point spectrum $\sigma_{\alpha p}(T) of a pure p-hyponormal operator T is empty, and obtains the compact perturbation of T.

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