8,767 research outputs found
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
-to-Glueball form factor and Glueball production in decays
We investigate transition form factors of meson decays into a scalar
glueball in the light-cone formalism. Compared with form factors of to
ordinary scalar mesons, the -to-glueball form factors have the same power in
the expansion of . Taking into account the leading twist light-cone
distribution amplitude, we find that they are numerically smaller than those
form factors of to ordinary scalar mesons. Semileptonic ,
and decays are subsequently investigated. We
also analyze the production rates of scalar mesons in semileptonic decays
in the presence of mixing between scalar and glueball states. The
glueball production in meson decays is also investigated and the LHCb
experiment may discover this channel. The sizable branching fraction in , or 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 -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 , transforms the wavefunction via a Mellin
transform on to the critial line . 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 or .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 -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 . Hopefully, in upcoming work, this will be
proved for any value of .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
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