• Title, Summary, Keyword: compact perturbations

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GENERALIZED WEYL'S THEOREM FOR FUNCTIONS OF OPERATORS AND COMPACT PERTURBATIONS

  • Zhou, Ting Ting;Li, Chun Guang;Zhu, Sen
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.899-910
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    • 2012
  • Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

Pathological Vibratory patterns of the Vocal Folds Observed by the High Speed Digital Imaging System

  • Niimi, Seiji
    • Proceedings of the KSLP Conference
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    • pp.208-209
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    • 1998
  • It is generally known that many cases of pathological rough voice are characterized not by simple random perturbations but by quasi-periodic perturbations in the speech wave. However, there are few studies on the characteristics of perturbations in vocal fold vibrations associated with this type of voice. We have been conducting studies of pathological vocal fold vibration using a high-speed digital image recording system developed by our institute, Compared to the ordinary high-speed-motion picture system, the present system is compact and simple to operate and thus, it suited for pathological data collection. (omitted)

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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.

SPECTRAL CONTINUITY OF ESSENTIALLY p-HYPONORMAL OPERATORS

  • Kim, An-Hyun;Kwon, Eun-Young
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.389-393
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    • 2006
  • In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.

ON SURJECTIVITY OF m-ACCRETIVE OPERATORS IN BANACH SPACES

  • Han, Song-Ho;Kim, Myeong-Hwan;Park, Jong An.
    • Bulletin of the Korean Mathematical Society
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    • v.26 no.2
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    • pp.203-209
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    • 1989
  • Recently many authors [2,3,5,6] proved the existence of zeros of accretive operators and estimated the range of m-accretive operators or compact perturbations of m-accretive operators more sharply. Their results could be obtained from differential equations in Banach spaces or iteration methods or Leray-Schauder degree theory. On the other hand Kirk and Schonberg [9] used the domain invariance theorem of Deimling [3] to prove some general minimum principles for continuous accretive operators. Kirk and Schonberg [10] also obtained the range of m-accretive operators (multi-valued and without any continuity assumption) and the implications of an equivalent boundary conditions. Their fundamental tool of proofs is based on a precise analysis of the orbit of resolvents of m-accretive operator at a specified point in its domain. In this paper we obtain a sufficient condition for m-accretive operators to have a zero. From this we derive Theorem 1 of Kirk and Schonberg [10] and some results of Morales [12, 13] and Torrejon[15]. And we further generalize Theorem 5 of Browder [1] by using Theorem 3 of Kirk and Schonberg [10].

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Swirl Flow Effects on Flame-Flame Interactions in a Model Lean-Premixed Gas Turbine Combustor (희박 예혼합 모델 가스터빈 연소기에서 스월유동 특성이 화염 간 상호작용에 미치는 영향)

  • Lee, Jiho;Park, Junhyeong;Han, Dongsik;Kim, Kyu Tea
    • Journal of the Korean Society of Combustion
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    • v.23 no.1
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    • pp.21-27
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    • 2018
  • The effect of swirl flow structures on combustion dynamics of two interacting, lean-premixed flames was experimentally investigated, with a particular emphasis on swirl numbers and swirl rotational directions. Our results show that the amplitude of limit cycle oscillations is very sensitive to the combination of swirl numbers and rotational directions, while the instability frequency remains nearly unchanged. The counter-rotating cases show significantly lower pressure perturbations, and this behavior appears to be related to the formation of compact interacting zone with higher heat release rate, indicating the presence of increased flame surface wrinkling caused by intense turbulence.

Role of Arbitrary Intensity Profile Laser Beam in Trapping of RBC for Phase-imaging

  • Kumar, Ranjeet;Srivastava, Vishal;Mehta, Dalip Singh;Shakher, Chandra
    • Journal of the Optical Society of Korea
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    • v.20 no.1
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    • pp.78-87
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    • 2016
  • Red blood cells (RBCs) are customarily adhered to a bio-functionalised substrate to make them stationary in interferometric phase-imaging modalities. This can make them susceptible to receive alterations in innate morphology due to their own weight. Optical tweezers (OTs) often driven by Gaussian profile of a laser beam is an alternative modality to overcome contact-induced perturbation but at the same time a steeply focused laser beam might cause photo-damage. In order to address both the photo-damage and substrate adherence induced perturbations, we were motivated to stabilize the RBC in OTs by utilizing a laser beam of ‘arbitrary intensity profile’ generated by a source having cavity imperfections per se. Thus the immobilized RBC was investigated for phase-imaging with sinusoidal interferograms generated by a compact and robust Michelson interferometer which was designed from a cubic beam splitter having one surface coated with reflective material and another adjacent coplanar surface aligned against a mirror. Reflected interferograms from bilayers membrane of a trapped RBC were recorded and analyzed. Our phase-imaging set-up is limited to work in reflection configuration only because of the availability of an upright microscope. Due to RBC’s membrane being poorly reflective for visible wavelengths, quantitative information in the signal is weak and therefore, the quality of experimental results is limited in comparison to results obtained in transmission mode by various holographic techniques reported elsewhere.