A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

Thesis (Ph.D.); Submitted to the University of California at Berkeley, Berkeley, CA (US); 1 Sep 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--55023" Li, Liang-shi. USDOE Director. Office of Science. Office of Basic Energy Sciences (US) 09/01/2003. Report is also available in paper and microfiche from NTIS.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-27Bitstream added on 2014-06-13T20:08:06Z : No. of bitstreams: 1 rayzaro_os_me_sjrp.pdf: 628267 bytes, checksum: 09181fbba2d539fd6135f0b473b3b345 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho vemos que a imagem de um ideal do anel dos inteiros dos corpos de números, via o homomorfismo de Minkowski, é um reticulado, chamado de reticulado algébrico. Assim, o principal objetivo deste trabalho é a construção de reticulados algébricos de dimensão 2; 4; 6 e 8, com densidade de centro ótimo. / In this work, we see that the image of an ideal from the algebraic integer ring of the numbers ¯elds by the Minkowski homomorphism is a lattice, named algebraic lattice. In this way, the main aim of this work is the construction of algebraic lattices of dimensions 2,4,6 and 8, with the center density excellent.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-12-10Bitstream added on 2014-06-13T20:08:00Z : No. of bitstreams: 1 ramos_gm_me_sjrp.pdf: 353629 bytes, checksum: 1030312b97bd0bb7f95093162b227e48 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo principal deste trabalho é estudar a densidade de centro de reticulados obtidos por meio do Método de Minkowski em subcorpos de Q(?pq), com p e q primos ímpares distintos e satisfazendo a condição oq(p) = op(q) = 1 (mod 2). O cálculo da densidade de centro é feito a partir do discriminante do corpo, da norma do ideal e da minimização da forma traço. / This work aims at studying the center density of the lattices got through the Minkowski's Method in subfields of Q(?pq), p and q prime number and oq(p) = op(q) = 1 (mod 2). The calcule of the center density is done using the discriminant of the field, the norm of the ideal and the minimization of trace form.

Made available in DSpace on 2014-10-09T12:36:59Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:56:24Z (GMT). No. of bitstreams: 1 04491.pdf: 3155069 bytes, checksum: aa854e4a23f31eb334f216ec1ea726c2 (MD5) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Made available in DSpace on 2014-10-09T12:27:11Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:57:37Z (GMT). No. of bitstreams: 0 / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

Hydrocarbon chains are a basic component in a number of systems as diverse as biological membranes, phospholipids and polymers. A better understanding of the physical properties of n-alkane chains should provide a better understanding of these more complex systems. With this aim, vibrational spectroscopy has been extensively used. This technique, sensitive to molecular details, is the only one able to both identify and quantify conformational disorder present in paraffinic systems. To achieve this, methyl deformations have been widely used as "internal standards" for the normalisation of peak areas. However, in the case of n-alkanes with short chain length, such as n-C[44]H[90] for example, the infrared spectra recorded at liquid nitrogen temperature and reported here show the sensitivity of these latter peaks to the various crystal structures formed. Indeed, the main frequencies of the symmetric methyl bending mode were found between 1384 cm[-1] and 1368 cm[-1] as a function of the crystal form. Changes in the frequency of the first order of the L.A.M. present in the Raman spectra were also observed. At higher temperatures, non all-trans conformers, inferred from different infrared bands present in the wagging mode region, were found to be essentially placed at the end of the n-alkane chains. At the monoclinic phase transition, the concentration of end-gauche conformers, proportional to the area of the infrared band at 1342 cm[-1], increases abruptly. On the contrary, in the spectra recorded at liquid nitrogen temperature no such band is observed. We also studied the degree of disorder in two purely monodisperse long chain n-alkanes, namely n-C[198]H[398] and n-C[246]H[494]. The chain conformation as well as the tilt angle of the chains from the crystal surfaces were determined by means of low frequency Raman spectroscopy and S.A.X.S. measurements on solution-crystallised samples. The increase in the number of end-gauche conformers which was expected to occur with the increase of the tilt angle as a function of the temperature was not detected due to a perfecting of the crystals. Indeed, due to successive heating and cooling to -173&deg;C, the concentration of non all-trans conformers was found to decrease within the crystals. Their numbers were found to be up to six times higher in n-C[198]H[398] crystallised in once folded form than when crystallised in extended form. The C-C stretching mode region of the spectra was used to identify the chain conformation and to estimate the length of the all-trans stem passing through the crystal layers at -173&deg;C. The transition between once folded and extended form crystals was indicated by the presence of additional bands in this region at 1089 cm[-1], 1078 cm[-1] and 1064 cm[-1]. Some of those bands may be related to the fold itself. At the same time, a strong decrease of the intensity of the infrared bands present in the wagging mode region was observed. Finally, the triple layered structure proposed on the basis of X-ray measurements obtained from the crystals of a binary mixture of long chain n-alkanes, namely n-C[162]H[326] and n-C[246]H[494], was confirmed from the study of the C-C stretching mode region of the infrared spectra.

Au cours de cette thèse, nous avons étudiés théoriquement les propriétés structurelles et électroniques des super-réseaux d'oxyde de manganèse en structure perovskiteö au moyen de calculs ab initio.Les oxydes de manganèse au lanthane, donnés avec la formule générique La(1-x)A(x)MnO(3) (LAMO) (A un élément divalent), constituent une classe importante d'oxydes de manganèse en raison de leurs diverses propriétés, telles que l'effet de magnétorésistance colossale, leur riche diagramme de phase en fonction du dopage, de la température ou de champs externes, et leur grande température Curie. Ces propriétés peuvent être exploitées dans de nombreuses applications technologiques potentielles telles que les valves de spin ou les injecteurs de spin. Le contrôle des propriétés de ces matériaux peut se faire par dépôt sous forme de films minces ou comme blocs de construction dans des super-réseaux. Lorsque x = 1/3, le La(1-x)A(x)MnO(3) massif est ferromagnétique et métallique grâce au mécanisme de double échange dans la electrons 3d de Mn. Lorsque Mn est dans un état de valence mixte, les orbitales eg (dx2-y2 and dz2) sont partiellement occupées et peuvent se délocaliser sur les atomes de Mn voisins, seulement si ceux-ci sont alignés ferromagnétiquement. Dans des films très minces, puisque la direction perpendiculaire au substrat, c, n'a que quelques cellules unitaires d'épaisseur, seules les interactions dans le plan (ab) sont importantes pour les propriétés thermodynamiques. En agissant sur la géométrie de la couche LAMO, on peut ainsi maximiser l'occupation de l'orbitales dx2-y2 et augmenter l'échange magnétique et la température Curie associée.Notre but était donc de concevoir de nouveaux matériaux avec un ordre orbital 3d spécifique afin d'assurer les propriétés magnétiques souhaitées.Dans cette thèse, nous avons travaillé sur deux types de super-réseaux. Le premier était constitué de deux oxydes de manganèse antiferromagnétiques, non dopés, LaMnO(3) et SrMnO(3), c'est-à-dire des super-réseaux [LaMnO(3)]n/[SrMnO(3)]m. Nous avons étudié l'état fondamental magnétique pour différentes valeurs n et m afin d'expliquer les résultats expérimentaux surprenants. Le deuxième type de super-réseaux que nous avons étudiés est composé de couches métalliques LAMO en alternance avec des couches isolantes. En effet, les super-réseaux avec des interfaces métal-isolant ont un grand potentiel dans les applications de valves de spin. Ainsi, nous avons d'abord considéré des super-réseaux entre composés ferromagnétiques-métalliques et ferroélectriques-isolantes [LAMO](3)/[BTiO(3)](3) (A = Sr ou Ba, B = Ba ou Pb). Dans ces super-réseaux, les propriétés magnétiques sont malheuresement réduites en raison de la délocalisation d'électrons dz2 à l'interface entre Mn et Ti. Dans de tels super-réseaux , nous avons clarifié le rôle de la polarisation des couches ferroélectriques et le rôle des mouvements antiferrodistortifs dans les couches de manganite. Enfin, de manierè à 'éviter que la délocalisation ait lieu à l'interface, nous avons conçu un autre super-réseau avec interface métal-isolant dans lequel nous avons remplacé l'isolant (BTiO(3)) par un oxyde simple (BO): [LAMO]n/[BO]p superlattices (A = Sr ou Ba, B = Ba, Sr ou Mg et n = 3 ou 6, p = 6 ou 2). Dans ces nouveaux super-réseaux, nous avons réussi à promouvoir les occupations des orbitales dx2-y2 dans les interfaces assurant un fort moment magnetique à l'interface et a priori une fort temperature de Curie. Nous avons également montré une faible corrélation entre la conductivité électrique et l'ordre orbitaire. / This thesis theoretically studies structural and electronic properties of perovskite manganese oxide superlattices by means of ab-initio calculations.Lanthanum manganese oxides, given with the generic formula La1−xAxMnO3 (LAMO) (A a divalent element), are an important class of perovskite manganese oxides due to their various exotic properties, such as giant and colossal magnetoresistance effect, rich phase diagrams with respect to doping, temperature or external fields, and intinsic large Curie temperature. These properties can be exploited in many potential technological applications such as spin valves or spin injectors. Controlling the properties of these materials can be done through deposition as thin films or as building blocks in superlattices. When x = 1/3, bulk La1−xAxMnO3 is ferromagnetic and metallic due to the double-exchange mechanism in the Mn 3d shell. When Mn is in a mixed valence state, the eg orbitals (dx2-y2 and dz2) are partially occupied, and can delocalize on neighboring Mn atoms only if the latter are ferromagnetically aligned. In very thin films, since the direction perpendicular to the substrate, c, is only a few unit cell thick, only in-plane (ab) interactions are important for the thermodynamic properties. By acting on the LAMO layer geometry, one can thus maximize the dx2-y2 occupancy and increase the magnetic exchange and related Curie temperature.Our aim was thus to design new materials with desired 3d orbital order so that to ensure desired magnetic properties.In this thesis, we worked on two types of superlattices. The first one was made of two undoped antiferromagnetic manganese oxides LaMnO3 and SrMnO3, i.e. [LaMnO3]n/[SrMnO3]m superlattices. We investigated the magnetic ground state for different n and m values in order to explain suprising experimental results. The second type of superlattices is composed of metallic LAMO layers with alternated insulating layers. Indeed, the superlattices with metal-insulator interfaces have a great potential in spin valves applications. Thus, we first considered the ferromagnetic-metallic/ferroelectric-insulating [LAMO]3/[BTiO3]3 superlattices (A= Sr or Ba, B=Ba or Pb) where the magnetic properties are reduced due to delocalization of dz2 electrons at the interface from Mn to Ti. In such superlattices, we clarified the role of the polarization of the ferroelectric layers and the role of the antiferrodistortive motions in the manganite layers. In order to prevent the delocalization taking place at the interface, we designed another superlattice with metallic-insulator interface where we replaced the insulator (BTiO3) with a simple oxide (BO); that is [LAMO]n/[BO]p superlattices (A= Sr or Ba, B=Ba, Sr or Mg and n=3 or 6, p=6 or 2). Within this new superlattice, we successully managed to promote dx2-y2 orbital occupancies at the interfaces which ensures a large magnetic moment at the interfaces and an expected large Curie temperature. We also showed the weak correlation between electrical conductivity and orbital ordering.