Related papers: Second-order variational equations for spatial poi…
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of…
We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…
The article provides a local classification of singularities of meromorphic second order linear differential equation with respect to analytic/meromorphic linear point transformations. It also addresses the problem of determining the Lie…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…
This paper aims to demonstrate the applicability of the L_2-integral transform to Partial Differential Equations (PDEs). Of special interest is section (6), which contains an application of the L_2-transform to a PDE of exponential squared…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
A general solution for a second-order linear constant coefficient dynamic equation with polynomial forcing on time scales is given.
Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.
We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…
We study the pair correlations of the logarithms of the integral values of quadratic norm forms at various scalings, proving the existence of pair correlation measures. We describe a surprising set of asymptotic behaviours when the scaling…
The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the…
We study parametric estimation for second order linear parabolic stochastic partial differential equations (SPDEs) in two space dimensions driven by two types of $Q$-Wiener processes based on high frequency spatio-temporal data. First, we…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…
We propose a two-step estimating procedure for generalized additive partially linear models with clustered data using estimating equations. Our proposed method applies to the case that the number of observations per cluster is allowed to…