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Correction terms generated in the correlator analysis due to multiplicity-dependent observable mean are investigated. A procedure for subtraction of such terms from calculated correlator estimates is suggested and the obtained results are…
We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite…
By taking the viewpoint of Brownian additive functionals, we extend an existing approximation theorem of the two-dimensional Laplacian singularly perturbed at the origin. The approximate operators are defined by adding a rescaled function…
This volume is a collection of six papers on the use of auxiliary information and 'a priori' values in construction of improved estimators. The work included here will be of immense application for researchers and students who emply…
We describe a simple way of constructing exponentially growing solutions of the second order systems with the Laplacian as the principal term.
Estimation of the population total of a variable can be improved by calibration on a set of auxiliary variables. It is difficult to establish that such a set of variables is sufficient, that estimation could not be improved by calibration…
This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…
We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical results in regard to the generalized a posteriori error…
A novel definition of the Laplacian of 1/r is presented, suitable for advanced undergraduates.
Modified estimators for the contribution rates of population eigenvalues are given under an elliptically contoured distribution. These estimators decrease the bias of the classical estimator, i.e. the sample contribution rates. The…
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…
In recent contributions, algebraic multigrid methods have been designed and studied from the viewpoint of the spectral complementarity. In this note we focus our efforts on specific applications and, more precisely, on large linear systems…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of the problem and prove the convergence together with a priori…
Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…
In this paper, we give a method to construct bimetric conformal invarints by the linear metric perturbations and the conformal invarints. And we compute the metric perturbations of the Connes conformal invarints and the conformal Laplacian.…
An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
The aim of this paper is two-fold: first, we look at the fractional Laplacian and the conformal fractional Laplacian from the general framework of representation theory on symmetric spaces and, second, we construct new boundary operators…
We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.