Bill of Hayman Levy to K. K. S. I.

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Letter announcing election of Aaron Levy as trustee of K. K. S. I.

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Letters to Aaron Levy from Isaac M. Gomez

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Request of Simeon Levy to K. K. S. I. for matzoth

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Letter from Moses Levy regarding New York congregation's agreement to pay half cost for return of Reverend H. H. Samuel Cohen

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Letter of Simeon Levy regarding school

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Order to pay Aaron Levy, regarding K. K. Mikve Israel

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Letter from Isaac Seixas to Hayman Levy on proposed marriage of Benjamin Seixas to Zipporah Levy

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Newspaper clipping regarding presentation of flag by Mrs. Commodore Levy

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Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Clustering using Levy Flight Cuckoo Search

In this paper, a comparative study is carried using three nature-inspired algorithms namely Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Cuckoo Search (CS) on clustering problem. Cuckoo search is used with levy flight. The heavy-tail property of levy flight is exploited here. These algorithms are used on three standard benchmark datasets and one real-time multi-spectral satellite dataset. The results are tabulated and analysed using various techniques. Finally we conclude that under the given set of parameters, cuckoo search works efficiently for majority of the dataset and levy flight plays an important role.

Unusual eigenvalue spectrum and relaxation in the Levy-Ornstein-Uhlenbeck process

We consider the rates of relaxation of a particle in a harmonic well, subject to Levy noise characterized by its Levy index mu. Using the propagator for this Levy-Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form (n + m mu)nu where nu is the force constant characterizing the well, and n, m is an element of N. If mu is irrational, the eigenvalues are all nondegenerate, but rational mu can lead to degeneracy. The maximum degeneracy is shown to be 2. The left eigenfunctions of the fractional Fokker-Planck operator are very simple while the right eigenfunctions may be obtained from the lowest eigenfunction by a combination of two different step-up operators. Further, we find that the acceptable eigenfunctions should have the asymptotic behavior vertical bar x vertical bar(-n1-n2 mu) as vertical bar x vertical bar -> infinity, with n(1) and n(2) being positive integers, though this condition alone is not enough to identify them uniquely. We also assert that the rates of relaxation of LOUP are determined by the eigenvalues of the associated fractional Fokker-Planck operator and do not depend on the initial state if the moments of the initial distribution are all finite. If the initial distribution has fat tails, for which the higher moments diverge, one can have nonspectral relaxation, as pointed out by Toenjes et al. Phys. Rev. Lett. 110, 150602 (2013)].

[Discurso do Deputado Herbert Levy : Sessão da Câmara dos Deputados de 28 de agosto de 1957]

Discussão do Projeto nº 1.773-A, de 1956, que fixa a data para a mudança da Capital Federal. Apoio à mudança da Capital Federal em virtude de considerar não ter o Rio de Janeiro a austeridade necessária ao funcionamento de uma capital administrativa. Expectativa de que, em Brasília, os deputados tenham condições ambientais e materiais para o melhor exercício do mandato. Relatório do presidente da Companhia Urbanizadora da Nova Capital, Israel Pinheiro, sobre a exequibilidade da mudança da capital no prazo estipulado.

[Discurso do Deputado Herbert Levy : Sessão da Câmara dos Deputados de 02 de maio de 1960]

Discurso proferido durante a 1ª Sessão da Câmara dos Deputados na nova capital do país. Alteração da Bandeira Nacional por decreto do Presidente da República sem audiência do Congresso Nacional.