Packing six T-joins in plane graphs

Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G contains k edge-disjoint T-joins. The case k = 3 is equivalent to the Four Color Theorem, and the cases k = 4, which was conjectured by Seymour, and k = 5 were proved by Guenin. We settle the next open case k = 6

The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio of the binary components and the initial distance ratio of the planet relative to the stellar separation distance. Our theoretical results allow us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.Comment: 10 pages, 8 figures, 3 tables; accepted by Astronomy and Astrophysic

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus' equilateral equilibrium points is investigated with respect to the inclination of the asteroid's orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L4 and L5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 billion years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 < a < 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids' orbit was varied in the range 0 < i < 60 and the semimajor axes were fixed. It turned out that only four 'windows' of stable orbits survive: these are the orbits for the initial inclinations 0 < i < 7, 9 < i < 13, 31 < i < 36 and 38 < i < 50. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.Comment: 15 pages, 12 figures, submitted to CMD

Physical mapping of chromosomes 3HS and 3DS

Relatório de estágio do mestrado em Ensino da Educação Física nos Ensinos Básico e Secundário, apresentado à Faculdade de Ciências do Desporto e Educação Física da Universidade de CoimbraO presente documento divide-se em duas partes: a reflexão dos aspetos relacionados com o estágio pedagógico e o desenvolvimento do tema-problema. Numa primeira fase será dado enfoque à prática da docência, desenvolvida na escola E.B.2,3 Dr. Daniel de Matos. Serão apresentadas as expectativas iniciais em relação à prática, serão apresentadas e justificadas as opções metodológicas tomadas ao longo do estágio, serão relatadas as atividades desenvolvidas durante o estágio e será realçada a componente ética e profissional da profissão. De seguida será realizada uma justificação das opções tomadas. Para finalizar a primeira parte do presente trabalho será feita uma análise reflexiva sobre a prática pedagógica. Na segunda parte temos o tema-problema e seu desenvolvimento, num documento que se pretende orientador da prática docente e auxiliar de como resolver comportamentos de desvio da tarefa por parte dos alunos. Servirá também para analisar e mostrar conclusões sobre o problema que a escola atual, enquanto organização enfrenta, a indisciplina. Será efetuada uma pequena investigação, em que o objetivo é analisar a perceção dos docentes de uma escola pública sobre a gravidade dos comportamentos de indisciplina praticados. O objetivo é chegar a alguma conclusão que possa ajudar/beneficiar os professores da escola na procura de estratégias e metodologias que possam minimizar o impacto deste tipo de comportamentos no normal funcionamento da aula. This document is divided into two parts: a reflection of aspects related to teaching practice and development of the “theme-issue”. Initially focus will be given to the practice of teaching, developed in E.B.2, 3 Dr. Daniel de Matos school. Initial expectations will be presented, as well as the methodological choices made along the stage and its reasons. The activities made during the internship will be reported and I will emphasize ethics and professional component of the teacher’s profession. Then I will do a justification of the choices made. To finish the first part of this work I will make a reflective analysis of teaching practice. In the second part we have the “theme-issue” and its development, a document intended to be the guiding teaching practice and assist in solving the task behaviors of misuse by students. Will also serve to analyze and display conclusions about the problem that the current school, as an organization, faces, the indiscipline. Will be performed a little investigation, in which the objective is to analyze the perceptions of teachers in a public school on the severity of disruptive behaviors committed. The goal is to achieve some conclusion that can help / benefit school teachers in finding strategies and methodologies that can minimize the impact of such behaviors on normal class

The complexities of breast cancer desmoplasia

The stromal, or 'desmoplastic', responses seen histologically in primary breast carcinomas can vary from being predominantly cellular (fibroblasts/myofibroblasts) with little collagen to being a dense acellular tissue. The mechanisms underlying the stromal response are complex; paracrine activation of myofibroblasts by growth factors is important but the contribution of cytokines/chemokines should not be ignored. A recent xenograft study has proposed that platelet-derived growth factor (PDGF) is the initiator of the desmoplastic response, but this has not been confirmed by (limited) analyses in vivo. Further studies are required to elaborate the mechanisms of the desmoplastic response, to determine its role in breast cancer progression and whether it is the same for all carcinomas

Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. VIII: The Eighth Year (2015-2016)

Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 128 SU UMa-type dwarf novae observed mainly during the 2015-2016 season and characterized these objects. The data have improved the distribution of orbital periods, the relation between the orbital period and the variation of superhumps, the relation between period variations and the rebrightening type in WZ Sge-type objects. Coupled with new measurements of mass ratios using growing stages of superhumps, we now have a clearer and statistically greatly improved evolutionary path near the terminal stage of evolution of cataclysmic variables. Three objects (V452 Cas, KK Tel, ASASSN-15cl) appear to have slowly growing superhumps, which is proposed to reflect the slow growth of the 3:1 resonance near the stability border. ASASSN-15sl, ASASSN-15ux, SDSS J074859.55+312512.6 and CRTS J200331.3-284941 are newly identified eclipsing SU UMa-type (or WZ Sge-type) dwarf novae. ASASSN-15cy has a short (~0.050 d) superhump period and appears to belong to EI Psc-type objects with compact secondaries having an evolved core. ASASSN-15gn, ASASSN-15hn, ASASSN-15kh and ASASSN-16bu are candidate period bouncers with superhump periods longer than 0.06 d. We have newly obtained superhump periods for 79 objects and 13 orbital periods, including periods from early superhumps. In order that the future observations will be more astrophysically beneficial and rewarding to observers, we propose guidelines how to organize observations of various superoutbursts.Comment: 123 pages, 162 figures, 119 tables, accepted for publication in PASJ (including supplementary information