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1	Densidade local em grafos / Local density in graphs Fernandez, Luis Eduardo Zambrano 14 November 2018 (has links) Nós consideramos o seguinte problema. Fixado um grafo H e um número real \\alpha \\in (0,1], determine o menor \\beta = \\beta(\\alpha, H) que satisfaz a seguinte propriedade: se G é um grafo de ordem n no qual cada subconjunto de [\\alpha n] vértices induz mais que \\beta n^2 arestas então G contém H como subgrafo. Este problema foi iniciado e motivado por Erdös ao conjecturar que todo grafo livre de triângulo de ordem n contém um subconjunto de [n/2] vértices que induz no máximo n^2 /50 arestas. Nosso resultado principal mostra que i) todo grafo de ordem n livre de triângulos e pentágonos contém um subconjunto de [n/2] vértices que induz no máximo n^2 /64 arestas, e ii) se G é um grafo regular de ordem n livre de triângulo, com grau excedendo n/3, então G contém um subconjunto de [n/2] vértices que induz no máximo n^2 /50 arestas. Se além disso G não é 3-cromático então G contém um subconjunto de [n/2] vértices que induz menos de n^2 /54 arestas. Como subproduto e confirmando uma conjectura de Erdös assintoticamente, temos que todo grafo regular de ordem n livre de triângulo com grau excedendo n/3 pode ser tornado bipartido pela omissão de no máximo (1/25 + o(1))n^2 arestas. Nós também fornecemos um contraexemplo a uma conjectura de Erdös, Faudree, Rousseau e Schelp. / We consider the following problem. Fixed a graph H and a real number \\alpha \\in (0,1], determine the smallest \\beta = \\beta(\\alpha, H) satisfying the following property: if G is a graph of order n such that every subset of [\\alpha n] vertices spans more that \\beta n^2 edges then G contains H as a subgraph. This problem was initiated and motivated by Erdös who conjectured that every triangle-free graph of order n contains a subset of [n/2] vertices that spans at most n^2 /50 edges. Our main result shows that i) every triangle- and pentagon-free graph of order n contains a subset of [n/2] vertices inducing at most n^2 /64 edges and, ii) if G is a triangle-free regular graph of order n with degree exceeding n/3 then G contains a subset of [n/2] vertices inducing at most n^2 /50 edges. Furthermore, if G is not 3-chromatic then G contains a subset of [n/2] vertices inducing less than n^2 /54 edges. As a by-product and confirming a conjecture of Erdös asymptotically, we obtain that every n-vertex triangle-free regular graph with degree exceeding n/3 can be made bipartite by removing at most (1/25 + o(1))n^2 edges. We also provide a counterexample to a conjecture of Erdös, Faudree, Rousseau and Schelp. Bisecções de grafos Bisections of graphs Densidade local Local density Metades esparsas Sparse-halves Teorema de Turán Turán's theorem
2	Densidade local em grafos / Local density in graphs Luis Eduardo Zambrano Fernandez 14 November 2018 (has links) Nós consideramos o seguinte problema. Fixado um grafo H e um número real \\alpha \\in (0,1], determine o menor \\beta = \\beta(\\alpha, H) que satisfaz a seguinte propriedade: se G é um grafo de ordem n no qual cada subconjunto de [\\alpha n] vértices induz mais que \\beta n^2 arestas então G contém H como subgrafo. Este problema foi iniciado e motivado por Erdös ao conjecturar que todo grafo livre de triângulo de ordem n contém um subconjunto de [n/2] vértices que induz no máximo n^2 /50 arestas. Nosso resultado principal mostra que i) todo grafo de ordem n livre de triângulos e pentágonos contém um subconjunto de [n/2] vértices que induz no máximo n^2 /64 arestas, e ii) se G é um grafo regular de ordem n livre de triângulo, com grau excedendo n/3, então G contém um subconjunto de [n/2] vértices que induz no máximo n^2 /50 arestas. Se além disso G não é 3-cromático então G contém um subconjunto de [n/2] vértices que induz menos de n^2 /54 arestas. Como subproduto e confirmando uma conjectura de Erdös assintoticamente, temos que todo grafo regular de ordem n livre de triângulo com grau excedendo n/3 pode ser tornado bipartido pela omissão de no máximo (1/25 + o(1))n^2 arestas. Nós também fornecemos um contraexemplo a uma conjectura de Erdös, Faudree, Rousseau e Schelp. / We consider the following problem. Fixed a graph H and a real number \\alpha \\in (0,1], determine the smallest \\beta = \\beta(\\alpha, H) satisfying the following property: if G is a graph of order n such that every subset of [\\alpha n] vertices spans more that \\beta n^2 edges then G contains H as a subgraph. This problem was initiated and motivated by Erdös who conjectured that every triangle-free graph of order n contains a subset of [n/2] vertices that spans at most n^2 /50 edges. Our main result shows that i) every triangle- and pentagon-free graph of order n contains a subset of [n/2] vertices inducing at most n^2 /64 edges and, ii) if G is a triangle-free regular graph of order n with degree exceeding n/3 then G contains a subset of [n/2] vertices inducing at most n^2 /50 edges. Furthermore, if G is not 3-chromatic then G contains a subset of [n/2] vertices inducing less than n^2 /54 edges. As a by-product and confirming a conjecture of Erdös asymptotically, we obtain that every n-vertex triangle-free regular graph with degree exceeding n/3 can be made bipartite by removing at most (1/25 + o(1))n^2 edges. We also provide a counterexample to a conjecture of Erdös, Faudree, Rousseau and Schelp. Bisecções de grafos Densidade local Metades esparsas Teorema de Turán Bisections of graphs Local density Sparse-halves Turán's theorem
3	Phase diagram for the S equals one-half and J equals three-halves Kondo lattice model Abele, Miguel January 2018 (has links) A Kondo lattice Hamiltonian for arbitrary total angular momentum J is formulated using a pseudofermion representation and without addition of RKKY interaction terms. An Hartree-Fock treatment is applied, and both variational and Green's function methods are used to calculate physical quantities from the linearized Hamiltonian. The Kondo phase is represented by finite hybridization. Magnetic ordering is examined via ordering vectors, but coexistence with the Kondo phase is not allowed. Phase diagrams are produced in S=1/2 and J=3/2 with second-order transitions at Kondo-paramagnetic and magnetic-paramagnetic boundaries, and first order transitions between Kondo and magnetic phases. Various coupling strengths are explored. Magnetic phases found include antiferromagnetism, ferromagnetism, and spin-density wave ordering of both commensurate and incommensurate varieties. In S=1/2, the magnetic phase exhibits a spike in critical temperature at half-filling. In J=3/2, the Kondo phase is reentrant at weaker coupling but not at stronger coupling. / Physics Physics, Condensed Matter Theoretical Physics 3d J Equals Three-halves Kondo Model Lattice Mean-field Phase Diagram
4	Shift Arnold, Amanda Suzanne 03 August 2007 (has links) The following is a collection of original poetry. The manuscript consists of an introduction explaining influences and style, and four chapters of poems categorized by subject matter: object/nature, writing/creativity, relationships, and family/figures. INDEX WORDS: Poetry, Poem Giving Thanks Transportation 1:43 a.m. Our Heavenly Father Silver Lining Old Neighbor Halves December 1982 Medicate Friend Home Economics Missing Keeper Passing Dream Tango Lesson Words Edge Untitled Poem Get-away Poem If You Stay Puppy Moon Winter Pine Loneliness The Truth Bone Potato Slip Sad Kentucky Old Shirt Isolation Cleaning the Sink Manhattan Root Posture Keep How it is Personal Business Gun One and the Other Sestina Poets Snow Globe The Romantics Idea The Black Dot Dissection English Language and Literature

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