Relevant bibliographies by topics / Spectral shift function

Academic literature on the topic 'Spectral shift function'

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Published: 4 June 2021
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Journal articles on the topic "Spectral shift function"

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Azamov, N. A., A. L. Carey, and F. A. Sukochev. "The Spectral Shift Function and Spectral Flow." Communications in Mathematical Physics 276, no. 1 (August 28, 2007): 51–91. http://dx.doi.org/10.1007/s00220-007-0329-9.

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Azamov, N. A., A. L. Carey, P. G. Dodds, and F. A. Sukochev. "Operator Integrals, Spectral Shift, and Spectral Flow." Canadian Journal of Mathematics 61, no. 2 (April 1, 2009): 241–63. http://dx.doi.org/10.4153/cjm-2009-012-0.

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Abstract. We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fréchet differentiation of operator functions that sharpen existing results, and establish the Birman–Solomyak representation of the spectral shift function of M.G. Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow.
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Birman, M. Sh, and A. B. Pushnitski. "Spectral shift function, amazing and multifaceted." Integral Equations and Operator Theory 30, no. 2 (June 1998): 191–99. http://dx.doi.org/10.1007/bf01238218.

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Potapov, Denis, Anna Skripka, and Fedor Sukochev. "Spectral shift function of higher order." Inventiones mathematicae 193, no. 3 (November 17, 2012): 501–38. http://dx.doi.org/10.1007/s00222-012-0431-2.

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GEISLER, R., V. KOSTRYKIN, and R. SCHRADER. "CONCAVITY PROPERTIES OF KREIN’S SPECTRAL SHIFT FUNCTION." Reviews in Mathematical Physics 07, no. 02 (February 1995): 161–81. http://dx.doi.org/10.1142/s0129055x95000098.

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We prove that the integrated Krein’s spectral shift function for one particle Schrödinger operators in R3 is concave with respect to the perturbation potential. The proof is given by showing that the spectral shift function is the limit in the distributional sense of the difference of the counting functions for the given Hamiltonian and the free Hamiltonian in a finite domain Λ with Dirichlet boundary conditions when Λ→∞.
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Man Lo, Pok. "Phase shift and spectral function from PWA." EPJ Web of Conferences 199 (2019): 05024. http://dx.doi.org/10.1051/epjconf/201919905024.

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I illustrate a robust method for extracting an effective phase shift and an effective spectral weight for a coupled-channel system. These quantities are useful for describing the thermodynamics of an interacting hadron gas within the S-matrix formulation.
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Bruneau, Vincent, and Mouez Dimassi. "Weak asymptotics of the spectral shift function." Mathematische Nachrichten 280, no. 11 (August 2007): 1230–43. http://dx.doi.org/10.1002/mana.200410549.

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Albeverio, Sergio, Konstantin A. Makarov, and Alexander K. Motovilov. "Graph Subspaces and the Spectral Shift Function." Canadian Journal of Mathematics 55, no. 3 (June 1, 2003): 449–503. http://dx.doi.org/10.4153/cjm-2003-020-7.

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AbstractWe obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.
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Petkov, Vesselin, and Vincent Bruneau. "Meromorphic continuation of the spectral shift function." Duke Mathematical Journal 116, no. 3 (March 2003): 389–430. http://dx.doi.org/10.1215/s0012-7094-03-11631-2.

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Rzeszotnik, Ziemowit, and Marcin Bownik. "The spectral function of shift-invariant spaces." Michigan Mathematical Journal 51, no. 2 (April 2003): 387–414. http://dx.doi.org/10.1307/mmj/1060013204.

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Dissertations / Theses on the topic "Spectral shift function"

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Azamov, Nurulla, and azam0001@infoeng flinders edu au. "Spectral shift function in von Neumann algebras." Flinders University. Informatics and Engineering, 2008. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20080129.121422.

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The main subsect of this thesis is the theory of Lifshits-Krein spectral shift function in semifinite von Neumann algebras and its connection with the theory of spectral flow. Main results are an analogue of the Krein trace formula for semifinite von Neumann algebras, the semifinite analogue of the Birman-Solomyak spectral averaging formula, a connection between the spectral shift function and the spectral flow and a Lidskii type formula for Dixmier traces. In particular, it is established that in the case of operators with compact resolvent, the spectral shift function and the spectral flow are identical notions.
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fr, vbruneau@math u.-bordeaux. "Meromorphic Continuation of the Spectral Shift Function." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1073.ps.

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at, Andreas Cap@esi ac. "Smoothness and High Energy Asymptotics of the Spectral Shift Function in Many--Body Scattering." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1048.ps.

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Assal, Marouane. "Analyse spectrale des systèmes d'opérateurs h-pseudodifférentiels." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0586/document.

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Dans ce travail, nous nous intéressons à l’analyse spectrale des systèmes d’opérateurs pseudodifférentiels semi-classiques. Dans la première partie, nous étudions la généralisation du théorème d’Egorov en temps longs dans le cas où l’Hamiltonien quantique qui génère l’évolution en temps et l’observable quantique initiale sont deux opérateurs pseudodifférentiels semiclassiques associés à des symboles à valeurs matricielles. Sous une condition d’hyperbolicité sur le symbole principal de l’Hamiltonien qui assure l’existence des projecteurs semi-classiques, et pour une classe d’observables "semi-classiquement" diagonales par blocs par rapport à ces projecteurs, nous démontrons un théorème de type Egorov valable pour un temps long d’ordre log(h-1) connu comme le temps d’Ehrenfest. Ici h 0 est le paramètre semi-classique. Dans la deuxième partie, nous nous intéressons à la théorie spectrale et la théorie de la diffusion pour des systèmes d’opérateurs pseudodifférentiels auto-adjoints. Nous développons une approche stationnaire pour l’étude de la fonction de décalage spectral associée à une paire d’opérateurs de Schrödinger semi-classiques à potentiels matriciels. Une asymptotique de type Weyl avec reste optimal sur la fonction de décalage spectral est établie, et sous l’hypothèse d’existence d’une fonction fuite scalaire, un développement asymptotique complet en puissancesde h au sens fort sur sa dérivée est obtenu. Ce dernier résultat est une généralisation au cas matriciel d’un résultat de Robert et Tamura établi dans le cas scalaire près des énergies non-captives. Notre méthode indépendante du temps nous permet de traiter certains potentiels avec des croisements des valeurs propres
In this work, we are interested in the spectral analysis of systems of semiclassical pseudodifferentialoperators. In the first part, we study the extension of the long time semiclassical Egorovtheorem in the case where the quantum Hamiltonian which generates the time evolution andthe initial quantum observable are two semiclassical pseudodifferential operators with matrixvaluedsymbols. Under an hyperbolicity condition on the principal symbol of the Hamiltonianwhich ensures the existence of the semiclassical projections, and for a class of observable thatare "semi-classically" block-diagonal with respect to these projections, we prove an Egorov theoremvalid in a large time interval of order log(h-1) known as the Ehrenfest time. Here h & 0is the semiclassical parameter.In the second part, we are interested in the spectral and scattering theories for self-adjointsystems of pseudodifferential operators. We develop a stationary approach for the study of thespectral shift function (SSF) associated to a pair of self-adjoint semiclassical Schrödinger operatorswith matrix-valued potentials. We prove a Weyl-type asymptotics with sharp remainderestimate on the SSF, and under the existence of a scalar escape function, a pointwise completeasymptotic expansion on its derivative. This last result is a generalisation in the matrix-valuedcase of a result of Robert and Tamura established in the scalar case near non-trapping energies.Our time-independent method allows us to treat certain potentials with energy-level crossings
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AL, SALEH-MAHROUSSEH SALOUA. "Calcul relativiste, en electrodynamique quantique, de la diffusion compton sur un electron lie." Clermont-Ferrand 2, 1988. http://www.theses.fr/1988CLF21098.

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Pour expliquer le deplacement et l'elargissement du pic compton,lorsque l'energie du photon est voisine de l'energie de liaison de l'electron, il est necessaire d'introduire non seulement la liaison et le mouvement de l'electron, mais aussi le recul du mnoyau. On donne un calcul relativiste de la valeur quadratique moyenne de l'impulsion de l'electron et une expression generale des fonctions d'onde radiales. Pour le calcul analytique covariant de l'element de matrice ou utilise un propagateur pour un electron lie dans le schema de furry et determine la secton efficace, sans aucune integration
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Khochman, Abdallah. "Résonances et diffusion pour les opérateurs de Dirac et de Schrödinger magnétique." Thesis, Bordeaux 1, 2008. http://www.theses.fr/2008BOR13689/document.

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Le sujet de cette thèse est l’étude de certaines équations de physique mathématique. Dans un premier temps, on étudie les résonances et la fonction de décalage spectral pour les opérateurs de Dirac semi-classique et de Schrödinger magnétique en dimension 3. On dé?nit les résonances comme des valeurs propres d’un opérateur non-autoadjoint obtenu par distortion complexe. Pour l’opérateur de Dirac, on majore le nombre de résonances par O(h-3) où h ? 0 est le paramètre semi-classique. Dans le cas de Schrödinger magnétique, l’opérateur de référence génère des valeurs propres de multipli- cité in?nie plongées dans le spectre continu. Dans une couronne centrée en une de ces valeurs propres et de rayons (r, 2r), on établit une borne supérieure, quand r ? 0, du nombre de résonances. Une approximation de type Breit-Wigner de la dérivée de la fonction de décalage spectral en fonction des résonances et une formule de trace locale sont obtenues pour ces deux opérateurs. De plus, on prouve une formule asymptotique de Weyl pour la fonction de décalage spectral pour l’opérateur de Dirac avec un potentiel électro-magnétique. Dans un deuxième temps, on s’intéresse à l’opérateur de Dirac semi-classique en dimension 1 avec un potentiel ayant des limites constantes mais pas nécessairement les mêmes à ±8. En utilisant la méthode BKW complexe, on construit des solutions analytiques de l’opérateur de Dirac. On étudie la théorie de la di?usion en fonction des solutions entrantes et sortantes. On obtient une asymptotique semi-classique de la matrice de di?usion dans di?érents cas, notamment dans le cas où le paradoxe de Klein apparaît. Le calcul des valeurs propres et des résonances est aussi traité pour l’opérateur de Dirac semi-classique unidimensionnel
In this thesis, we consider equations of mathematical physics. First, we study the reso- nances and the spectral shift function for the semi-classical Dirac operator and the magnetic Schrö- dinger operator in three dimensions. We de?ne the resonances as the eigenvalues of a non-selfadjoint operator obtained by complex distortion. For the Dirac operator, we establish an upper bound O(h-3), as the semi-classical parameter h tends to 0, for the number of resonances. In the Schrödinger magne- tic case, the reference operator has in?nitely many eigenvalues of in?nite multiplicity embedded in its continuous spectrum. In a ring centered at one of this eigenvalues with radiuses (r, 2r), we establish an upper bound, as r tends to 0, of the number of the resonances. A Breit-Wigner approximation formula for the derivative of the spectral shift function related to the resonances and a local trace formula are obtained for the considered operators. Moreover, we prove a Weyl-type asymptotic of the SSF for the Dirac operator with an electro-magnetic potential. Secondly, we consider the semi-classical Dirac ope- rator on R with potential having constant limits, not necessarily the same at ±8. Using the complex WKB method, we construct analytic solutions for the Dirac operator. We study the scattering theory in terms of incoming and outgoing solutions. We obtain an asymptotic expansion, with respect to the semi-classical parameter h, of the scattering matrix in di?erent cases, in particular, in the case when the Klein paradox occurs. Quantization conditions for the resonances and for the eigenvalues of the one-dimensional Dirac operator are also obtained
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Allam, Lévi. "Etude de la diffusion unidimensionnelle dans les chaines finies : application au tmmc-cd." Toulouse 3, 1987. http://www.theses.fr/1987TOU30063.

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Etude rpe de (ch::(3))::(4) nmn::(1-x) cd::(x) cl::(5) entre 20 et 300 k, pour x = 0,02; 0,08 et 0,2; mesure des temps de relaxation spin-reseau. Mise en evidence de variations importantes en fonction de la composition. Interpretation des resultats au moyen du formalisme de la fonction memoire et d'un modele de la fonction de correlation de spins des chaines finies
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Marten, Tobias. "Ab-initio study of disorder broadening of core photoemission spectra in random metallic alloys." Thesis, Linköping University, The Department of Physics, Chemistry and Biology, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2580.

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Ab-initio results of the core-level shift and the distribution about the average for the 3d5/2 electrons of Ag, Pd and 2p3/2 of Cu are presented for the face-centered-cubic AgPd and CuPd random alloys. The complete screening model, which includes both initial and final states effects in the same scheme, has been used in the investigations.

The alloys have been modeled with a supercell containing 256 atoms. Density-functional theory calculations are carried out using the locally self consistent Green's function approach.

Results from the calculations clearly shows that the core-level shift distributions characteristic is Gaussian, but the components reveals a substantial difference in the FWHM (Full-Width at Half-Maximum). Comparison between the experimental and the calculated broadening shows a remarkable agreement.

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Durbeej, Bo. "Quantum Chemical Studies of Protein-Bound Chromophores, UV-Light Induced DNA Damages, and Lignin Formation." Doctoral thesis, Uppsala University, Quantum Chemistry, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4531.

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Quantum chemical methods have been used to provide a better understanding of the photochemistry of astaxanthin and phytochromobilin; the photoenzymic repair of UV-light induced DNA damages; and the formation of lignin.

The carotenoid astaxanthin (AXT) is responsible for the colouration of lobster shell. In solution, the electronic absorption spectra of AXT peak in the 470-490 nm region, corresponding to an orange-red colouration. Upon binding to the lobster-shell protein-complex α-crustacyanin, the absorption maximum is shifted to 632 nm, yielding a slate-blue colouration. Herein, the structural origin of this bathochromic shift is investigated on the basis of recent experimental work.

The tetrapyrrole phytochromobilin (PΦB) underlies the photoactivation of the plant photoreceptor phytochrome. Upon absorption of 660-nm light, PΦB isomerizes from a C15-Z,syn configuration (in the inactive form of the protein) to C15-E,anti (in the active form). In this work, a reaction mechanism for this isomerization is proposed.

DNA photolyases are enzymes that repair DNA damages resulting from far-UV-light induced [2+2] cycloaddition reactions involving pyrimidine nucleobases. The catalytic activity of these enzymes is initiated by near-UV and visible light, and is governed by electron transfer processes between a catalytic cofactor of the enzyme and the DNA lesions. Herein, an explanation for the experimental observation that the repair of cyclobutane pyrimidine dimers (CPD) – the major type of lesion – proceeds by electron transfer from the enzyme to the dimer is presented. Furthermore, the formation of CPD is studied.

Lignin is formed by dehydrogenative polymerization of hydroxycinnamyl alcohols. A detailed understanding of the polymerization mechanism and the factors controlling the outcome of the polymerization is, however, largely missing. Quantum chemical calculations on the initial dimerization step have been performed in order to gain some insight into these issues.

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Azamov, Nurulla Abdullaevich. "Spectral shift function in von Neumann algebras." 2008. http://catalogue.flinders.edu.au/local/adt/public/adt-SFU20080129.121422/index.html.

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Books on the topic "Spectral shift function"

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Treatise on the shift operator: Spectral function theory. Berlin: Springer-Verlag,c, 1986.

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Taylor, A. N. Non-linear cosmological power spectra in real and redshift space. [Washington, DC: National Aeronautics and Space Administration, 1996.

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Taylor, A. N. Non-linear cosmological power spectra in real and redshift space. [Washington, DC: National Aeronautics and Space Administration, 1996.

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Taylor, A. N. Non-linear cosmological power spectra in real and redshift space. [Washington, DC: National Aeronautics and Space Administration, 1996.

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Taylor, A. N. Non-linear cosmological power spectra in real and redshift space. [Washington, DC: National Aeronautics and Space Administration, 1996.

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Nikolskii, N. K. Treatise on the Shift Operator: Spectral Function Theory. Springer, 2011.

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Nikol'Skii, Nikolai Kapitonovich. Treatise on the Shift Operator: Spectral Function Theory (Grundlehren Der Mathematischen Wissenschaften). Springer, 1986.

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Treatise on the Shift Operator: Spectral Function Theory (Grundlehren der mathematischen Wissenschaften). Springer, 1986.

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Book chapters on the topic "Spectral shift function"

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Müller, Werner. "The spectral shift function." In Lecture Notes in Mathematics, 74–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077669.

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Yafaev, D. "The spectral shift function and trace formulas." In Mathematical Surveys and Monographs, 341–68. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/surv/158/12.

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Raikov, Georgi. "Spectral Shift Function for Magnetic Schrödinger Operators." In Mathematical Physics of Quantum Mechanics, 451–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/3-540-34273-7_32.

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Bollé, D. "Krein’s Spectral Shift Function and Supersymmetric Quantum Mechanics." In Recent Developments in Mathematical Physics, 201–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-73104-4_12.

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Carey, Alan, Fritz Gesztesy, Galina Levitina, and Fedor Sukochev. "The Spectral Shift Function and the Witten Index." In Operator Theory: Advances and Applications, 71–105. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29992-1_5.

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Behrndt, Jussi, Fritz Gesztesy, and Shu Nakamura. "A spectral shift function for Schröodinger operators with singular interactions." In The Diversity and Beauty of Applied Operator Theory, 89–110. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75996-8_4.

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Yavrian, V. A. "On M.G. Krein’s Spectral Shift Function for Canonical Systems of Differential Equations." In Differential Operators and Related Topics, 393–417. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8403-7_30.

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Langer, H., H. S. V. De Snoo, and V. A. Yavrian. "A relation for the spectral shift function of two self-adjoint extensions." In Recent Advances in Operator Theory and Related Topics, 437–45. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8374-0_24.

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Combes, Jean-Michel, Peter Hislop, and Frederic Klopp. "Some new estimates on the spectral shift function associated with random Schrödinger operators." In Probability and Mathematical Physics, 85–95. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/crmp/042/04.

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Nikol’skiĭ, Nikolaĭ K. "Compressions of the Shift and the Spectra of Inner Functions." In Grundlehren der mathematischen Wissenschaften, 62–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-70151-1_4.

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Conference papers on the topic "Spectral shift function"

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Arora, P., A. S. Kozlov, I. V. Il'ichev, A. V. Chamray, V. M. Petrov, J. Petter, and T. Tschudi. "Synthesis of the Transfer Function of a Spectral Bragg Filter using Electro-Optical Phase-Shift Keying." In CLEO 2007. IEEE, 2007. http://dx.doi.org/10.1109/cleo.2007.4452527.

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Ghanekar, Alok, Yi Zheng, Laura Lin, Zongqin Zhang, and Mingdi Sun. "Spectral Tuning of Radiative Heat Transfer Using Nanoparticles." In ASME 2016 Heat Transfer Summer Conference collocated with the ASME 2016 Fluids Engineering Division Summer Meeting and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/ht2016-7493.

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Microscopic thin films are known to have narrow band selective thermal radiation whch have potential applications in selective emitter and absorbers. We propose a methodology to shift the wavelength selectivity in the desired location. Calculation of emissivity and near field radiation for different materials and structures is presented. Emissivity calculations are performed using the standard expressions for Fresnel reflection coefficients. For the near field thermal radiation, we use the analytical expression for transitivity between two half spaces obtained using the dyadic Greens function formalism. We use Maxwell-Garnett-Mie theory to calculate effective dielectric function of media doped with nanoparticles. We observe that spectrum of thermal radiation in far-field and in near-field can be altered using nanoparticles. Moreover spectral properties of mixtures can be characterized using refractive indices. Influence of nanoparticle size and concentration is also studied.
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Miyazaki, Koji, Masahiro Kihara, and Hiroshi Tsukamoto. "Thermal Radiative Properties of Photonic Crystals." In ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems collocated with the ASME 2005 Heat Transfer Summer Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/ipack2005-73135.

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We investigate the spectral directional reflectivity of photonic crystals assembled with 2μm silica particles. The propagation of electromagnetic wave can be controlled by photonic crystals. Therefore photonic crystals are anticipated for advanced control of thermal radiation beyond solid state properties. Samples are prepared by Catalysts & Chemicals Industries Co., Ltd. The close-packed photonic crystals are fabricated on a Si wafer by using self-assembly of the colloidal particles under the specific condition. We measure reflectivities of the samples by using a FT-IR (Fourier Transform – Infrared Spectroscopy). The spectral reflectivity is enhanced at specific wavenumber. The peaks of spectral reflectivity shift to larger wavenumber as a function of an increased incident angle. The angular dependency of reflectivity can be roughly explained by using the modified Bragg’s equation taking into account Snell’s law. We show that the reflectivity in IR range is well enhanced by using a photonic crystal. This paper was also originally published as part of the Proceedings of the ASME 2005 Heat Transfer Summer Conference.
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Corti, Enrico, Giorgio Mancini, Claudio Forte, and Davide Moro. "Automatic Combustion Phase Calibration With Extremum Seeking Approach." In ASME 2013 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icef2013-19132.

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Combustion control is assuming a crucial role in reducing engine tailpipe emissions and maximizing performance. The number of actuations influencing the combustion is increasing, and, as a consequence, the calibration of control parameters is becoming challenging. One of the most effective factors influencing performance and efficiency is the combustion phasing: for gasoline engines control variables such as Spark Advance (SA), Air-to-Fuel Ratio (AFR), Variable Valve Timing (VVT), Exhaust Gas Recirculation (EGR) are mostly used to set the combustion phasing. The optimal control setting can be chosen according to a target function (cost or merit function), taking into account performance indicators, such as Indicated Mean Effective Pressure (IMEP), Brake Specific Fuel Consumption (BSFC), pollutant emissions, or other indexes inherent to reliability issues, such as exhaust gas temperature, or knock intensity. Many different approaches can be used to reach the best calibration settings: Design Of Experiment (DOE) is a common option when many parameters influence the results, but other methodologies are in use: some of them are based on the knowledge of the controlled system behavior, by means of models that are identified during the calibration process. The paper proposes the use of a different concept, based on the extremum seeking approach. The main idea consists in changing the values of each control parameter at the same time, identifying its effect on the monitored target function, allowing to shift automatically the control setting towards the optimum solution throughout the calibration procedure. An original technique for the recognition of control parameters variations effect on the target function is introduced, based on spectral analysis. The methodology has been applied to data referring to different engines and operating conditions, using IMEP, exhaust temperature and knock intensity for the definition of the target function, and using SA and AFR as control variables. The approach proved to be efficient in reaching the optimum control setting, showing that the optimal setting can be achieved rapidly and consistently.
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Lai, Kevin, Wei Xu, and Xin Sun. "An Inverse Algorithm for Resonance Inspection." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85485.

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Compared to other contemporarily used non-destructive evaluation (NDE) techniques, resonance inspection (RI), which employs the natural vibrational frequency spectra shift induced by the damage to detect defects, is advantageous in many aspects such as low cost, high testing speed, and broad applicability to complex structures. However, the inability to provide damage details, i.e. location, dimension, or types, of the flaws severely hinders its wide spread applications and further development despite its early success in the automobile industry for quality inspections of safety critical parts. In this study, an inverse RI algorithm using a maximum correlation function as the filtering function is proposed to quantify the location and size of flaws for a discrepant part. The algorithm and the numerical schemes are validated using a dog-bone shaped stainless steel sample, while the spectrum data for the original part and flawed parts were generated by a commercial FEM package. The results show that multiple flaws can be accurately identified using the proposed RI inversion method. The study further showed that the reliability of the inversion method is sensitive to the spectrum range included in the correlation function computation. It is demonstrated that the frequency range required to provide accurate predictions is inversely correlated to the defect size. Large defects can be detected using lower frequency spectrum data only, while smaller defects require a higher frequency range.
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6

Ikeda, Takashi, and Raouf A. Ibrahim. "Random Excitation of a Structure Interacting With Liquid Sloshing Dynamics." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32934.

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The nonlinear random interaction of an elastic structure with liquid sloshing dynamics in a cylindrical tank is investigated in the neighborhood of 1:2 internal resonance. Such internal resonance takes place when the natural frequency of the elastic structure is close to twice the natural frequency of the antisymmetric sloshing mode (1,1). The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. The analytical model involves three sloshing modes; (1,1), (0,1) and (2,1). The system response statistics and stability boundaries are numerically estimated using Monte Carlo simulation. The influence of the excitation center frequency, its bandwidth, and the liquid level on the system responses is studied. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. As the liquid depth decreases, the region of nonlinear interaction shrinks which is associated with a shift of the peak of the structure mean square response toward the left side of the frequency axis.
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Rathna Prasad, Sagi, and A. S. Sekhar. "Diagnostics of Fatigue Crack in the Shaft Using Spectral Kurtosis." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90373.

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Abstract Rotating machinery components like shafts subjected to continuous fluctuating loads are prone to fatigue cracks. Fatigue cracks are severe threat to the integrity of rotating machinery. Therefore it is indispensable for early diagnostics of fatigue cracks in shaft to avoid catastrophic failures. From the literature, it is evident that the spectral kurtosis (SK) and fast kurtogram were used to detect the faults in bearings and gears. The present study illustrates the use of SK and fast kurtogram for early fatigue crack detection in the shaft using vibration data. To perform this study, experiments are conducted on a rotor test rig which is designed and developed according to the function specification proposed by ASTM E468-11 standard. Fatigue crack is developed, on three shaft specimens, each seeded with the same circumferential V-Notch configuration, by continuous application of stochastic loads on the shaft using electrodynamic shaker in addition to the unbalance forces that arise in normal operating conditions. Vibration data is acquired from various locations of the rotor, using different sensors like miniature accelerometers, laser vibrometer and wireless telemetry strain gauge, till the shaft specimen develops fatigue crack. The analysis results show that the combination of SK and fast kurtogram is an effective signal processing technique for detecting the fatigue crack in the shaft.
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Toso, M., A. Baz, and D. Pines. "Active Vibration Control of Periodic Rotating Shafts." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61514.

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The propagation of transverse waves in periodic rotating shafts is controlled actively by using piezoelectric inserts which are placed periodically along these shafts. The control strategies aim at tuning the unique filtering characteristis of the periodic shafts in such manner that prevent the propagation of the waves within specific frequency bands called “stop bands.” The spectral characteristics of these “stop bands” are controlled in response to the shaft vibration. A finite element model is developed for this class of actively controlled periodic shafts which is then used to generate the “transfer matrix” for the unit cell of these shafts. The eigenvalues of the resulting transfer matrix are utilized to predict the characteristics of the stop and the pass bands of the rotating shaft as function of the shaft geometry, rotation speed, and control gains of the active inserts. The obtained characteristics are validated experimentally using shafts driven via gearbox assembly which subject the shafts to broadband excitations. The obtained results are also compared with the characteristics of passive shafts with stepped periodic geometries. Such a comparison aims at demonstrating the effectiveness of the active periodic shafts in redistributing the energy spectrum by confining the propagation to specific frequency bands. Particular emphasis is placed on studying the effect of the active control strategies on the vibration damping characteristics of the shafts. The proposed class of active periodic shafts can be useful in numerous critical applications such as the drive shafts of helicopters where transmitted vibrations can have detrimental effect on the performance of the tail rotor. Other applications are only limited by our imagination.
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9

Chen, Da Jun, and Wei Ji Wang. "Pattern Changes of Time-Shifted Vibration Signals on Wavelet Time-Scale Maps." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0381.

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Abstract As a multi-resolution signal decomposition and analysis technique, the wavelet transforms have been already introduced to vibration signal processing. In this paper, a comparison on the time-scale map analysis is made between the discrete and the continuous wavelet transform. The orthogonal wavelet transform decomposes the vibration signal onto a series of orthogonal wavelet functions and the number of wavelets on one wavelet level is different from those on the other levels. Since the grids are unevenly distributed on the time-scale map, it is shown that a representation pattern of a vibration component on the map may be significantly altered or even be broken down into pieces when the signal has a shift along the time axis. On contrary, there is no such uneven distribution of grids on the continuous wavelet time-scale map, so that the representation pattern of a vibration signal component will not change its shape when the signal component shifts along the time axis. Therefore, the patterns in the continuous wavelet time-scale map are more easily recognised by human visual inspection or computerised automatic diagnosis systems. Using a Gaussian enveloped oscillation wavelet, the wavelet transform is capable of retaining the frequency meaning used in the spectral analysis, while making the interpretation of patterns on the time-scale maps easier.
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10

Höss, B., D. Leinhos, and L. Fottner. "Stall Inception in the Compressor System of a Turbofan Engine." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-475.

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Compressor flow instabilities have been the subject of a great number of investigations during the past decade. While most of this research work was done on isolated test-rig compressors this paper presents stall inception measurements in the compressor system of a two-spool turbofan engine at various power settings. Several analysing techniques such as temporal low-pass and band-pass filtering, temporal and spatial Fourier transforms including power-spectral-density calculations of the spatial coefficients and a wavelet analysing technique are applied. For the low pressure compressor three different types of stall inception processes were observed depending on the rotor speed. At low-speed stall originates from spike-type precursors, while long wavy pressure fluctuations corresponding to modal waves were observed prior to stall at mid-speed for undistorted inlet flow. At high-speed the rotor shaft unbalancing dominates the stall inception process as an external forcing function. In the case of distorted inlet flow spike-type stall inception behavior dominates throughout the speed range. While filtering and the Fourier spectra give a good insight into the physical background of the stall inception process (but with a very short warning time), the wavelet transform indicates the approach of the stalling process a few hundred rotor revolutions in advance independendy of the type of precursor. Setting up a reliable stall avoidance control based on this analysis scheme seems to be promising.
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