Berry phase in homogeneous K\"ahler manifolds with linear Hamiltonians

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of {\em classical} objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.Comment: LaTeX fil

Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n

The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.Comment: LaTeX, 3 figures, 12 page

On Motives Associated to Graph Polynomials

The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions.Comment: 54

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament

Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Componentes da variância genética no cruzamento de feijões andinos e mesoamericanos.

Quando os cruzamentos são viáveis, frequentemente a população obtida apresenta desempenho abaixo da média dos pais para produtividade de grãos. Entretanto a partir do cruzamento entre as linhagens ESAL 686 (Andina) e Carioca MG (Mesoamericana) foram obtidas linhagens com bom desempenho (BRUZI et al., 2007). Seria importante estimar os componentes da variância genética e fenotípica desse cruzamento a fim de verificar se a variabilidade obtida é diferente do que é normalmente observado em outros cruzamentos de feijoeiro do mesmo conjunto gênico.CONAFE

Análise genética do início do florescimento em feijoeiro pelo "Triple Test Cross".

objetivo deste trabalho foi detectar a presença de epistasia e estimar os componentes da variância genética para o caráter início do florescimento em populações de feijoeiro (Phaseolus vulgaris L.) oriundas de genitores de diferentes conjuntos gênicos (pools gênicos)

Potencial de populações segregantes de feijoeiro oriundas de cruzamentos intra e inter conjuntos gênicos.

Esse trabalho teve como objetivo comparar o potencial de populações segregantes de feijoeiro oriundas do cruzamento de genitores de mesmo conjunto gênico e de conjuntos gênicos diferentes por meio de estimativas de alguns parâmetros genéticos e fenotípicos

Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem