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Boolean functions are accepted to be cryptographically strong if they satisfy some common pre-determined criteria. It is expected that any design criteria should remain invariant under a large group of transformations due to the theory of similarity of secrecy systems proposed by Shannon. One of the most important design criteria for cryptographically strong Boolean functions is the nonlinearity criterion. Meier and Staffelbach studied nonlinearity preserving transformations, by considering the invertible transformations acting on the arguments of Boolean functions, namely the pre-transformations. In this thesis, first, the results obtained by Meier and Staffelbach are presented. Then, the invertible transformations acting on the truth tables of Boolean functions, namely the post-transformations, are studied in order to determine whether they keep the nonlinearity criterion invariant. The equivalent counterparts of Meier and Staffelbach&rsquo / s results are obtained in terms of the post-transformations. In addition, the existence of nonlinearity preserving post-transformations, which are not equivalent to pre-transformations, is proved. The necessary and sufficient conditions for an affine post-transformation to preserve nonlinearity are proposed and proved. Moreover, the sufficient conditions for an non-affine post-transformation to keep nonlinearity invariant are proposed. Furthermore, it is proved that the smart hill climbing method, which is introduced to improve nonlinearity of Boolean functions by Millan et. al., is equivalent to applying a post-transformation to a single Boolean function. Finally, the necessary and sufficient condition for an affine pre-transformation to preserve the strict avalanche criterion is proposed and proved.

International Telemetering Conference Proceedings / October 13-16, 1986 / Riviera Hotel, Las Vegas, Nevada / In most transmission channels, bandwidth is at a premium and an important attribute of any good digital signalling scheme is to optimally utilise the bandwidth for transmitting the information. The Data Compression System in this way plays a significant role in the transmission of picture data from any Remote Sensing Satellite by exploiting the statistical properties of the imagery. The data rate required for transmission to ground can be reduced by using suitable compression technique. A data compression algorithm has been developed for processing the images of Indian Remote Sensing Satellite. Sample LANDSAT imagery and also a reference photo are used for evaluating the performance of the system. The reconstructed images are obtained after compression for 1.5 bits per pixel and 2 bits per pixel as against the original of 7 bits per pixel. The technique used is uni-dimensional Hadamard Transform Technique. The Histograms are computed for various pictures which are used as samples. This paper describes the development of such a hardware and software system and also indicates how hardware can be adopted for a two dimensional Hadamard Transform Technique.

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Made available in DSpace on 2015-04-22T22:16:03Z (GMT). No. of bitstreams: 1 Edson Lopes de Souza.pdf: 437278 bytes, checksum: 4779bec085d95fd52b2a2756e302b47d (MD5) Previous issue date: 2007-11-19 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Consider an isometric immersion (phormula) of a compact, connected, orientable, n-dimensional (phormula), C1 Riemannian manifold Mn in a simply connected Riemannian manifold Nn+1 of constant sectional curvature. When Nn+1 is the Euclidean space Rn+1 and Mn has non-negative sectional curvatures, the following results, usually associated with the names of Hadamard and Conh-Vossen, are already known: (a) The image (phormula) is the boundary of a convex body of Rn+1, the map x is an embedding and Mn is diffeomorphic the unit sphere (phormula). (b) If (phormula) is another isometric immersion, fulfilling the hypotheses above, then exists an isometry (phormula) such that (phormula). The main goal of this work is to give a detailed proof of a version of the Theorem of Hadamard and Conh-Vossen due to the authors M. P. do Carmo and F. W. Warner, for the case where Nn+1 is the unit sphere (phormula) endowed with the Euclidean metric induced from (phormula), considering the hypothesis of that sectional curvatures of Mn compact, connected, orientable Riemannian manifold are bigger or equal to the curvature of the ambient manifold Sn+1. / Considere uma imersão isométrica (fórmula) de uma variedade Riemanniana Mn, n-dimensional (fórmula), C1, compacta, conexa, orientável em uma variedade Riemanniana simplesmente conexa Nn+1 de curvatura seccional constante. Quando Nn+1 é o espaço Euclidiano Rn+1 e Mn tem curvaturas seccionais não-negativas, os seguintes resultados normalmente associados com os nomes de Hadamard e Conh-Vossen, já são conhecidos: (a) A imagem (fórmula) é o bordo de um corpo convexo do Rn+1, x é um mergulho e Mn é difeomorfa à esfera unitária (fórmula) (b) Se (fórmula)é outra imersão isométrica, cumprindo as hipóteses acima, então existe uma isometria (fórmula) tal que (fórmula). O objetivo central desse trabalho é dar uma prova detalhada de uma versão do Teorema de Hadamard e Conh-Vossen, devido aos autores M. P. do Carmo e F. W. Warner, para o caso em que Nn+1 é a esfera unitária (fórmula) munida com a métrica canônica induzida por Rn+2, considerando a hipótese de que as curvaturas seccionais de Mn variedade Riemanniana compacta, conexa, orientável sejam maiores ou iguais que a curvatura da variedade ambiente Sn+1.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 1990. / Thesis Advisor(s): Miller, James H. Second Reader: Tummala, Murali. "September 1990." Description based on title screen as viewed on December 17, 2009. DTIC Identifier(s): Acoustic tomography, inverse problems, Fast Hadamard Transforms, theses. Author(s) subject terms: Acoustic tomography, Fast Hadamard Transform, maximal-length sequences, Doppler processing. Includes bibliographical references (p. 95-96). Also available in print.

ALBUQUERQUE, R. M. Obtenção de portas lógicas quânticas em condensados de bose - Einstein. 2017. 77 f. Dissertação (Mestrado em Engenharia Elétrica e da Computação) - Campus de Sobral, Universidade Federal do Ceará, Sobral, 2017. / Submitted by Programa de Pós-Graduação Engenharia Elétrica e de Computação (secretaria_ppgeec@sobral.ufc.br) on 2017-10-31T21:38:15Z No. of bitstreams: 1 2016_dis_rmdealbuquerque.pdf: 2544760 bytes, checksum: f4f3c8e0b7dd85d6b593e5bfc7b367eb (MD5) / Approved for entry into archive by Djeanne Costa (djeannecosta@gmail.com) on 2017-11-01T12:09:26Z (GMT) No. of bitstreams: 1 2016_dis_rmdealbuquerque.pdf: 2544760 bytes, checksum: f4f3c8e0b7dd85d6b593e5bfc7b367eb (MD5) / Made available in DSpace on 2017-11-01T12:09:26Z (GMT). No. of bitstreams: 1 2016_dis_rmdealbuquerque.pdf: 2544760 bytes, checksum: f4f3c8e0b7dd85d6b593e5bfc7b367eb (MD5) Previous issue date: 2017-10 / Bose-Einstein condensate (BEC) coupled is a promising candidate to quantum computing. Being a macroscopic quantum phenomenon, Being a strong quantum system (BÖIH et al., 2009), its assembly and experimental control inside an atomic chip (HÄNSEL et al.,2001), further the optical networks (GREINER OLAF MANDEL, 2001), where it is found and manipulated in different network sites, assuring implementation conditions of Quantum Information Protocol. The definition of a Qubit in BECs was proposed considering the couple of two BEC’s in different hyperfine states throught a two-photon transition. We have identified each one of the condensates in their respective hyperfine levels like the states and the Qubit. Experimentally, it is possible both the identification of atoms that ate in each one of the hyperfine levels and the measurement of the condensate phase. With these information is possible to determine the superposition coefficients . In this coursework, we have studied the dynamics of two Bose-Einstein condensate (BEC) on its fundamental state, trapped and coupled by a quantum tunneling. Because of this coupling, there is population transference between two condensed modes. The coupling is adjusted in a way we have probability of occupation in two levels. We have shown that this system can be considerate viable to a Qubit. So, we have simulated the quantum gates NOT and Hadamard. / Condensados de Bose-Einstein (CBE) acoplados é candidato promissor à computação quântica. Por ser um fenômeno quântico macroscópico, por ser um sistema quântico robusto (BÖHI et al., 2009), por sua montagem e controle experimental dentro de um chip atômico (HÄNSEL et al., 2001), além das construções em redes ópticas (GREINER OLAF MANDEL, 2001), onde são localizados e manipulados em diferentes sítios da rede, garantindo condições de implementação de protocolos de Informação Quântica. A definição de um q-bit em CBEs foi proposta considerando o acoplamento de dois CBEs em diferentes estados hiperfinos através de uma transição de dois fótons. Identificamos cada um dos condensados nos seus respectivos níveis hiperfinos como os estados j0i e j1i do q-bit. Experimentalmente, é possível tanto a identificação dos átomos que estão em cada um dos níveis hiperfinos quanto a medição da fase dos condensados. Com estas informações é possível determinar os coeficientes de superposição a j0i+b j1i. No presente trabalho, estudamos a dinâmica de dois condensados de Bose - Eisntein (CBE) no estado fundamental, armadilhados e acoplados por tunelamento quântico. Devido a esse acoplamento, há transferência de população entre os dois modos condensados. O acoplamento é ajustado de maneira que tenhamos probabilidade de ocupação em dois níveis. Demonstramos que este sistema pode ser considerado viável a um q-bit. Então, simulamos as portas quânticas NOT e Hadamard.

Ingeniero Civil Matemático / El presente trabajo de Memoria de Título para la carrera Ingeniería Civil Matemática consiste en el estudio de difusiones en la recta real. Se pretende caracterizar la familia de procesos estocásticos generada por los operadores inversos de las n-ésimas potencias de Haddamard el operador de Green del Movimiento Browniano. En una primera instancia, se estudian las potencias de Haddamard del operador de Green asociado al movimiento Browniano en un intervalo acotado. Con ciertas propiedades encontradas para estos operadores, se obtienen propiedades que impiden la existencia de una inversa contínua. Luego, se calcula una fórmula para un operador diferencial en L^2, demostrando que corresponde a una inversa para la potencia del operador de Green. Posteriormente, se estudia la familia de procesos estocásticos cuyo semigrupo generador está dado por los operadores anteriormente obtenidos truncados en el coeficiente lineal. Este estudio permite obtener ciertas propiedades para el posterior estudio de la familia de procesos generada por los operadores obtenidos en la primera etapa, y además entrega una caracterización que resulta en sí misma interesante de una familia de procesos estocásticos. Luego, se caracteriza la familia de procesos estocásticos cuyo semigrupo generador está dado por los operadores obtenidos en la etapa inicial, en función de la familia de procesos obtenida en la parte anterior. Se demuestra la igualdad en ley con un proceso que es identico al anterior hasta un instante aleatorio de muerte y se obtienen cotas para la probabilidad de muerte en función del tiempo elapsado y de la potencia de Haddamard que genera el proceso, que se verifica una ecuación de semigrupo, que el generador de dicho proceso efectivamente corresponde a la inversa de una potencia de Hadamard del operador de Green del Movimiento Browniano, y que el Kernel de Green para estos procesos corresponde a una potencia de Hadamard de dicho operador. Finalmente, se presentan métodos numéricos desarrollados para simular ambas familias de procesos estocásticos, sus limitaciones, posibles errores, y se muestran un par de resultados obtenidos junto con una discusión acerca de la sensibilidad de los parámetros y los errores de aproximación.

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Let A be an m x n, (0, 1)-matrix. A submatrix of A is odd if the sum of its entries is an odd integer and even otherwise. The maximum number of 2 x 2 odd submatrices in a (0, 1)-matrix is related to the existence of Hadamard matrices and bounds on Turán numbers. Pinelis [On the minimal number of even submatrices of 0-1 matrices, Designs, Codes and Cryptography, 9:85-93, 1994] exhibits an asymptotic formula for the minimum possible number of p x q even submatrices of an m x n (0, 1)-matrix. Assuming the Hadamard conjecture, specific techniques are provided on how to assign the 0's and 1's, in order to yield the maximum number of 2 x 2 odd submatrices in an m x n (0, 1)-matrix. Moreover, formulas are determined that yield the exact maximum counts with one exception, in which case upper and lower bounds are given. These results extend and refine those of Pinelis.