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Point Spectra (point + spectrum)
Selected AbstractsOn the spectra of some integral operators related to the potential theory in the planeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2010Oleg F. Gerus Abstract We study point spectra of the two integral operators that are generated by the boundary values of the simple-layer potential and of the integral tightly related to the double-layer potential; the operators act on the Hölder space Hµ(,), µ,(0,1), and on the Lebesgue space Lp(,), p>2, where , is a closed Lyapunov curve. Copyright © 2010 John Wiley & Sons, Ltd. [source] Combined Fourier transform infrared and Raman spectroscopic approach for identification of multidrug resistance phenotype in cancer cell linesBIOPOLYMERS, Issue 5 2006C. Murali Krishna Abstract Cancer cells escape cytotoxic effects of anticancer drugs by a process known as multidrug resistance (MDR). Identification of cell status by less time-consuming methods can be extremely useful in patient management and treatment. This study aims at evaluating the potentials of vibrational spectroscopic methods to perform cell typing and to differentiate between sensitive and resistant human cancer cell lines, in particular those that exhibit the MDR phenotype. Micro-Raman and Fourier transform infrared (FTIR) spectra have been acquired from the sensitive promyelocytic HL60 leukemia cell line and two of its subclones resistant to doxorubicin (HL60/DOX) and daunorubicin (HL60/DNR), and from the sensitive MCF7 breast cancer cell line and its MDR counterpart resistant to verapamil (MCF7/VP). Principal components analysis (PCA) was employed for spectral comparison and classification. Our data show that cell typing was feasible with both methods, giving two distinct clusters for HL60- and MCF7-sensitive cells. In addition, phenotyping of HL60 cells, i.e., discriminating between the sensitive and MDR phenotypes, was attempted by both methods. FTIR could not only delineate between the sensitive and resistant HL60 cells, but also gave two distinct clusters for the resistant cells, which required a two-step procedure with Raman spectra. In the case of MCF7 cell lines, both the sensitive and resistant phenotypes could be differentiated very efficiently by PCA analysis of their FTIR and Raman point spectra. These results indicate the prospective applicability of FTIR and micro-Raman approaches in the differentiation of cell types as well as characterization of the cell status, such as the MDR phenotype exhibited in resistant leukemia cell lines like HL60 and MCF7. © 2006 Wiley Periodicals, Inc. Biopolymers 82: 462,470, 2006 This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com [source] On some subsets of Schechter's essential spectrum of a matrix operator and application to transport operatorMATHEMATISCHE NACHRICHTEN, Issue 9 2010Naouel Ben Ali Abstract This paper is devoted to the investigation of the essential approximate point spectrum and the essential defect spectrum of a 2 × 2 block operator matrix on a product of Banach spaces. The obtained results are applied to a two-group transport operators with general boundary conditions in the Banach space Lp ([,a, a ] × [,1, 1]) × Lp ([,a, a ] × [,1, 1]), a > 0, p , 1 (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On the point spectrum of ,,2 -singular perturbationsMATHEMATISCHE NACHRICHTEN, Issue 1-2 2007Sergio Albeverio Abstract We prove that for any self-adjoint operator A in a separable Hilbert space , and a given countable set , = {,i}i ,, of real numbers, there exist ,,2 -singular perturbations à of A such that , , ,p(Ã). In particular, if , = {,1,,, ,n} is finite, then the operator à solving the eigenvalues problem, Ã,k = ,k,k, k = 1,,, n, is uniquely defined by a given set of orthonormal vectors {,k}nk =1 satisfying the condition span {,k}nk =1 , dom (|A |1/2) = {0}. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||