The a-graph coloring problem

AbstractNo proof of the 4-color conjecture reveals why it is true; the goal has not been to go beyond proving the conjecture. The standard approach involves constructing an unavoidable finite set of reducible configurations to demonstrate that a minimal counterexample cannot exist. We study the 4-color problem from a different perspective. Instead of planar triangulations, we consider near-triangulations of the plane with a face of size 4; we call any such graph an a-graph. We state an a-graph coloring problem equivalent to the 4-color problem and then derive a coloring condition that a minimal a-graph counterexample must satisfy, expressing it in terms of equivalence classes under Kempe exchanges. Through a systematic search, we discover a family of a-graphs that satisfy the coloring condition, the fundamental member of which has order 12 and includes the Birkhoff diamond as a subgraph. Higher-order members include a string of Birkhoff diamonds. However, no member has an applicable parent triangulation that is internally 6-connected, a requirement for a minimal counterexample. Our research suggests strongly that the coloring and connectivity conditions for a minimal counterexample are incompatible; infinitely many a-graphs meet one condition or the other, but we find none that meets both

In the eye of the beholder: What determines how people sort others into social classes?

Contrary to much conventional wisdom, this article shows that class is still used by people to sort others into groups, that this sorting is largely on the basis of income and occupation and that it occurs in conditions of both high and low income inequality. Uniquely, we use both open-ended survey questions and a factorial survey experiment to show that people from high (Britain) and low (Denmark) inequality countries are willing to define classes and they do so mainly in terms of job and income. Even though people in the two countries classify others using somewhat different class labels – with working class labels being used more frequently in Britain than in Denmark – we find a common underlying pattern to the classification. This indicates that class categorization takes place according to a strong underlying mental schema.FSW – Publicaties zonder aanstelling Universiteit Leide

Screening current effects in Josephson junction arrays

The purpose of this work is to compare the dynamics of arrays of Josephson junctions in presence of magnetic field in two different frameworks: the so called XY frustrated model with no self inductance and an approach that takes into account the screening currents (considering self inductances only). We show that while for a range of parameters the simpler model is sufficiently accurate, in a region of the parameter space solutions arise that are not contained in the XY model equations.Comment: Figures available from the author

Linear Responses in Time-dependent Hartree-Fock-Bogoliubov Method with Gogny Interaction

A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22 and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), and magnesium isotopes (A = 24 and 34). The isoscalar quadrupole and isovector dipole strength functions are calculated from the expectation values of the isoscalar quadrupole and isovector dipole moments.Comment: 10 pages, 13 figure

Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound state properties of 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(3He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a_0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading-order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the Effective Field Theory "without pions" at next-to-leading order for the root mean square charge radius of 3H of (1.6\pm 0.2) fm, for the 4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data of (0.10\mp 0.03) MeV is model independently attributed to higher order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.Comment: 24 pages revtex4, including 8 figures as .eps files embedded with includegraphicx, leading-order results added, calculations include the LO three-nucleon interaction explicitly, comment on Wigner bound added, minor modification

Produtividade e valor nutritivo de pasto de capim-elefante manejado sob princípios agroecológicos.

Objetivou-se avaliar o valor nutritivo do capim-elefante, quanto aos teores de PB e FDN e a digestibilidade in vitro da MS (DIVMS), submetido a algumas práticas agroecológicas. Foram usados dois piquetes (0,15 ha cada), onde foi estabelecido o capim-elefante, em 2001, com espaçamento entrelinhas de três metros. Nas entrelinhas, estabeleceram-se aveia (Avena strigosa Schreb.) e azevém (Lolium multiflorum Lam.) no período hibernal e, no estival, permitiu-se o desenvolvimento de espécies de crescimento espontâneo. A adubação foi feita com fertilizantes orgânicos (150 kg de N /ha). No período experimental (24/04/2004 a 05/05/2005), foram conduzidos sete pastejos. Os animais experimentais foram vacas da raça Holandesa que receberam, como complementação alimentar, 3,5 kg/dia de concentrado. Avaliaram-se a massa de forragem inicial, composição botânica do pasto e os componentes estruturais. Para as análises de valor nutritivo do pasto, foram feitas amostragens simulando o pastejo. O delineamento experimental foi de blocos ao acaso com duas repetições (piquetes) e sete tratamentos (pastejos). Os melhores resultados do valor nutritivo foram obtidos no período hibernal. Foram encontradas correlações negativas da PB e DIVMS e positivas da FDN com a biomassa de lâminas foliares do capim-elefante. O capim-elefante, manejado sob princípios agroecológicos, apresentou alto valor nutritivo e produtividade, tanto no verão quanto no inverno, possibilitando que a produção animal seja mais sustentável no decorrer do ano

Produção e valor nutritivo da forragem de capim-elefante em dois sistemas de produção.

Esta pesquisa foi realizada com o objetivo de avaliar a produção e o valor nutritivo da forragem de capimelefante cultivado em sistemas convencional e agroecológico. No sistema convencional, o capim-elefante foi estabelecido em cultivo exclusivo, em linhas com espaçamento de 1,4 m e, no sistema agroecológico, em linhas afastadas 3 m. Nas entrelinhas, estabeleceu-se azevém no período hibernal para desenvolvimento de espécies de crescimento espontâneo no período estival. Avaliaram-se a massa, a produção e a composição botânica e estrutural da forragem e a carga animal. Amostras de simulação de pastejo foram coletadas para determinação dos teores de proteína bruta e fibra em detergente neutro e da digestibilidade in vitro da matéria seca e matéria orgânica. O delineamento experimental foi o inteiramente casualizado com dois tratamentos (sistemas convencional e agroecológico) e duas repetições (piquetes). Valores mais elevados para massa de forragem, produção de forragem, taxa de acúmulo diário e carga animal foram observados no sistema convencional. A relação folha:colmo foi similar entre os sistemas. Valor mais elevado de proteína bruta foi observado no sistema agroecológico. O capim-elefante sob manejo convencional apresenta maior produção de forragem, com menores teores de proteína bruta. O sistema agroecológico apresenta melhor distribuição da produção de forragem no decorrer do ano