Search results for "Mathematical analysis"
showing 10 items of 2409 documents
p-harmonic coordinates for Hölder metrics and applications
2017
We show that on any Riemannian manifold with H¨older continuous metric tensor, there exists a p-harmonic coordinate system near any point. When p = n this leads to a useful gauge condition for regularity results in conformal geometry. As applications, we show that any conformal mapping between manifolds having C α metric tensors is C 1+α regular, and that a manifold with W1,n ∩ C α metric tensor and with vanishing Weyl tensor is locally conformally flat if n ≥ 4. The results extend the works [LS14, LS15] from the case of C 1+α metrics to the H¨older continuous case. In an appendix, we also develop some regularity results for overdetermined elliptic systems in divergence form. peerReviewed
Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
2013
We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the hig…
Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
2016
We analyze the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to their form factor expansion. Its explicit form is obtained from a saddle-point analysis of the corresponding double integral. It describes the propagation of a wave front with velocity $v_{c_1}$ which is found to be the maximal possible group velocity. Like in wave propagation in dispersive media the wave front is preceded by a precursor running ahead with velocity $v_{c_2}$. As a special case we obta…
Partition function of the trigonometric SOS model with reflecting end
2010
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Corrigendum: Partial inner product spaces, metric operators and generalized hermiticity
2013
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Wardowski conditions to the coincidence problem
2015
In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T, S:X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as well as a rate of convergence for this iteration scheme. Finally, we shall apply our results to study the existence and uniqueness of a solution as well as the convergence of the Picard-Juncgk iteration process toward the solution of a second order differential equation. Ministerio de Economía y Competi…
Posterior moments and quantiles for the normal location model with Laplace prior
2021
We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter η in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of η.
Hitting straight lines by compound Poisson process paths
1990
In a recent article Mallows and Nair (1989,Ann. Inst. Statist. Math.,41, 1–8) determined the probability of intersectionP{X(t)=αt for somet≥0} between a compound Poisson process {X(t), t≥0} and a straight line through the origin. Using four different approaches (direct probabilistic, via differential equations and via Laplace transforms) we extend their results to obtain the probability of intersection between {X(t), t≥0} and arbitrary lines. Also, we display a relationship with the theory of Galton-Watson processes. Additional results concern the intersections with two (or more) parallel lines.
Exact and approximate calculations for the conductivity of sandstones
1999
We analyze a three-dimensional pore space reconstruction of Fontainebleau sandstone and calculate from it the eective conductivity using local porosity theory. We compare this result with an exact calculation of the eective conductivity that solves directly the disordered Laplace equation. The prediction of local porosity theory is in good quantitative agreement with the exact result. c 1999 Elsevier Science B.V. All rights reserved.
A generalization of the inhomogeneity measure for point distributions to the case of finite size objects
2008
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L we use a sliding cell-sampling approach. For given patterns, particularly in the case of clusters polydispersed in size, the comparison between the statistical measure and the entropic one reveals differences in detection of the first peak while at other sca…