Residence time and collision statistics for exponential flights: the rod problem revisited

Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.Comment: 9 pages, 8 figure

BB-to-Glueball form factor and Glueball production in BB decays

We investigate transition form factors of $B$ meson decays into a scalar glueball in the light-cone formalism. Compared with form factors of $B$ to ordinary scalar mesons, the $B$-to-glueball form factors have the same power in the expansion of $1/m_B$. Taking into account the leading twist light-cone distribution amplitude, we find that they are numerically smaller than those form factors of $B$ to ordinary scalar mesons. Semileptonic $B\to Gl\bar\nu$, $B\to Gl^+l^-$ and $B_s\to Gl^+l^-$ decays are subsequently investigated. We also analyze the production rates of scalar mesons in semileptonic $B$ decays in the presence of mixing between scalar $\bar qq$ and glueball states. The glueball production in $B_c$ meson decays is also investigated and the LHCb experiment may discover this channel. The sizable branching fraction in $B_c\to (\pi^+\pi^-)l^-\bar\nu$, $B_c\to (K^+K^-)l^-\bar\nu$ or $B_c\to (\pi^+\pi^-\pi^+\pi^-)l^-\bar\nu$ could be a clear signal for a scalar glueball state.Comment: 17 pages, 3 figure, revtex

Functions of several Cayley-Dickson variables and manifolds over them

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated

The Quantum Mellin transform

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.Comment: 23 pages, 6 Figure

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.Comment: 55 pages, 53 reference

Functional characterization of generalized Langevin equations

We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the noise, neither the fluctuation dissipation theorem. We found that the characteristic functional of the linear process can be expressed in terms of noise's functional and the Green function of the deterministic (memory-like) dissipative dynamics. This object allow us to get a procedure to calculate all the Kolmogorov hierarchy of the non-Markov process. As examples we have characterized through the 1-time probability a noise-induced interplay between the dissipative dynamics and the structure of different noises. Conditions that lead to non-Gaussian statistics and distributions with long tails are analyzed. The introduction of arbitrary fluctuations in fractional Langevin equations have also been pointed out

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Couples that work full time and are happily married : myth or reality?

Este trabalho apresenta parte de uma pesquisa quantitativa cujo principal objetivo foi avaliar a satisfação no casamento de homens e mulheres que optaram por relacionamentos de duplo trabalho. Participaram do estudo 222 homens e 222 mulheres casados/as, funcionários/as em diversas instituições públicas de Brasília - DF. A maior concentração de respondentes de ambos os sexos está na faixa etária entre 31 a 40 anos. Os participantes responderam a um questionário demográfico e à Escala de Ajustamento Diádico - DAS. Os resultados mostraram que a maioria dos participantes está satisfeita com seus relacionamentos, sendo que as mulheres apresentaram média de satisfação inferior à dos homens. Quanto à percepção do futuro do relacionamento, ficou evidente o comprometimento de homens e mulheres em investirem na manutenção do casamento. Os resultados questionam a idéia vigente de falência do casamento e da família e apontam para uma transformação das relações. _________________________________________________________________________________________________________ ABSTRACTThis paper presents part of a quantitative research regarding marriages in which men and women are engaged in full time work. The main objective was to evaluate marital satisfaction in dual worker couples. Subjects were 222 married men and 222 married women that work in several public institutions in Brasilia - DF. The majority of the participants were between 31 to 40 years old. They answered a demographic questionnaire and the Dyadic Adjustment Scale - DAS. Results showed that the majority of participants were satisfied with their relationships although women presented lower satisfaction scores then men. Regarding the perception of the future of the relationship, the results showed that subjects were committed to preserve their marriage. These data question current ideas that marriages and families are outmoded and point in the direction of a transformation in interpersonal relationships

Hilbert--Schmidt volume of the set of mixed quantum states

We compute the volume of the convex N^2-1 dimensional set M_N of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area of the boundary of this set is also found and its ratio to the volume provides an information about the complex structure of M_N. Similar investigations are also performed for the smaller set of all real density matrices. As an intermediate step we analyze volumes of the unitary and orthogonal groups and of the flag manifolds.Comment: 13 revtex pages, ver 3: minor improvement