325 research outputs found

    On a problem of Ishmukhametov

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    Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question. © 2013 Springer-Verlag Berlin Heidelberg

    Plasmon confinement in fractal quantum systems

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    Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum scale.Comment: 5 pages, 4 figures, comments are welcom

    O desenvolvimento de um algoritmo eficiente em busca de números pseudo-primos fortes

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    The problem of searching for strictly pseudoprime numbers is relevant in the field of number theory, and it also has a number of applications in cryptography: in particular, with the help of numbers in this class one can strengthen the efficiency of the Miller-Rabin simplicity test by transforming it from probabilistic into deterministic. At the present time, several algorithms for constructing sequences of such numbers are known, but they have a rather high complexity, which makes it impossible to obtain strictly pseudoprime numbers of large magnitude in an acceptable time. The theme of this paper is the construction of strictly pseudoprime numbers of the special form n = pq = (u + 1) (2u + 1), where p, q are prime numbers, u is a natural number. Numbers of this kind are present in the sequence Ψk, used to estimate the number of iterations in the Miller-Rabin simplicity test. We denote by Fk the smallest odd composite number of the above-mentioned type, which successfully passes the Miller-Rabin test with k first prime numbers. The paper proposes a new algorithm for constructing Fk numbers, gives data on its speed and efficiency on the memory used, and specifies the features of the software implementation.El problema de la búsqueda de números estrictamente pseudoprimos es relevante en el campo de la teoría de números, y también tiene varias aplicaciones en criptografía: en particular, con la ayuda de números en esta clase se puede fortalecer la eficiencia de la simplicidad de Miller-Rabin Prueba transformándolo de probabilístico en determinístico. En la actualidad, se conocen varios algoritmos para construir secuencias de tales números, pero tienen una complejidad bastante alta, lo que hace imposible obtener números estrictamente pseudoprimos de gran magnitud en un tiempo aceptable. El tema de este artículo es la construcción de números estrictamente pseudoprime de la forma especial n = pq = (u + 1) (2u + 1), donde p, q son números primos, u es un número natural. Los números de este tipo están presentes en la secuencia Ψk, utilizada para estimar el número de iteraciones en la prueba de simplicidad de Miller-Rabin. Denotamos por Fk el número compuesto impar más pequeño del tipo mencionado anteriormente, que pasa con éxito la prueba de Miller-Rabin con k primeros números primos. El documento propone un nuevo algoritmo para construir números Fk, proporciona datos sobre su velocidad y eficiencia en la memoria utilizada y especifica las características de la implementación del software.O problema de encontrar números pseudoprimos é estritamente relevante no campo da teoria dos números, e também tem muitas aplicações em criptografia: em particular, com a ajuda de números nesta classe pode fortalecer a eficiência da simplicidade de Miller Teste de Rabin transformando-o de probabilístico para determinístico. Atualmente, vários algoritmos são conhecidos por construir seqüências de tais números, mas eles têm uma complexidade bastante alta, o que torna impossível obter números estritamente pseudoprimo de grande magnitude em um tempo aceitável. O assunto deste artigo é a construção de números estritamente pseudoprimo forma especial com n = pq = (L + 1) (2u + 1) em que p, q são números primos, u é um número natural. Números desse tipo estão presentes na seqüência Ψk, usada para estimar o número de iterações no teste de simplicidade de Miller-Rabin. Denotamos por Fk o menor número composto ímpar do tipo mencionado acima, que passa com sucesso no teste de Miller-Rabin com k primeiros números primos. O documento propõe um novo algoritmo para a construção de números Fk, fornece dados sobre sua velocidade e eficiência na memória utilizada e especifica as características da implementação do software

    Investigating the Rotary Mechanism of ATP Synthase Using Molecular Dynamics Simulations

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    F1-ATPase is a motor protein that can use ATP hydrolysis to drive rotation of the central subunit. The γ C-terminal helix constitutes of the rotor tip that is seated in an apical bearing formed by the α3β3 head. It remains uncertain to what extent the γ conformation during rotation differs from that seen in rigid crystal structures. Existing models assume that the entire γ subunit participates in every rotation. Here we develop a molecular dynamics (MD) strategy to model the off-axis forces acting on γ in F1-ATPase. MD runs showed stalling of the rotor tip and unfolding of the γ C-terminal helix. MD-predicted H-bond opening events coincided with experimental HDX patterns obtained in our laboratory. HDX-MS data suggests that in vitro operation of F1-ATPase is associated with significant rotational resistance in the apical bearing. These conditions cause the γ C-terminal helix to get “stuck” while the remainder of γ continues to rotate. This scenario contrasts the traditional “greasy bearing” model that envisions smooth rotation of the γ C-terminal helix. Our work also demonstrates that MD simulations can provide insights into protein dynamic features that are invisible in static X-ray crystal structures

    Implementing a lightweight Schmidt-Samoa cryptosystem (SSC) for sensory communications

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    One of the remarkable issues that face wireless sensor networks (WSNs) nowadays is security. WSNs should provide a way to transfer data securely particularly when employed for mission-critical purposes. In this paper, we propose an enhanced architecture and implementation for 128-bit Schmidt-Samoa cryptosystem (SSC) to secure the data communication for wireless sensor networks (WSN) against external attacks. The proposed SSC cryptosystem has been efficiently implemented and verified using FPGA modules by exploiting the maximum allowable parallelism of the SSC internal operations. To verify the proposed SSC implementation, we have synthesized our VHDL coding using Quartus II CAD tool targeting the Altera Cyclone IV FPGA EP4CGX22CF19C7 device. Hence, the synthesizer results reveal that the proposed cryptographic FPGA processor recorded an attractive result in terms of critical path delay, hardware utilization, maximum operational frequency FPGA thermal power dissipation for low-power applications such as the wireless sensor networks

    Computably enumerable Turing degrees and the meet property

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    Working in the Turing degree structure, we show that those degrees which contain computably enumerable sets all satisfy the meet property, i.e. if a is c.e. and b < a, then there exists non-zero m < a with b ^m = 0. In fact, more than this is true: m may always be chosen to be a minimal degree. This settles a conjecture of Cooper and Epstein from the 80s
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