308 research outputs found
On second order elliptic equations with a small parameter
The Neumann problem with a small parameter
is
considered in this paper. The operators and are self-adjoint second
order operators. We assume that has a non-negative characteristic form
and is strictly elliptic. The reflection is with respect to inward
co-normal unit vector . The behavior of
is effectively described via
the solution of an ordinary differential equation on a tree. We calculate the
differential operators inside the edges of this tree and the gluing condition
at the root. Our approach is based on an analysis of the corresponding
diffusion processes.Comment: 28 pages, 1 figure, revised versio
Multiplicative decompositions and frequency of vanishing of nonnegative submartingales
In this paper, we establish a multiplicative decomposition formula for
nonnegative local martingales and use it to characterize the set of continuous
local submartingales Y of the form Y=N+A, where the measure dA is carried by
the set of zeros of Y. In particular, we shall see that in the set of all local
submartingales with the same martingale part in the multiplicative
decomposition, these submartingales are the smallest ones. We also study some
integrability questions in the multiplicative decomposition and interpret the
notion of saturated sets in the light of our results.Comment: Typos corrected. Close to the published versio
Prescription-induced jump distributions in multiplicative Poisson processes
Generalized Langevin equations (GLE) with multiplicative white Poisson noise
pose the usual prescription dilemma leading to different evolution equations
(master equations) for the probability distribution. Contrary to the case of
multiplicative gaussian white noise, the Stratonovich prescription does not
correspond to the well known mid-point (or any other intermediate)
prescription. By introducing an inertial term in the GLE we show that the Ito
and Stratonovich prescriptions naturally arise depending on two time scales,
the one induced by the inertial term and the other determined by the jump
event. We also show that when the multiplicative noise is linear in the random
variable one prescription can be made equivalent to the other by a suitable
transformation in the jump probability distribution. We apply these results to
a recently proposed stochastic model describing the dynamics of primary soil
salinization, in which the salt mass balance within the soil root zone requires
the analysis of different prescriptions arising from the resulting stochastic
differential equation forced by multiplicative white Poisson noise whose
features are tailored to the characters of the daily precipitation. A method is
finally suggested to infer the most appropriate prescription from the data
Multiple G-It\^{o} integral in the G-expectation space
In this paper, motivated by mathematic finance we introduce the multiple
G-It\^{o} integral in the G-expectation space, then investigate how to
calculate. We get the the relationship between Hermite polynomials and multiple
G-It\^{o} integrals which is a natural extension of the classical result
obtained by It\^{o} in 1951.Comment: 9 page
Lorentz-covariant deformed algebra with minimal length
The -dimensional two-parameter deformed algebra with minimal length
introduced by Kempf is generalized to a Lorentz-covariant algebra describing a
()-dimensional quantized space-time. For D=3, it includes Snyder algebra
as a special case. The deformed Poincar\'e transformations leaving the algebra
invariant are identified. Uncertainty relations are studied. In the case of D=1
and one nonvanishing parameter, the bound-state energy spectrum and
wavefunctions of the Dirac oscillator are exactly obtained.Comment: 8 pages, no figure, presented at XV International Colloquium on
Integrable Systems and Quantum Symmetries (ISQS-15), Prague, June 15-17, 200
The Local Time Distribution of a Particle Diffusing on a Graph
We study the local time distribution of a Brownian particle diffusing along
the links on a graph. In particular, we derive an analytic expression of its
Laplace transform in terms of the Green's function on the graph. We show that
the asymptotic behavior of this distribution has non-Gaussian tails
characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included
Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions,
i.e., including a linear pseudoscalar potential and quadratic scalar and vector
potentials which have equal or opposite signs. We consider positive and
negative quadratic potentials and discuss in detail their bound-state solutions
for fermions and antifermions. The main features of these bound states are the
same as the ones of the generalized three-dimensional relativistic harmonic
oscillator bound states. The solutions found for zero pseudoscalar potential
are related to the spin and pseudospin symmetry of the Dirac equation in 3+1
dimensions. We show how the charge conjugation and chiral
transformations relate the several spectra obtained and find that for massless
particles the spin and pseudospin symmetry related problems have the same
spectrum, but different spinor solutions. Finally, we establish a relation of
the solutions found with single-particle states of nuclei described by
relativistic mean-field theories with scalar, vector and isoscalar tensor
interactions and discuss the conditions in which one may have both nucleon and
antinucleon bound states.Comment: 33 pages, 10 figures, uses revtex macro
Finite groups with all minimal subgroups solitary
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order
Comment on ``the Klein-Gordon Oscillator''
The different ways of description of the particle with oscillator-like
interaction are considered. The results are in conformity with the previous
paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p
Approximation of Feynman path integrals with non-smooth potentials
We study the convergence in of the time slicing approximation of
Feynman path integrals under low regularity assumptions on the potential.
Inspired by the custom in Physics and Chemistry, the approximate propagators
considered here arise from a series expansion of the action. The results are
ultimately based on function spaces, tools and strategies which are typical of
Harmonic and Time-frequency analysis.Comment: 18 page
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