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Статті в журналах з теми "E-eigenvalues"
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Grinevich, Petr, and Roman Novikov. "TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS." Eurasian Journal of Mathematical and Computer Applications 9, no. 4 (December 2021): 17–25. http://dx.doi.org/10.32523/2306-6172-2021-9-4-17-25.
Повний текст джерелаАнотація:
We study the transmission eigenvalues for the multipoint scatterers of the Bethe- Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.
2
Ahmad, Sk, and Rafikul Alam. "On Wilkinson's problem for matrix pencils." Electronic Journal of Linear Algebra 30 (February 8, 2015): 632–48. http://dx.doi.org/10.13001/1081-3810.3145.
Повний текст джерелаАнотація:
Suppose that an n-by-n regular matrix pencil A -\lambda B has n distinct eigenvalues. Then determining a defective pencil Eâ\lambda F which is nearest to Aâ\lambda B is widely known as Wilkinsonâs problem. It is shown that the pencil E â\lambda F can be constructed from eigenvalues and eigenvectors of A â\lambda B when A â \lambda B is unitarily equivalent to a diagonal pencil. Further, in such a case, it is proved that the distance from A â\lambda B to E â \lambdaF is the minimum âgapâ between the eigenvalues of A â \lambdaB. As a consequence, lower and upper bounds for the âWilkinson distanceâ d(L) from a regular pencil L(\lambda) with distinct eigenvalues to the nearest non-diagonalizable pencil are derived.Furthermore, it is shown that d(L) is almost inversely proportional to the condition number of the most ill-conditioned eigenvalue of L(\lambda).
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VAIDYA, SAMIR K., and KALPESH POPAT. "On Equienergetic, Hyperenergetic and Hypoenergetic Graphs." Kragujevac Journal of Mathematics 44, no. 4 (December 2020): 523–32. http://dx.doi.org/10.46793/kgjmat2004.523v.
Повний текст джерелаАнотація:
The eigenvalue of a graph G is the eigenvalue of its adjacency matrix and the energy E(G) is the sum of absolute values of eigenvalues of graph G. Two non-isomorphic graphs G1 and G2 of the same order are said to be equienergetic if E(G1) = E(G2). The graphs whose energy is greater than that of complete graph are called hyperenergetic and the graphs whose energy is less than that of its order are called hypoenergetic graphs. The natural question arises: Are there any pairs of equienergetic graphs which are also hyperenergetic (hypoenergetic)? We have found an affirmative answer of this question and contribute some new results.
4
G, Sridhara, and Rajesh Kanna. "Bounds on Energy and Laplacian Energy of Graphs." Journal of the Indonesian Mathematical Society 23, no. 2 (December 24, 2017): 21–31. http://dx.doi.org/10.22342/jims.23.2.316.21-31.
Повний текст джерелаАнотація:
Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and another in terms of largest absolute eigenvalue and the smallest absoluteeigenvalue. The paper also contains upper bounds for Laplacian energy of graph.
5
Hall, Richard L. "A simple eigenvalue formula for the quartic anharmonic oscillator." Canadian Journal of Physics 63, no. 3 (March 1, 1985): 311–13. http://dx.doi.org/10.1139/p85-048.
Повний текст джерелаАнотація:
The eigenvalues Enl(λ) of the Hamiltonian H = −Δ + r2 + λr4 are analysed with the help of "potential envelopes" and "kinetic potentials." The result is the following simple approximate eigenvalue formiula:[Formula: see text]where E ≥ P = (4n + 2l − 1) and Q = 3(An + Bl − C)4/322/3. E is a lower bound to Enl if (A, B, C) = (1, 1/2, 1/4) and a good approximation if (A, B, C) = (1.125, 0.509, 0.218).
6
Korek, M., and K. Fakhreddine. "A canonical approach for computing the eigenvalues of the Schrödinger equation for double-well potentials." Canadian Journal of Physics 78, no. 11 (November 1, 2000): 969–76. http://dx.doi.org/10.1139/p00-072.
Повний текст джерелаАнотація:
The problem of obtaining the eigenvalues of the Schrödinger equation for a double-well potential function is considered. By replacing the differential Schrödinger equation by a Volterra integral equation the wave function will be given by [Formula: see text] where the coefficients ai are obtained from the boundary conditions and the fi are two well-defined canonical functions. Using these canonical functions, we define an eigenvalue function F(E) = 0; its roots E1, E2, ... are the eigenvalues of the corresponding double-well potential. The numerical application to analytical potentials (either symmetric or asymmetric) and to a numerical potential of the (2)1 [Formula: see text] state of the molecule Na2 shows the validity and the high accuracy of the present formulation. PACS No.: 03.65Ge
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Tan, Shenyang, Tiren Huang, and Wenbin Zhang. "Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds." Advances in Mathematical Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/387953.
Повний текст джерелаАнотація:
We investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds(M,g,e-ϕdv). We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere.
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Kobeissi, Hafez, Majida Kobeissi, and Chafia H. Trad. "On nonintegral E corrections in perturbation theory: application to the perturbed Morse oscillator." Canadian Journal of Physics 72, no. 1-2 (January 1, 1994): 80–85. http://dx.doi.org/10.1139/p94-013.
Повний текст джерелаАнотація:
A new formulation of the Rayleigh–Schrödinger perturbation theory is applied to the derivation of the vibrational eigenvalues of the perturbed Morse oscillator (PMO). This formulation avoids the conventional projection of the Ψ corrections on the basis of unperturbed eigenfunctions [Formula: see text], or the projection of the nonhomogeneous Schrödinger equations on [Formula: see text], it gives simple expressions for each E correction [Formula: see text] free of summations and integrals. When the PMO is characterized by the potential U = UM + UP (where UM is the unperturbed Morse potential), the eigenvalue of a vibrational level ν is given by: [Formula: see text]. According to the new formulation the correction £, [Formula: see text] is given by [Formula: see text], where σp(r) is a particular solution of the nonhomogeneous differential equation y″ + f y = sp; here [Formula: see text], sp is well known for each p: for p = 0, [Formula: see text]; for [Formula: see text]. For the numerical application one single routine is used, that of integrating y″ + f y = s, where the coefficients are known as well as the initial values. An example is presented for the Huffaker PMO of the (carbon monoxide) CO-X1Σ+ state. The vibrational eigenvalues Eν are obtained to a good accuracy (with p = 4) even for high levels. This result confirms the validity of this new formulation and gives a semianalytic expression for the PMO eigenvalues.
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Abolarinwa, Abimbola. "Eigenvalues of the weighted Laplacian under the extended Ricci flow." Advances in Geometry 19, no. 1 (January 28, 2019): 131–43. http://dx.doi.org/10.1515/advgeom-2018-0022.
Повний текст джерелаАнотація:
Abstract Let ∆φ = ∆ − ∇φ∇ be a symmetric diffusion operator with an invariant weighted volume measure dμ = e−φ dν on an n-dimensional compact Riemannian manifold (M, g), where g = g(t) solves the extended Ricci flow. We study the evolution and monotonicity of the first nonzero eigenvalue of ∆φ and we obtain several monotone quantities along the extended Ricci flow and its volume preserving version under some technical assumption. We also show that the eigenvalues diverge in a finite time for n ≥ 3. Our results are natural extensions of some known results for Laplace–Beltrami operators under various geometric flows.
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Loginov, B., O. Makeeva, and E. Foliadova. "Pseudoperturbation method for computation of E. Schmidt eigenvalues." PAMM 6, no. 1 (December 2006): 643–44. http://dx.doi.org/10.1002/pamm.200610302.
Повний текст джерелаДисертації з теми "E-eigenvalues"
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Dalmas, Sergio. "Obtenção de autovalores de soluções em série de problemas de condução de calor com condições de contorno convectivas." Universidade Estadual de Campinas, 2015. http://repositorio.utfpr.edu.br/jspui/handle/1/2162.
Повний текст джерелаАнотація:
Excluídos problemas simples de condução de calor nos quais a temperatura depende apenas do tempo ou apenas de uma coordenada de posição, os demais levam a equações diferenciais parciais, as quais tem soluções em termos de séries obtidas de vários métodos como a separação de variáveis, a superposição, a função de Green, a técnica da transformada integral, a transformada de Laplace e o teorema de Duhamel. Estas soluções dependem de autovalores que são obtidos das raízes de equações transcendentais que na maioria dos casos não podem ser expressas em forma fechada, mas podem ser obtidas de tabelas, expressões aproximadas, e expressões iterativas. O objetivo desse estudo é encontrar novas expressões para estas raízes, que sejam mais simples ou que tenham mais exatidão do que as já existentes. As três equações transcendentais que são consideradas aqui são as mais frequentemente utilizadas entre as que não tem solução fechada, e surgem quando as condições de contorno são convectivas. Uma nova família de funções iterativas é obtida, a qual inclui várias funções clássicas e, em particular, toda a família de métodos de Householder. Um novo método obtido é o que tem convergência mais rápida para as presentes equações. Apesar das tabelas de raízes apresentarem valores com vários dígitos significativos, problemas reais dificilmente levam a um valor da variável independente que pode ser diretamente encontrado, tornando-se necessário o uso de interpolação. Então, a exatidão de raízes obtidas por estas tabelas é limitada pela exatidão da interpolação, a qual pode ser comparada com a das expressões aproximadas. As expressões existentes são analisadas utilizando propriedades das raízes. Uma expressão aproximada desenvolvida para a primeira raiz das três equações é baseada no método do ponto fixo, outra é obtida da aplicação do conceito de MiniMax para se reajustar expressões de outros autores, e uma final tem forma algébrica. O conceito de MiniMax não é obtido através de algum método que possa ser considerado elementar, e dois novos métodos são desenvolvidos para aplicá-lo. Modernos sistemas algébricos computacionais são utilizados para gerar novas expressões aproximadas para a primeira raiz, mas encontrou-se que elas podem ser melhoradas através de métodos analíticos. Expansão em frações contínuas e novamente a aproximação de Padé são utilizadas para se obter expressões de grande exatidão. Expressões que levam a bons resultados para a primeira raiz são generalizadas para que elas sirvam para as demais raízes. Finalmente, uma comparação é feita considerando todas expressões aproximadas, indicando quais são consideradas as melhores.Apart from simple problems of heat conduction in which the temperature depends only on the time or just on a position coordinate, the others lead to partial differential equations, which have solutions in terms of series obtained from various methods such as separation variables, superposition, the Green's function, the technique of integral transform, the Laplace transform and Duhamel's theorem. These solutions depend on eigenvalues, which are obtained from the roots of transcendental equations that in most cases cannot be expressed in closed form, but they can be obtained from tables, approximate expressions and iterative expressions. The objective of this study is to find new expressions for these roots, which are simpler or have more accuracy than the existing ones. The three transcendental equations that are considered here are the most frequently used among those that have not closed solution, and appear when the boundary conditions are convective. A new family of iterative functions is proposed, which includes several classical functions and, in particular, the entire family of Householder methods. A new method is obtained which has faster convergence to the present equations. Although the tables of roots present values with various significant digits, real problems hardly lead to a value of the independent variable that can be directly found, making it necessary to use interpolation. Then, the accuracy of the roots obtained from these tables is limited by the accuracy of the interpolation, which can be compared with the approximate expressions. Existing expressions are analyzed using the root properties. An approximate expression developed for the first root of the three equations is based on the fixed point method, another is obtained from the application of the concept of MiniMax to readjust expressions of others authors, and the last one has an algebraic form. The MiniMax concept is not obtained through any method that can be considered elementary, and two new methods are developed to apply it. Modern computer algebra systems are used to generate new approximate expressions for the first root, but it is found that they can be improved by analytical methods. Expansion in continuous fractions is adopted and the Padé approximation to obtain expressions of greater accuracy. Expressions leading to good results for the first root are generalized so that they serve for the other roots. Finally, a comparison is made considering all approximate expressions, indicating what are considered the best.
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Silva, Kaye Oliveira da. "Existência e multiplicidade de soluções de problemas de autovalor não lineares elípticos." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/8637.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we study two problems in partial differential equations. The first one is a nonlinear eigenvalue problem given by: ( div( (jruj)ru) = f(x; u) em , u = 0 em @ , where the nonlinearity f is oscilatory. By using Orlicz-Sobolev spaces and techniques of minimization, degree theory, lower and upper solutions and regularization of solutions, we show that for each sufficiently big, there is a family of solutions, which is finite when f oscillates a finite number of times (with respect to the second variable) and it is infinite when f oscillates infinitely many times. On the second problem, we use the shooting method, to show that the problem: ( (r (ju0(r)j)u0(r))0 = r f(u(r)); 0 < r < R; u(R) = u0(0) = 0; has for each sufficiently small, a family fukg1k =1 of solutions, where for each positive integer k, uk has exactly k roots in the interval (0;R).
Neste trabalho estudamos dois problemas de equações diferenciais parciais. O primeiro é um problema não linear de autovalores da forma: ( div( (jruj)ru) = f(x; u) em , u = 0 em @ , cuja não linearidade f é oscilatória. Utilizando os espaços de Orlicz-Sobolev e técnicas de minimização, teoria do grau, sub e super soluções e regularização de soluções, mostramos que para cada suficientemente grande, existe uma família de soluções, que é finita no caso de f oscilar um número finito de vezes (com relação a segunda variável) e infinita no caso de f oscilar um número infinito de vezes. No segundo problema, usamos o método de shooting, para mostrar que o problema ( (r (ju0(r)j)u0(r))0 = r f(u(r)); 0 < r < R; u(R) = u0(0) = 0; possui para cada > 0 suficientemente pequeno, uma família fukg1k =1 de soluções, onde para cada k inteiro positivo, uk tem exatamente k raízes no intervalo (0;R).
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Provenzano, Luigi. "On mass distribution and concentration phenomena for linear elliptic partial differential operators." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424499.
Повний текст джерелаАнотація:
In this thesis we study the dependence of the eigenvalues of elliptic partial differential operators upon mass density perturbations on open subsets of the N-dimensional euclidean space. We prove continuity and analyticity results for the eigenvalues of poly-harmonic operators and apply them
to certain optimization problems. In order to prove analyticity, we use a general technique of P.D. Lamberti and M. Lanza de Cristoforis, and we obtain formulas for the Frechet differentials of the eigenvalues which are used to characterize critical mass densities under the constraint that the total mass is preserved. Then we state a sort of `maximum principle' in spectral optimization problems for elliptic operators subject to mass density perturbations.
Moreover, we consider a special class of densities, namely densities which concentrate near the boundary of open subsets of the N-dimensional euclidean space. We study the asymptotic behavior of the eigenvalues of Neumann-type problems for the Laplace and the biharmonic operator. By
adapting a general technique of J.M. Arrieta, we prove that the Neumann eigenvalues converge to the appropriate limiting Steklov eigenvalues. In this way, we formulate a genuine Steklov eigenvalue problem for the biharmonic
operator. In the case of the Laplace operator we prove the validity of an asymptotic expansion of the Neumann eigenvalues and eigenfunctions and
provide formulas for the first terms in the expansions. We adapt to our case asymptotic analysis techniques used by M.E. Perez and S.A. Nazarov to describe vibrating systems with masses concentrated at points or along
curves. Moreover, we consider the problem of domain perturbations for the biharmonic Steklov problem obtained with this mass concentration procedure
and prove that balls are critical domains for all the eigenvalues. Then we adapt the arguments of F. Brock and R. Weinstock to prove that the ball is actually a maximizer for the rst positive eigenvalue among bounded
domains of given measure. Moreover, we provide a quantitative version of such an isoperimetric inequality, showing also that it is sharp.In questa tesi studiamo la dipendenza degli autovalori di operatori differenziali alle derivate parziali di tipo ellittico da perturbazioni della densità di massa su aperti dello spazio euclideo N-dimensionale. In particolare, proviamo risultati di dipendenza continua e analitica degli autovalori di operatori poliarmonici e li applichiamo ad alcuni problemi di ottimizzazione. Per provare i risultati di analiticità, adoperiamo una tecnica generale sviluppata da P.D. Lamberti e M. Lanza de Cristoforis, ottenendo formule per i differenziali di Frechet degli autovalori che ci permettono di caratterizzare le densità critiche sotto il vincolo di massa fissata. Inoltre, enunciamo un `principio di massimo' per la classe di problemi di ottimizzazione considerata. In seguito, prendiamo in esame una famiglia particolare di densità di massa, ovvero densità che si concentrano al bordo degli aperti dove i problemi differenziali sono definiti. In questo caso, studiamo il comportamento asintotico degli autovalori e delle autofunzioni dei problemi di Neumann per l'operatore di Laplace e l'operatore biarmonico quando la massa si concentra al bordo. Proviamo in entrambi i casi, adattando una tecnica generale sviluppata da J.M. Arrieta, che gli autovalori e le autofunzioni del problema di Neumann convergono agli autovalori e alle autofunzioni di appropriati problemi limite di tipo Steklov. In particolare, il problema di tipo Steklov per l'operatore biarmonico così formulato viene introdotto per la prima volta in questa tesi, dove ne vengono poi studiate alcune proprietà. Nel caso dell'operatore di Laplace, proviamo la validità di un'espansione asintotica degli autovalori e delle autofunzioni del problema di Neumann fino al primo ordine ed otteniamo formule esplicite per i primi termini delle espansioni. Per ottenere questi risultati adattiamo al nostro problema delle tecniche di analisi asintotica utilizzate da M.E. Perez e S.A. Nazarov per lo studio di sistemi vibranti con masse concentrate in punti o lungo certe curve. Per quanto riguarda il problema di Steklov per l'operatore biarmonico, consideriamo anche il problema della dipendenza degli autovalori dal dominio. Utilizzando sempre la tecnica generale sviluppata da P.D. Lamberti e M. Lanza de Cristoforis, proviamo che le palle sono domini critici per tutti gli autovalori. Inoltre, adattando l'argomento di F. Brock e R.Weinstock per il problema di Steklov per l'operatore di Laplace, riusciamo a mostrare che la palla massimizza il primo autovalore positivo del problema di Steklov per l'operatore biarmonico tra tutti gli aperti limitati di misura fissata. Proviamo infine una versione quantitativa di questa disuguaglianza isoperimetrica, mostrando poi che l'esponente che compare nella disuguaglianza è ottimale.
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Venceslau, Sheyla Maurício Maia. "Modelagem matemática de sistemas vibratórios com aplicação de autovalores." Universidade Federal de Sergipe, 2015. https://ri.ufs.br/handle/riufs/6476.
Повний текст джерелаАнотація:
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESThe present work aims to contribute to the teaching and learning process of disciplines such as Linear Algebra and Differential Equations, suggesting a study methodology based on mathematical modeling of mechanical systems and application of eigenvalues of problem, as well as encourage high school students to explore mathematics, a revealing and essential science, showing that content such as complex numbers, determinants, trigonometry, etc., some of these mistakenly questioned about its practical utility, can be used for the benefit of people, for example, providing more security and stability to buildings , essential in modern times. Initially, the contents will be displayed formally required for the understanding of vibrating systems with two degrees of freedom to apply them subsequently in the determination of natural frequencies of vibration of a two storey building. Also, a demo will be made of how to calculate the eigenvalues through of computational tools, the softwares MATLAB and R. Using the softwares, the determination of natural frequencies becomes even more practical and thus shows that the application of the problem is quite simple and has obvious practical use.
O presente trabalho visa contribuir para o processo de ensino e aprendizagem de disciplinas como Álgebra Linear e Equações Diferenciais, sugerindo uma metodologia de ensino baseada na modelagem matemática de sistemas mecânicos e na aplicação do problema de autovalores, assim como, estimular alunos do ensino médio a explorar a matemática, uma ciência reveladora e essencial, mostrando que conteúdos como números complexos, determinantes, trigonometria, etc, alguns destes equivocadamente questionados quanto a utilidade prática, podem ser usados em benefício das pessoas, por exemplo, proporcionando mais segurança e estabilidade às edi cações, fundamentais nos tempos atuais. Inicialmente, serão apresentados formalmente os conteúdos necessários ao entendimento de sistemas vibratórios com dois graus de liberdade, para posteriormente aplicá-los na determinação das frequências naturais de vibração de um edi- fício de dois andares. Além disso, será feita uma demonstração de como calcular os autovalores através de ferramentas computacionais, os softwares MATLAB e R. Com o uso do software, a determinação das frequências naturais torna-se ainda mais prática e, portanto, mostrar que a aplicação do referido problema é bastante simples e tem utilidade prática evidente.
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Ramos, Marco Aurélio David. "Transformações lineares, autovalores e autovetores." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3505.
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In this thesis we study linear transformations, eigenvalues and eigenvectors with the objective of solve a system of linear ordinary differential equations with constant coefficients.
Nesta dissertação estudamos transformações lineares, autovalores e autovetores com o intuito de resolvermos um sistema de equações diferenciais ordinárias lineares com coeficientes constantes.
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Diniz, Emanuel Cardozo. "Termalização de qubits sujeitos à ação de reservatórios coletivos markovianos." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5068.
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Previous issue date: 2014-08-26Universidade Federal de Sao Carlos
We are interested in understanding the process of Markovian thermalization in quantum systems when we have one or two qubits interacting with a quantum electromagnetic field mode, using the Rabi model, in situations where there is interaction with a reservoir modeling the environment surrounding the system. This analysis of the thermalization is based on the calculation of the eigenvalues of the Liouvillian of the Markovian master equation. We will focus mainly on situations where there is interaction with independent and collective reservoirs, for cases where the subsystems interact with reservoirs at T=0K and T >0K. We investigate situations where there is no thermalization of the system and how this may influence interesting physical properties, such as the statistical properties of the field in the ultra strong scheme using the theory of input-output and quantum correlations between qubits collectively interacting with Markovian reservoirs.
Estamos interessados em entender o processo de termalização em sistemas quânticos markovianos, quando temos um ou dois qubits interagindo com um modo quântico do campo eletromagnético, utilizando o modelo de Rabi, em situações onde há interação com estruturas de reservatório que modelam o ambiente que cerca o sistema. Essa análise da termalização é baseada no cálculo dos autovalores do liouvilliano da equação mestra markoviana. Iremos focar principalmente nas situações onde há interação com reservatórios independentes e coletivos, para casos onde o subsistema interage com reservatórios a T=0K e T >0K. Investigamos situações onde há termalização ou não do sistema e como esse fator pode influenciar nas propriedades físicas interessantes, como, por exemplo, a estatística de detecção de fótons no regime ultra forte utilizando a teoria de entrada e saída e correlações quânticas entre os qubits interagindo com reservatórios markovianos.
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Tavares, Fabiano Pinto. "Deformações de cônicas e quádricas por operadores lineares." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306627.
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Orientadores: Sueli Irene Rodrigues Costa, Simão Nicolau StelmastchukDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho focalizamos a deformação de cônicas e quádricas por transformações lineares. Deduzimos de forma explícita os autovalores e autovetores ortonormais de matrizes reais 2 x 2 e 3 x 3, para os quais não há quase referências na literatura e nem incorporação nos programas computacionais de cálculo simbólico usuais. Esta determinação levou -nos a estudar um pouco da história da resolução das equações de terceiro grau e das condições e formulações das raízes reais destas. Os resultados foram utilizados na determinação explícita das deformações por transformações lineares de cônicas e quádricas, sendo estas discutidas em termos de características das matrizes associadas
Abstract: We discuss here the deformations of conics and quadrics under linear mappings. We set explicitly the eingenvalues and the orthonormal eigenvectors of real symmetric 2 X 2 and 3 X 3 matrices. These expressions are scarce in the literature and not incorporated in symbolic calculus software. The determination of those eigenvalues leaded us to the study of the solution of third degree equations and some of related historical aspects with focus on conditions and expressions for their real solutions Those results are used in the exact determination of the linear deformation of conics and quadrics in terms of the characteristics of their associated matrices
Mestrado
Geometria Topologia
Mestre em Matemática
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Félix, Heron Martins 1985. "Polinômios núcleo na reta real e no círculo unitário." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307064.
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Orientador: Alagacone Sri RangaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O objetivo do presente trabalho se divide em duas partes: na primeira, estudaremos uma regra de quadratura interpolatória sobre os zeros de polinômios núcleo obtidos a partir de uma sequência de polinômios L-ortogonais, oferecendo técnicas numéricas para a obtenção dos nós e pesos dessa regra de quadratura. Na segunda parte, forneceremos uma caracterização dos polinômios de Szegö em termos de duas sequências reais, dentre as quais uma é sequência encadeada. Tal caracterização afeta a relação entre os polinômios núcleo e os polinômios ortogonais no círculo unitário aos quais estes estão associados
Abstract: The main goal of the present work falls under two parts: firstly, we'll study a quadrature rule over the zeros of the kernel polynomials obtained from a sequence of L-orthogonal polynomials, offering numerical techniques for evaluating the nodes and weights of such quadrature rule. Secondly, we'll give a characterization for Szegö polynomials in terms of two real sequences, in which one is a chained sequence. Such characterization influences the connection between the kernel polynomials and the related orthogonal polynomials over the unit circle
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Brito, Filho Joaquim Gomes. "CONTROLE ROBUSTO LQG/LTR COM RECUPERAÇÃO DO GANHO DA MALHA DE TRANSFERÊNCIA." Universidade Federal do Maranhão, 2006. http://tedebc.ufma.br:8080/jspui/handle/tede/392.
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Previous issue date: 2006-05-31In this work is presented a method to solve the Eigenstructure Allocation pro- blem for multivariable dynamic systems by means of Robust Controllers Design Linear Quadratic Gaussian, LQG/LTR Loop transfer Recovery and Hierarchical Genetic Algorithm in three levels. It shows an uni¯ed method for controllers ro- bust design that are one systematical of the three stages of LQG/LTR methodo- logy. The evolutionary computation is used in the primary level that is the gain controller optimal determination to guarantee the terms of robust stability. The intermediary level, consists in the utilization of a AG to determine the Kalman state observer gain. The last level of this hierarchy consists of recovery the ro- bustness properties of the LQR design which were lost due to inclusion of the LQG loop by means of a GA. The method is veri¯ed in a dynamic system which represents an aircraft in cruzeiro speed, a LQG/LQR-hierarchic design perfor- mance analysis in the frequency domain and of time show the commitments that should be taken over in applications of the real world systems.
Apresenta-se um método para resolver o problema de Alocação de Auto-estrutura para sistemas dinâmicos multivariáveis por meio do Projeto de Controladores Ro- busto Gaussiano Linear Quadrático, Recuperação da Malha de Transferência e Algoritmo Genético Hierárquico em três níveis. Mostra-se um método unificado para o projeto de controladores robustos que são uma sistematização das três etapas da metodologia LQG/LTR. A computação evolutiva é utilizada no nível primário que é a determinação dos ganhos do controlador ótimo para garantir as condições de estabilidade robusta. O nível intermediário, consiste na utilização de um AG para determinar os ganhos de Kalman do observador de estado. O último nível desta hierarquia consiste da recuperação das propriedades de ro- bustez do projeto LQR que foram perdidas devido a inclusão da malha LQG por meio de um AG. O método é verficado em um sistema dinâmico que re- presenta uma aeronave em velocidade cruzeiro, uma análise de desempenho do projeto LQG/LQR-hierárquico no domínio da frequência e do tempo mostram os compromissos que devem ser assumidos em aplicações de sistemas do mundo real.
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Chaves, Francisco Pereira. "Tempo mÃdio de saÃda e desigualdades isoperimÃtricas para subvariedades mÃnimas de N x R." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5723.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorFundaÃÃo de Amparo à Pesquisa do Estado do CearÃ
Estabelece desigualdades isoperimÃtricas e estimativas do tempo mÃdio de saÃda para subvariedades mÃnimas de N x R, onde N Ã uma variedade riemanniana completa com curvatura seccional nÃo-positiva. Prova desigualdades isoperimÃtricas para subvariedades com segunda forma fundamental dominada em espaÃos de Hadamard com curvatura seccional limitada.
It establishes isoperimetric inequalities and exit mean time estimates for minimal submanifolds of N x R, where N is a complete Riemannian manifold with sectional curvature non-positive. It proves isoperimetric inequalities for submanifolds with tamed second fundamental form in Hadamard spaces with bounded sectional curvature.
Книги з теми "E-eigenvalues"
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Acta Numerica 1998. Cambridge University Press, 1999.
Знайти повний текст джерелаЧастини книг з теми "E-eigenvalues"
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Székely, Gábor J., and Maria L. Rizzo. "Eigenvalues for One-Sample E-Statistics." In The Energy of Data and Distance Correlation, 99–120. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9780429157158-7.
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Dittmar, Bodo. "[109] (with J. Hersch and L. E. Payne) Some inequalities for Stekloff eigenvalues." In Menahem Max Schiffer: Selected Papers Volume 2, 345–63. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7949-9_16.
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Braak, Daniel. "What Kind of Insight Provide Analytical Solutions of Quantum Models?" In International Symposium on Mathematics, Quantum Theory, and Cryptography, 5–6. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_2.
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Abstract There are several concepts of what constitutes the analytical solution of a quantum model, as opposed to the mere “numerically exact” one. This applies even if one considers only the determination of the discrete spectrum of the corresponding Hamiltonian, setting aside such important questions as the asymptotic dynamics for long times. In the simplest case, the spectrum can be given in closed form, the eigenvalues $$E_{j}, j=0,\ldots ,N\le \infty $$ read $$E_{j} =f(j,\{p_{k}\})$$, where f is a known function of the label $$j\in \mathbb {N}_{0}$$ and the $$\{p_k\}$$ are a set of numbers parameterizing the Hamilton operator. This kind of solution exists only in cases where the classical limit of the model is Liouville-integrable. Some quantum-mechanical many-body systems allow the determination of the spectrum in terms of auxiliary parameters $$[\{k_j\},\{n_l\}]$$ as $$E(\{n_l\}) = f(\{k_{j}(\{n_{l}\})\})$$ where the $$\{k_{j}(\{n_{l}\})\}$$ satisfy a coupled set of transcendental equations, following from a certain ansatz for the eigenfunctions. These systems (integrable in the sense of Yang-Baxter (Eckle 2019)) may have a Hilbert space dimension growing exponentially with the system size L, i.e., $$N\sim e^{L}$$. The simple enumeration of the energies with the label j is replaced by the multi-index $$\{n_{l}\}$$. Although no priori knowledge about the spectrum is available, its statistical properties can be computed exactly (Berry and Tabor 1977). Other integrable and also non-integrable models exist where N depends polynomially on L and the energies $$E_j$$ are the zeroes of an analytically computable transcendental function, the so-called G-function $$G(E,\{p_k\})$$ (Braak 2013a, 2016), which is proportional to the spectral determinant. Although no closed formula for $$E_j$$ as function of the index j exists, detailed qualitative insight into the distribution of the eigenvalues can be obtained (Braak 2013b). Possible applications of these concepts to information compression and cryptography are outlined.
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Schiffer, Menahem. "Fredholm Eigenvalues and Conformal Mapping." In Autovalori e autosoluzioni, 203–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10994-2_6.
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Payne, L. E. "Isoperimetric Inequalities for Eigenvalues and Their Applications." In Autovalori e autosoluzioni, 107–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10994-2_3.
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Agmon, Shmuel. "On Eigenvalues Eigenfunctions and Resolvents of General Elliptic Problems." In Autovalori e autosoluzioni, 1–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10994-2_1.
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"Appendix E: Eigenvalues and the SVD." In Noise and Vibration Analysis, 417–19. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9780470978160.app5.
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Vinogradova, Elena D. "Resonance scattering of E-polarized plane waves by two-dimensional arbitrary open cavities: spectrum of complex eigenvalues." In Advances in Mathematical Methods for Electromagnetics, 329–58. Institution of Engineering and Technology, 2020. http://dx.doi.org/10.1049/sbew528e_ch14.
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Dyall, Kenneth G., and Knut Faegri. "Negative-Energy States and Quantum Electrodynamics." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0010.
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We now return to the problem of the negative-energy solutions that appeared when we solved the free particle Dirac equation in the previous chapter. The energy eigenvalues obtained there were either E+ = +√(m2c4 + p2c2) or E− = − √(m2c4 + p2c2) . The minimum absolute values we can have are therefore |E| = mc2 for p = 0 (that is, the particle at rest). As the momentum of the particle increases, we generate a continuum of solutions, either below − mc2 or above + mc2. This is a general feature of all solutions we will obtain from the Dirac equation—we will have continuum solutions on both sides of an energy gap stretching from − mc2 to + mc2, in addition to any discrete solutions. Classically and nonrelativistically we would expect a free particle to have a positive energy. The addition of a rest mass term mc2, which is definitely also positive, should not change this. However, the fact that we now have negative-energy states means that a single particle in a positive-energy state could spontaneously fall to a negative energy state with the emission of a photon. The interaction with the radiation field occurs via the operator α • A. The radiative transition moment therefore connects the large component of the positive-energy solution with the small component of the negative-energy solution. As we have seen, both of these should be large in magnitude, giving a large transition moment. Calculations (Bjorken and Drell 1964) show that the transition rate into the highest mc2 section of the negative continuum is approximately 108 s−1, and the rate of decay into the whole continuum is infinite. Any bound state would therefore immediately dissolve into the negative continuum with the emission of photons. This is clearly an unphysical situation. To resolve this dilemma, Dirac postulated in 1930 that the negative-energy states are fully occupied. The implications of this postulate are significant and wide-ranging.
Тези доповідей конференцій з теми "E-eigenvalues"
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Asghari, Mohsen, and Reza Naghdabadi. "Unified Basis-Free Relation Between Two Stress Tensors Conjugate to Arbitrary Hill’s Strain Measures." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93687.
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The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: E˙ provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T(g), respectively conjugate to two measures of Hill’s strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of distinct and repeated eigenvalues of the right stretch tensor U.
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Naghdabadi, Reza, Mohsen Asghari, and Kamyar Ghavam. "Compact Basis Free Relations for Stress Tensors Conjugate to Hill’s Strain Measures." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95367.
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If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T : E˙, produces the stress power then these stress and strain tensors are called a conjugate pair. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear continuum mechanics analysis such as modeling of constitutive equations of elastic-plastic materials. In this paper relations for stress tensors conjugate to an arbitrary Lagrangean strain measure of Hill’s class are obtained. The results of this paper are more compact and simpler in compare with those available in the literature. The results are valid for the three dimensional Euclidean inner product space and the case of distinct eigenvalues of the right stretch tensor U.
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Luk, Franklin T. "Architectures for Computing Eigenvalues and SVDs." In O-E/LASE'86 Symp (January 1986, Los Angeles), edited by Keith Bromley. SPIE, 1986. http://dx.doi.org/10.1117/12.960496.
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Locke, James, Ulyses Valencia, and Kosuke Ishikawa. "Design Studies for Twist-Coupled Wind Turbine Blades." In ASME 2003 Wind Energy Symposium. ASMEDC, 2003. http://dx.doi.org/10.1115/wind2003-1043.
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This study presents results obtained for three designs of the Northern Power Systems (NPS) 9.2-meter version of the ERS-100 wind turbine rotor blade. The ERS-100 wind turbine rotor blade was designed and developed by TPI composites. The baseline design uses e-glass unidirectional fibers in combination with ±45-degree and random mat layers for the skin and spar cap. This project involves developing structural finite element models of the baseline design and carbon hybrid designs with twist-bend coupling. All designs were evaluated for a unit load condition and two extreme wind conditions. The unit load condition was used to evaluate the static deflection, twist and twist-coupling parameter. Maximum deflections and strains were determined for the extreme wind conditions. Buckling eigenvalues were determined for a tip load condition. The results indicate that carbon fibers can be used to produce twist-coupled designs with comparable deflections, strains and buckling loads.
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Alsing, P. M., Vassilios Kovanis, and D. A. Cardimona. "Collapse and revival dynamics in a driven Jaynes-Cummings system." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.wj4.
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A single atom coupled to a quantized mode of an electromagnetic cavity, driven by an external coherent field, is described by the Hamiltonian H djc = ig(a†σ− − aσ+) + iε(a† − a), where (a†, a) and (σ+, σ) are the raising and lowering operators for the cavity mode and atom, respectively. This is the single atom version of the Hamiltonian used in the study of optical bistability. It describes the evolution of the atom-cavity system on time scales much smaller than the inverse spontaneous emission and cavity decay rates. For 2ε/g < 1, HDJC possesses a discrete set of interaction eigenstates1 with eigenvalues E n ± = ± g n [ 1 − ( 2 ε / g ) 2 ] 3 / 4 . These form a renormalized version of the usual Jaynes-Cummings eigenstates2, which correctly take into account the effect of the driving field to all orders of magnitude. We investigate the collapse and revival nature of the dynamical evolution of the single atom in a cavity, with and without dissipation and above and below the threshold 2ε/g = 1 of the driven Jaynes-Cummings Hamiltonian.
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Azevedo, Douglas, and Valdir A. Menegatto. "Eigenvalues of dot-product kernels on the sphere." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0039.
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Porto, Guilherme, and Vilmar Trevisan. "Sum of the k Largest Signless Laplacian Eigenvalues." In CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2018. http://dx.doi.org/10.5540/03.2018.006.01.0437.
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Grosu, Corina, and Marta Grosu. "REAL COMPLEX TRAVEL." In eLSE 2016. Carol I National Defence University Publishing House, 2016. http://dx.doi.org/10.12753/2066-026x-16-074.
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One of the main challenges we are facing whenever teaching Mathematics to first year Politehnica University students is how to enable them to establish a connection between abstract notions and their recognition and concrete use in specialized engineering courses or even in post graduate job problems. Such a connection is needed because the multipurpose mathematical models encountered during the first university year are more often than not general notions. Nevertheless, problems with which students are usually confronted later in their work life relate to a well delimited approach in a specific engineering field. In order to serve this purpose, our present paper relies on two key elements. The first one is the visual association between abstract elements (in our case solutions of systems of differential equations) and certain representations in a real world problem (specifically, predefined trajectories of motion). The second, equally important element, is the form in which the above mentioned link is presented. Since the use of mobile technology in higher education offers a very attractive, interactive method, we have chosen to merge the mathematical e-learning dimension with a platform game developed for Android systems (phones and tablets). Consequently, the recognition of abstract notions is encompassed in the levels of the game. The mathematics behind the game deals with systems of first order linear differential equations, their associated matrix and the corresponding eigenvalues. Nevertheless, there is also a captivating story to support the game and engage the player. The main character, RC (RealComplex) has been teleported, by a mad dentist, from his cabinet, straight into the habitat of the Bengali tiger. In fact, the mad dentist had secretly transformed his dental chair into a space traveling machine. RC must travel across grasslands, subtropical rain forests, mangroves and eventually escape to an island where the space traveling machine can be transformed into an escape plane. While the game comprises four levels, two of which are mathematical levels, evolution from one level to the next is only allowed if the previous level has been completed. Thus, no one can avoid going through a mathematical revision before reaching the island and the end of the game. Moreover, a deeper understanding of the geometric representation of complex numbers is also part of the game. In fact, trajectories corresponding to complex eigenvalues are solutions to be avoided by the player since this type of directions, if chosen, disable the character's freedom to move in the game world.
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Piantella, Ana C., Mario H. de Castro, and V. A. Menegatto. "Schatten p-classes and asymptotics for eigenvalues of positive integral operators on the sphere." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0030.
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Schneider, Vitor M., James A. West, and Karl W. Koch. "An E-field Eigenvalue Method for Computing Waveguides and Photonic Band-Gap Properties." In Integrated Photonics and Nanophotonics Research and Applications. Washington, D.C.: OSA, 2007. http://dx.doi.org/10.1364/ipnra.2007.imb4.
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