Dans cette thèse nous étudions des équations différentielles stochastiques sur quelques graphes simples dont les solutions sont des flots de noyaux au sens de Le Jan et Raimond. Dans une première partie, nous définissons une extension de l'équation de Tanaka sur un nombre fini de demi-droites orientées et issues de l'origine. Utilisant certaines propriétés de régularité du flot associé au mouvement brownien biaisé, nous donnons une description complète de toutes les solutions. S'appuyant sur une transformation discrète introduite par Csaki et Vincze, nous donnons dans un cas d'orientation particulière (qui couvre déjà l'équation de Tanaka usuelle) une approche discrète à quelques solutions. La dernière partie de ce travail est effectuée avec O. Raimond. Par une méthode de couplage des flots, nous classifions les solutions de l'équation de Tanaka sur le cercle. Nous établissons aussi que ces flots sont coalescents.

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.

A Boolean function can be represented in several different forms. These different representation have advantages and disadvantages of their own. The Algebraic Normal Form, truth table, and Walsh spectrum representations are widely studied in literature. In 1999, Claude Carlet and Phillippe Guillot introduced the Numerical Normal Form. NumericalNormal Form(NNF) of a Boolean function is similar to Algebraic Normal Form, with integer coefficients instead of coefficients from the two element field. Using NNF representation, just like the Walsh spectrum, characterization of several cryptographically important functions, such as resilient and bent functions, is possible. In 2002, Carlet had shown several divisibility results concerning resilient and correlation-immune functions using NNF. With these divisibility results, Carlet is able to give bounds concerning nonlinearity of resilient and correlation immune functions. In this thesis, following Carlet and Guillot, we introduce the Numerical Normal Form and derive the pairwise relations between the mentioned representations. Characterization of Boolean, resilient and bent functions using NNF is also given. We then review the divisibility results of Carlet, which will be linked to some results on the nonlinearity of resilient and correlation immune functions. We show the M&ouml / bius inversion properties of NNF of a Boolean function, using Gian-Carlo Rota&rsquo / s work as a guide. Finally, using a lot of the mentioned results, we prove a necessary condition on theWalsh spectrum of Boolean functions with given degree.

In cryptography especially in block cipher design, Boolean functions are the basic elements. A cryptographic function should have high nonlinearity as it can be attacked by linear attack. In this thesis the highest possible nonlinear boolean functions in the even dimension, that is bent functions, basic properties and construction methods of bent functions are studied. Also normal bent functions and generalized bent functions are presented.

Thesis (M.A. (Hons.)) -- University of Western Sydney, 2003. / "A thesis presented to the University of Western Sydney in partial fulfillment of the requirements for the degree of Master of Arts (Honours) Creative Arts, December 2003" Includes bibliography.

For the astrophysically relevant molecules, C3 and C6, ab initio calculations are performed to study the geometries of different neutral isomers, the electronic structures of C3 in its ground and excited states, and possible pathways for the reaction C3 + C3 = C6. For C3 we present calculations for the potential energy surfaces of C3 in different electronic configurations, including the singlet ground state, the triplet ground state, and some higher excited states. The geometries studied include triangular shapes with two identical bond lengths, but different bond angles between them. For the singlet and triplet ground states in the linear geometry, the total energies resulting from the mixed density functional-Hartree-Fock and quadratic configuration interaction methods reproduce the experimental values, i.e. the triplet occurs 2.1 eV above the singlet. In the geometry of an equilateral triangle, we find a low-lying triplet state with an energy of only 0.8 eV above the energy of the singlet in the linear configuration, so that the triangular geometry yields the lowest excited state of C3. For the higher excited states up to about 12 eV above the ground state, we apply time-dependent density functional theory. Even though the systematic error produced by this approach is of the order of 0.4 eV, the results give new insight into the potential energy landscape for higher excitation energies. For C6 we consider the known linear states and the lowest state of monocyclic ring. The potential energy surfaces, were built for various pathways for the reaction C3 + C3 = C6. For this investigation we apply a mixed density functional-Hartree-Fock method which gives good results with respect to the experimental values and does not demand much computational time. We have considered collinear and symmetric non-linear as well as some non-symmetric collision schemes of two C3 subunits, producing the 1Ag states of a D2h isomer, one in a cyclic shape, the other in the form of two triangles connected by the corners, and for the non-symmetric scheme the 1A' state of a Cs isomer. To investigate the pathways for the creation of C6 from two C3 we emphasize the importance of the electron configuration for the reacting C3 subunits. As a result we have obtained the following rule: The stable linear as well as the cyclic C6 molecule can only be created in the case when at least one C3 has a partially filled orbital, requiring an excited state with respect to the singlet ground state of C3. / Für die astrophysikalisch bedeutenden Moleküle C3 und C6 werden ab initio Berechnungen von elektronischen Zuständen verschiedener Isomere durchgeführt. Basierend auf der Optimierung verschiedener neutraler Isomere von C3 im Grundzustand und mehreren angeregten Zuständen werden mögliche Wege für die Reaktion C3 + C3 = C6 studiert. Für C3 werden ab initio Berechnungen für die Flächen der potentiellen Energie in verschiedenen elektronischen Konfigurationen durchgeführt, einschließlich des Singulett-Grundzustands, des Triplett-Grundzustands, und einiger höherer Anregungszustände. Die untersuchten Geometrien schließen gleichschenklige Dreiecke mit zwei identischen Bindungslängen ein, wobei der Bindungswinkel dazwischen variiert wird. Die Gesamtenergien, die sich in einem gemischten Hartree-Fock-Dichtefunktional-Verfahren und unter Verwendung der quadratischen Konfigurationswechselwirkung ergeben, reproduzieren die experimentell beobachtete Energiedifferenz von 2.1 eV zwischen dem niedrigsten Triplett-Zustand und dem Singulett-Grundzustand. In der Geometrie des gleichseitigen Dreiecks ergibt sich ein niedrigerliegender Triplett-Zustand mit einer Energie von nur 0.8 eV über der Energie des Singuletts im linearen Isomer, so dass die dreieckige Geometrie den niedrigsten Anregungszustand von C3 ergibt. Für höhere Anregungsenergien bis zu 12 eV über dem Grundzustand wird zeitabhängige Dichtefunktional-Theorie zur Ermittlung der Energie angeregter elektronischer Konfigurationen eingesetzt. Obwohl der von dieser Methode produzierte systematische Fehler von der Größenordnung von 0.4 eV ist, ergeben sich interessante neue Einblicke in die Potentiallandschaft angeregter Zustände. Für C6 betrachten wir das bekannte lineare Isomer und das zyklische Isomer. Der Verlauf der Potentialoberflächen wird für verschiedene Reaktionspfade C3+C3 = C6 untersucht, wobei ein gemischtes Hartree-Fock-Dichtefunktional-Verfahren einesetzt wird. Im Mittelpunkt des Interesses stehen dabei kollineare Anordnungen linearer C3 Moleküle, symmetrische Kollisionen nichtlinearer Reaktanden, sowie einige nichtsymmetrische koplanare Geometrien des Zusammenstosses zweier linearer Moleküle. Als Ergebnis der Reaktionen mit symmetrischen Anordnungen ergibt sich lineares C6 oder zyklisches C6 mit D2h Symmetrie in einem elektronischen Zustand der höchsten Symmetrie 1Ag. Das nicht-symmetrische Reaktionsschema führt zu einem planaren Isomer Cs im Zustand 1A'. Um die Wege für die Bildung von C6 aus zwei C3 zu untersuchen, ist die elektronische Konfiguration der Reaktanden von entscheidender Bedeutung. Als Ergebnis erhält man die folgende Regel: sowohl ein stabiles lineares als auch ein zyklisches C6 Molekül können nur gebildet werden, wenn zumindest eines der C3 Moleküle ein teilweise gefülltes Orbital hat, wofür eine Anregung aus dem Singulett-Grundzustand heraus erforderlich ist.

No description available.

A passive wireless surface acoustic wave sensor of a delay-line type is composed of an antenna, a transducer that converts the EM signal into a surface acoustic wave, and a set of acoustic reflectors that reflect the incoming signal back out through the antenna. A cavity forms between the transducer and the reflectors, trapping energy and causing multiple unwanted echoes. The work in this dissertation aims to reduce the unwanted echoes so that only the main transit signal is left--the signal of interest with sensor information. The contributions of this dissertation include reflective delay-line device response in the form of an infinite impulse response (IIR) filter. This may be used in the future to subtract out unwanted echoes via post-processing. However, this dissertation will use a physical approach to echo suppression by using a unidirectional transducer. Thus a unidirectional transducer is used and also optimized for 3rd harmonic operation. Both the directionality and the coupling of the 3rd harmonic optimized SPUDT are improved over a standard electrode width controlled (EWC) SPUDT. New type of reflectors for the reflective delay-line device are also presented. These use BPSK type coding, similar to that of the Walsh-Hadamard codes. Two types are presented, variable reflectivity and variable chip-lengths. The COM model is used to simulate devices and compare the predicted echo suppression level to that of fabricated devices. Finally, a device is mounted on a tunable antenna and the echo is suppressed on a wireless operating device.

No description available.

No description available.