相关论文: Metric Regularity of the Sum of Multifunctions and…
We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in super-critical dimensions. As a consequence of such a…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
Our work builds on known results for k-uniform hypergraphs including the existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here is a theory of measures on ultraproduct spaces which establishes a correspondence…
We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in…
The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Assertions on this topic have been proven. The implementation of…
It has often been observed that the Multifractal Formalism and the Large Deviation Principles are intimately related. In fact, Multifractal Formalism was heuristically derived using the Large Deviations ideas. In numerous examples in which…
In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.
Metrics have been used to investigate the relationship between wavefunction distances and density distances for families of specific systems. We extend this research to look at random potentials for time-dependent single electron systems,…
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
In the setting of a metric space equipped with a doubling measure and supporting a Poincar\'e inequality, and based on results by Bj\"orn and Shanmugalingam (2007), we show that functions of bounded variation can be extended from any…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing metric regularity of a (set-valued) mapping. First, we demonstrate that one should always use directly the so-called general…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…