Le sujet de cette thèse est sur les propriétés non-locales des états symétriques invariant sous les permutations des systèmes et les usages potentiels de ces états dans le domaine de traitement d'information quantique. La non-localité de presque tous les états sysmétriques, hors les états de Dicke, est établie par une version étendue du paradoxe de Hardy. Grâce à la représentation de Majorana pour les états symétriques, des paramètres de mesure avec lesquels toutes les conditions du paradoxe sont satisfaites peuvent être trouvés. Une version étendue de l'inégalité de CH peut être dérivée à partir des conditions probabilistes de ce paradoxe. Cette inégalité est violée par tous les états symétriques. Les propriétés de la non-localité et les propriétés de l'intrication sont aussi discutées et comparées, notamment par rapport à la persistance et la monogamie. Des résultats indiquent que la dégénérescences de certains états symétriques est liée à la persistance, qui donne une façon d'inventer des tests qui sont indépendants des dispositifs visés pour séparer les différentes classes de non-localité. Il est aussi montré que l'inégalité utilisée pour démontrer la non-localité de tous les états symétriques n'est pas monogame dans le sens strict. Néanmoins, une nouvelle inégalité pour les états de Dicke est proposée, qui est monogame quand le nombre de participants tends vers l'infinité. Malheureusement, toutes ces inégalités sont incapables de détecter la non-localité authentique. Des applications de la non-localité à la complexité de communication et aux jeux bayésiens sont discutées. / This thesis is about the nonlocal properties of permuation symmetric states and the potential usefulness of such properties in quantum information processing. The nonlocality of almost all symmetric states, except Dicke states is shown by constructing an $n$-party Hardy paradox. With the help of the Majorana representation, suitable measurement settings can be chosen for these symmetric states which satisfy the paradox. An extended CH inequality can be derived from the probabilistic conditions of the paradox. The inequality is shown to be violated by all symmetric states. The nonlocality properties and entanglement properties of symmetric states are also discussed and compared, natbly with respect to persistency and monogamy. It is shown that te degeneracy of some symmetric states is linked to the persistency, which provides a way to use device independent tests to separte nonlocality classes. It is also shown that the inequalities used to show the nonlocality of all symmetric states are not strictly monogamous.A new inequality for Dicke states is shown to be monogamous when the number of parties goes to infinity. But all these inequalites can not detect genuine nonlocality. Applications of nonlocality to communication complexity and Bayesian game theory are also discussed.

Cette thèse a pour objet d'étude les algorithmes de chiffrement par blocet les fonctions de hachage cryptograpiques, qui sont deux primitives essentielles de la cryptographie dite «symétrique».Dans une première partie, nous étudions des éléments utiles pour la conception de chiffres par bloc: tout d'abord des matrices de diffusion de grande dimension issues de codes correcteurs géométriques, puis une boîte de substitution offrant une bonne diffusion. Dans le second cas, nous montrons aussi comment utiliser cet élément pour construire un chiffre compact et efficace sur petits processeurs.Dans une seconde partie, nous nous intéressons à des attaques en collision à initialisation libre sur la fonction de hachage SHA-1. Nous montrons comment les attaques classiques sur cette fonction peuvent être rendues plus efficaces en exploitant la liberté supplémentaire offerte par ce modèle. Ceci nous permet en particulier de calculer explicitement des collisions pour la fonction de compression de SHA-1 non réduite. / This thesis is about block ciphers and cryptographic hash functions, which are two essential primitives of symmetric-key cryptography. In the first part of this manuscript, we study useful building blocks for block cipher design. We first consider large diffusion matrices builtfrom algebraic-geometry codes, and then construct a small S-box with good diffusion. In the second case, we show how the S-box can be used to define a compact and efficient block cipher targetting small processors. In the second part, we focus on the SHA-1 hash function, for which we develop a free start collision attack. We show how classical collision attacks can be made more efficient by exploiting the additional freedom provided by the model. This allows us in particular to compute explicit collisions for the full compression function of SHA-1.

Graded Hecke algebras are deformations of skew group algebras which arise from a group acting on a polynomial ring. Over fields of characteristic zero, these deformations have been studied in depth and include both symplectic reflection algebras and rational Cherednik algebras as examples. In Lusztig's graded affine Hecke algebras, the action of the group is deformed, but not the commutativity of the vectors. In Drinfeld's Hecke algebras, the commutativity of the vectors is deformed, but not the action of the group. Lusztig's algebras are all isomorphic to Drinfeld's algebras in the nonmodular setting. We find new deformations in the modular setting, i.e., when the characteristic of the underlying field divides the order of the group. We use Poincare-Birkhoff-Witt conditions to classify these deformations arising from the symmetric group acting on a polynomial ring in arbitrary characteristic, including the modular case.

This licentiate thesis is devoted to the investigation of how bonding in simple organic molecules are affected by X-ray beam irradiation. The investigation targets molecules with three carbons as their main-chain structure. The stability of the bonds under ionization are simulated using the SIESTA package. SIESTA is a simulation package that provides molecular dynamics simulations based on density functional theory within the Born-Oppenheimer approximation. The aim of this study is to understand statistically the damaging process and selectivity among different types of bond. As the first targets, 4 hydrocarbons are investigated. They are propane, propene, propyne and propadiene, which have different combinations of single, double and triple bonds as their main-chain structures. Depending on the combinations, the structures can be either symmetric around the central atom or not. The structure of the symmetric molecules propane and propadiene are  stable until charge +3. In contrast, the asymmetric molecules propene and propyne, the  main-chain bonds show a tendency towards a more similar bond-distance as the level of ionization increases. In addition, hydrogens relocation occurs in propene, leading to a symmetric structure. Secondly, the bond fluctuations are investigated among 4 types of three-carbon molecules which have functional parts. Alcohol and carboxyl groups molecules show the stable bond integrities at charging 0 to +2. On the other hand, the carbon-carbon bonds in molecules with  acetyl and ketone groups are broken by ionization. Comparing the 8 kinds of bond breaking processes in these molecules, this statistical study gives an insight to organic molecules bonding systems.

No description available.

Prior work in the field of set theory has looked at the properties of union-free families. This thesis investigates families based on a different set operation, the symmetricc difference. It provides a complete characterization of maximal symmetric differencefree families of subsets of {1, . . . n}

No description available.

Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of matrices in S(G), sometimes diagonal entries corresponding to specific vertices of G must be zero for all matrices in MR(G). These vertices are known as nil vertices (see [6]). In this paper I discuss some basic results about nil vertices in general and nil vertices in cographs and prove that cographs with a nil vertex of a particular form contain two other nil vertices symmetric to the first. I discuss several open questions relating to these results and a counterexample. I prove that for all cographs G without an induced complete tripartite graph with independent sets all of size 3, the zero-forcing number Z(G), a graph theoretic parameter, is equal to M(G). In fact this result holds for a slightly larger class of cographs and in particular holds for all threshold graphs. Lastly, I prove that the maximum of the minimum ranks of all cographs on n vertices is the floor of 2n/3.

In this thesis we analyze the phase of the heavy symmetric top and the tippe top. These tops are two examples of physical systems for which the usefulness of integrals of motion and invariant manifolds, in phase space picture analysis, can be illustrated In the case of the heavy symmetric top, simplified proofs of stability of the vertical rotation have been perpetuated by successive textbooks during the last century. In these proofs correct perturbations of integrals of motion are missing. This may seem harmless since the deduced threshold value for stability is correct. However, perturbations of first integrals are essential in rigorous proofs of stability of motions for both tops. The tippe top is a toy that has the form of a truncated sphere equipped with a little peg. When spun fast on the spherical bottom its center of mass rises above its geometrical center and after a few seconds the top is spinning vertically on the peg. We study the tippe top through a sequence of embedded invariant manifolds to unveil the structure of the top's phase space. The last manifold, consisting of the asymptotic trajectories, is analyzed completely. We prove that trajectories in this manifold attract solutions in contact with the plane of support at all times and we give a complete description of their stability/instability properties for all admissible choices of model parameters and of the initial conditions. / <p>Report code: LiU-TEK-LIC-2004:35.</p>

In this study, polypyrrole (PPy) prepared by chemical and electrochemical polymerization was investigated as the electrode of electrochemical supercapacitor (ES). New strategies were developed for the fabrication of nano-structured PPy and PPy based nano-composites, which included discovery of advanced anionic dopants and multi-functional nano-crystals, and development of co-dispersing agents. These methods improved the capacitive performance and cycle stability of PPy electrodes. The results indicated that high material loading and good capacitance retention of PPy was achieved using an electrochemical polymerization method and Ni plaque as the current collectors. Nano-crystalline (CTA)2S2O8 formed by a chemical precipitation method from solutions, containing anionic oxidant (S2O82-) and cationic surfactant (CTA+), could be used as the oxidant to synthesize PPy nano-fibers. We demonstrated that multi-wall carbon nanotubes (MWCNT) can be efficiently dispersed using such nano-crystals. Application of multi-functional nano-crystals is a conceptually new approach for the fabrication PPy coated MWCNT. Moreover, safranin and malachite green were found as universal dispersing and charging agents for cataphoretic deposition of graphene, MWCNT and PPy nano-fibers. It opens new strategies in colloidal and electrochemical processing of PPy nano-composites for ES electrodes. PPy coated MWCNT, prepared by the multi-functional nano-crystals (CTA)2S2O8, was employed for the fabrication of N-doped activated carbon-coated MWCNT (N-AC-MWCNT). The obtained N-AC-MWCNT was uniformly coated and possessed with high surface area. The use of N-AC-MWCNT enabled the fabrication of ES electrodes with high mass loading and high active material to current collector mass ratio. Symmetric and asymmetric ES cells, fabricated by N-AC-MWCNT and aqueous Na2SO4 electrolyte, showed high specific capacitance, good capacitance retention and large voltage window. The positive electrode of asymmetric ES, MnO2 coated MWCNT, was successfully prepared by the chemical reaction between KMnO4 and N-AC-MWCNT. The problem of degradation of MWCNT was avoided by the use of N-AC as the sacrificial carbon. Significant progress on ES technology has allowed for the development of capacitive dyes removal (CDR) methods using ES devices. In our study, porous carbon materials, N-doped activated carbon coated MWCNT (N-AC-MWCNT) and N-doped activated carbon nano-fibers (N-AC-NF), were developed as the electrodes for CDR applications. The experimental results indicated that capacitive performance of ES cells was influenced by the chemical structure, size, charge-to mass ratio, concentration and redox-active ligands of the dyes. CDR is a promising method for removal of various cationic and anionic dyes, which offers advantages of energy saving and simple electrode regeneration. / Thesis / Doctor of Philosophy (PhD)