177,736 research outputs found
Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case
The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary differential equations obtained by spatial finite-element discretisation of linear parabolic initial-boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments
Parabolic and Hyperbolic Contours for Computing the Bromwich Integral
Some of the most effective methods for the numerical inversion of the Laplace transform are based on the approximation of the Bromwich contour integral. The accuracy of these methods often hinges on a good choice of contour, and several such contours have been proposed in the literature. Here we analyze two recently proposed contours, namely a parabola and a hyperbola. Using a representative model problem, we determine estimates for the optimal parameters that define these contours. An application to a fractional diffusion equation is presented.\ud
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JACW was supported by the National Research Foundation in South Africa under grant FA200503230001
Stable marked point processes
In many contexts such as queuing theory, spatial statistics, geostatistics
and meteorology, data are observed at irregular spatial positions. One model of
this situation involves considering the observation points as generated by a
Poisson process. Under this assumption, we study the limit behavior of the
partial sums of the marked point process , where X(t) is a
stationary random field and the points t_i are generated from an independent
Poisson random measure on . We define the sample
mean and sample variance statistics and determine their joint asymptotic
behavior in a heavy-tailed setting, thus extending some finite variance results
of Karr [Adv. in Appl. Probab. 18 (1986) 406--422]. New results on subsampling
in the context of a marked point process are also presented, with the
application of forming a confidence interval for the unknown mean under an
unknown degree of heavy tails.Comment: Published at http://dx.doi.org/10.1214/009053606000001163 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Foundations of Fractional Calculus on Time Scales
Bakalářská práce pojednává o zlomkovém kalkule na časových škálach, přesněji - zavádí zlomkový kalkulus na časových škálach a taktéž vyšetřuje jednoznačnost axiomatické definice zavádějící mocninné funkce. Po zavedení základních pojmů je předmětem diskuze hlavně zobecněná Laplaceova transformace a důkaz jednoznačnosti zobecněné Laplaceovy transformace, která je použita jako nástroj pro dokázání jednoznačnosti zlomkových mocniných funkcií na časových škálach.The bachelor thesis concerns fractional calculus on time scales, more precisely, it introduces fractional calculus on time scales and also investigates the property of uniqueness of the axiomatic definition of the power functions. After introducing basic concepts, the subject of discussion is mostly generalized Laplace transform as well as proof of uniqueness of generalized Laplace transform, which is used as a tool to proving the uniqueness of fractional power functions on time scales.
Modified Laplace transformation method and its application to the anharmonic oscillator
We apply a recently proposed approximation method to the evaluation of
non-Gaussian integral and anharmonic oscillator. The method makes use of the
truncated perturbation series by recasting it via the modified Laplace integral
representation. The modification of the Laplace transformation is such that the
upper limit of integration is cut off and an extra term is added for the
compensation. For the non-Gaussian integral, we find that the perturbation
series can give accurate result and the obtained approximation converges to the
exact result in the limit ( denotes the order of perturbation
expansion). In the case of anharmonic oscillator, we show that several order
result yields good approximation of the ground state energy over the entire
parameter space. The large order aspect is also investigated for the anharmonic
oscillator.Comment: 26 pages including tables, Late
The Behaviour of the Green Function for the BFKL Pomeron with Running Coupling
We analyse here in LO the physical properties of the Green function solution
for the BFKL equation. We show that the solution obeys the orthonormality
conditions in the physical region and fulfills the completeness requirements.
The unintegrated gluon density is shown to consists of a set of few poles with
parameters which could be determined by comparison with the DIS data of high
precision
Shocks, Superconvergence, and a Stringy Equivalence Principle
We study propagation of a probe particle through a series of closely situated
gravitational shocks. We argue that in any UV-complete theory of gravity the
result does not depend on the shock ordering - in other words, coincident
gravitational shocks commute. Shock commutativity leads to nontrivial
constraints on low-energy effective theories. In particular, it excludes
non-minimal gravitational couplings unless extra degrees of freedom are
judiciously added. In flat space, these constraints are encoded in the
vanishing of a certain "superconvergence sum rule." In AdS, shock commutativity
becomes the statement that average null energy (ANEC) operators commute in the
dual CFT. We prove commutativity of ANEC operators in any unitary CFT and
establish sufficient conditions for commutativity of more general light-ray
operators. Superconvergence sum rules on CFT data can be obtained by inserting
complete sets of states between light-ray operators. In a planar 4d CFT, these
sum rules express (a-c)/c in terms of the OPE data of single-trace operators.Comment: 93 pages plus appendice
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