We study universal cycles of the set P(n,k) of k-partitions of the set [n]:={1,2,…,n} and prove that the transition digraph associated with P(n,k) is Eulerian. But this does not imply that universal cycles (or ucycles) exist, since vertices represent equivalence classes of partitions. We use this result to prove, however, that ucycles of P(n,k) exist for all n≥3 when k=2. We reprove that they exist for odd n when k=n−1 and that they do not exist for even n when k=n−1. An infinite family of (n,k) for which ucycles do not exist is shown to be those pairs for which (Formula presented) is odd (3≤k

We say that a function f:V→{0,1,...,diam(G)} is a broadcast if for every vertex v∈V, f(v)≤e(v), where diam(G) denotes the diameter of G and e(v) denotes the eccentricity of v. The cost of a broadcast is the value f(V)=∑v∈Vf(v). In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs, including dominating, independent and efficient broadcasts.

S(5,8,24) is one of the largest known Steiner systems and connects combinatorial designs, error-correcting codes, finite simple groups, and sphere packings in a truly remarkable way. This thesis discusses the underlying structure of S(5,8,24), its construction via the (24,12) Golay code, as well its automorphism group, which is the Mathieu group M24, a member of the sporadic simple groups. Particular attention is paid to the calculation of the size of automorphism groups of Steiner systems using the Orbit-Stabilizer Theorem. We conclude with a section on the sphere packing problem and elaborate on how the 8-sets of S(5,8,24) can be used to form Leech's Lattice, which Leech used to create the densest known sphere packing in 24-dimensions. The appendix contains code written for Matlab which has the ability to construct the octads of S(5,8,24), permute the elements to obtain isomorphic S(5,8,24) systems, and search for certain subsets of elements within the octads. / Master of Science

Em virtude do crescente volume da utilização de embalagens multicamadas na preservação de alimentos, torna-se necessário o estudo visando a reciclagem desses materiais através de seu reaproveitamento como matéria-prima e a transformação em novos produtos ou materiais. Dentre os vários tipos de reciclagem utilizados atualmente, a formação de blendas poliméricas com material descartado apresenta-se como uma alternativa viável, pois se trata de uma atividade moderna que une o desenvolvimento tecnológico e a preservação ambiental. O presente trabalho faz um estudo sobre a reciclagem de resíduos de embalagens multicamadas pós-consumo no setor alimentício para a formação de uma blenda. O filme multicamada composto por poliamida 6 e polietileno de baixa densidade foi previamente moído para obtenção de flocos e a ele foi adicionado primeiramente o aditivo etileno-propileno-dieno monômero e em seguida foi feito uma nova mistura composta apenas de anidrido maléico com filme multicamada na forma de flocos, no intuito de melhorar as propriedades mecânicas das blendas formadas pelo processo da extrusão. Para a verificação dos resultados obtidos foram realizados testes de tração, alongamento e permeabilidade ao gás oxigênio no filme de poliamida 6 e polietileno, e ensaios mecânicos, análises térmicas e microscopia eletrônica de varredura nas blendas obtidas. Também se estudou o efeito da radiação (100 kGy) sobre as propriedades das blendas utilizando-se um acelerador de elétrons. / In virtue of the increasing volume of the multilayers packings use in the food preservation, the study for the recycling of these materials through its reverse speed-exploitation as raw material and the transformation in new products or materials becomes necessary. Amongst some types of recycling used currently, the polymers blendes formation with discarded material is presented as a viable alternative, therefore if it deals with a modern activity that joins the technological development and the ambient preservation. The present research, therefore makes a study on the recycling of residues from multilayers packings after-consumes in the nourishing sector for the blend formation. The multilayer film composed by polyamide 6 and polyethylene of low density was previously worn out for flake attainment and it was added first the Ethylene-Propylene-Diene-Monomer (EPDM) additive and after that a new composed maleic anhydride mixture was made only with multilayer film in the flake form, in intention to improve the mechanical properties of blendes formed for the process of the drawing. For verification of the results assays had been carried through traction tests, rupture lengthening tests and permeability to the gas oxygen in the film of polyamide 6 and mechanical properties of blendes formed for the process of the drawing. For verification of the results assays had been carried through traction tests, rupture lengthening tests and permeability to the gas oxygen in the film of polyamide 6 and mechanical polyethylene, and assays, thermal analyses and scanning electronic microscopy in the blendes. It was also studied radiation dose (100 kGy) on the blends properties using an electron beam accelerator.

In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of: (1) a single cycle of length v, (2) f fixed points and a cycle of length v − f, or (3) two disjoint cycles. The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv.

There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs Dv, packing and covering complete bipartite digraphs, Dm,n, and packing and covering the complete digraph on v vertices with hole of size w, D(v,w), with three of the orientations of a 4-cycle, including C4, X, and Y.

Let F0 be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F0-packing of H is a family F of edge-disjoint copies of F0 which are subhypergraphs in H. Let nF0(H) denote the maximum size |F| of an F0-packing F of H. It is well-known that computing nF0(H) is NP-hard for nearly any choice of F0. In this thesis, we consider the special case when F0 is a linear hypergraph, that is, when no two edges of F0 overlap in more than one vertex. We establish for z > 0 and n &ge n0(z) sufficiently large, an algorithm which, in time polynomial in n, constructs an F0-packing F of H of size |F| ≥ nF0(H) - znk. A central direction in our proof uses so-called fractional F0-packings of H which are known to approximate nF0(H). The driving force of our argument, however, is the use and development of several tools within the theory of hypergraph regularity.

Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

Made available in DSpace on 2014-12-17T14:53:12Z (GMT). No. of bitstreams: 1 VaniaMNFS.pdf: 638557 bytes, checksum: 93d8303b75ad696c18c0e1c6e19e8b6c (MD5) Previous issue date: 2006-05-19 / O presente trabalho tem o objetivo de apresentar uma investiga??o sobre o n?vel de clareza dos textos informativos dos r?tulos de embalagens de caf? torrado e mo?do, considerando os aspectos ling??sticos e ergon?micos presentes nos r?tulos do produto. Ling?isticamente analisar se a linguagem utilizada nos r?tulos ? adequada para a compreens?o das informa??es pelo consumidor, ainda expor como a ling??stica preconiza a organiza??o e estrutura??o dos textos a partir da classifica??o do g?nero textual. Do ponto de vista da ergonomia a pesquisa pretende identificar a conformidade ergon?mica presente nas informa??es dos r?tulos das embalagens de caf?. Devido ? evolu??o das atividades comerciais, a embalagem passou ao longo do tempo a acumular fun??es, transformando-se em um consider?vel ve?culo de comunica??o, informa??o e sedu??o do seu p?blico consumidor, por isso, a ado??o de normas adequadas relativas ?s informa??es pode evitar que o consumidor desenvolva conceitos inadequados ou at? mesmo empregue erroneamente um produto aliment?cio em sua dieta. A engenharia de produ??o considera importante a inser??o de melhores pr?ticas de produ??o e gest?o do produto nas empresas, com vistas ao aumento de sua competitividade, compatibilizando as caracter?sticas ergon?micas do produto embalagem, com as necessidades do consumidor enquanto parte integrante do processo de desenvolvimento do produto. A pesquisa prop?e, ent?o, um roteiro para avalia??o dos r?tulos de embalagens, utilizando para isso um question?rio com quest?es fechadas e uma aberta, aplicados em consumidores de caf? torrado e mo?do no momento da compra em quatro supermercados de Natal. Os principais resultados da investiga??o demonstram que os aspectos ling??sticos dos textos informativos foram considerados bons, enquanto os aspectos ergon?micos informacionais analisados podem vir a contribuir para uma melhoria visual das informa??es contidas nos r?tulos das embalagens das marcas de caf? investigadas

Em virtude do crescente volume da utilização de embalagens multicamadas na preservação de alimentos, torna-se necessário o estudo visando a reciclagem desses materiais através de seu reaproveitamento como matéria-prima e a transformação em novos produtos ou materiais. Dentre os vários tipos de reciclagem utilizados atualmente, a formação de blendas poliméricas com material descartado apresenta-se como uma alternativa viável, pois se trata de uma atividade moderna que une o desenvolvimento tecnológico e a preservação ambiental. O presente trabalho faz um estudo sobre a reciclagem de resíduos de embalagens multicamadas pós-consumo no setor alimentício para a formação de uma blenda. O filme multicamada composto por poliamida 6 e polietileno de baixa densidade foi previamente moído para obtenção de flocos e a ele foi adicionado primeiramente o aditivo etileno-propileno-dieno monômero e em seguida foi feito uma nova mistura composta apenas de anidrido maléico com filme multicamada na forma de flocos, no intuito de melhorar as propriedades mecânicas das blendas formadas pelo processo da extrusão. Para a verificação dos resultados obtidos foram realizados testes de tração, alongamento e permeabilidade ao gás oxigênio no filme de poliamida 6 e polietileno, e ensaios mecânicos, análises térmicas e microscopia eletrônica de varredura nas blendas obtidas. Também se estudou o efeito da radiação (100 kGy) sobre as propriedades das blendas utilizando-se um acelerador de elétrons. / In virtue of the increasing volume of the multilayers packings use in the food preservation, the study for the recycling of these materials through its reverse speed-exploitation as raw material and the transformation in new products or materials becomes necessary. Amongst some types of recycling used currently, the polymers blendes formation with discarded material is presented as a viable alternative, therefore if it deals with a modern activity that joins the technological development and the ambient preservation. The present research, therefore makes a study on the recycling of residues from multilayers packings after-consumes in the nourishing sector for the blend formation. The multilayer film composed by polyamide 6 and polyethylene of low density was previously worn out for flake attainment and it was added first the Ethylene-Propylene-Diene-Monomer (EPDM) additive and after that a new composed maleic anhydride mixture was made only with multilayer film in the flake form, in intention to improve the mechanical properties of blendes formed for the process of the drawing. For verification of the results assays had been carried through traction tests, rupture lengthening tests and permeability to the gas oxygen in the film of polyamide 6 and mechanical properties of blendes formed for the process of the drawing. For verification of the results assays had been carried through traction tests, rupture lengthening tests and permeability to the gas oxygen in the film of polyamide 6 and mechanical polyethylene, and assays, thermal analyses and scanning electronic microscopy in the blendes. It was also studied radiation dose (100 kGy) on the blends properties using an electron beam accelerator.