相关论文: Reconsideration of the multivariate moment problem…
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications, including global optimization of polynomials and rational…
In this paper we develop a new approximation method valid for a wide family of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a reduced set of ordinary differential equations for a finite set of parameters measuring…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the…
A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
We construct a class of homogeneous Cantor-Moran measures with all contraction ratios being reciprocal of integers, and prove that they are pointwise absolutely normal. Our approach relies on methods developed by Davenport, Erd{\H{o}}s, and…
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary…
We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
The present paper is a sequel to papers dealing with recent developments on the issue of `quantum measurement'. In this paper `measurement within the domain of application of quantum mechanics' is treated as a \emph{quantum mechanical}…
In this paper an explicit algorithm is proposed for solving an equilibrium problem whose associated bifunction is pseudomonotone and satisfies a Lipschitz-type condition. Contrary to many algorithms, our algorithm is done without using…
We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problem \begin{equation}\label{ab eqn} \begin{cases} \partial_t u(t,x)=\psi(t,-i\nabla)u(t,x)+f(t,x),\quad &(t,x)\in(0,T)\times\mathbb{R}^d,\\…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
The emphasis of this course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic functions and on the theory of positive closed currents. Applications of…
We generalize a recent class of tests for univariate normality that are based on the empirical moment generating function to the multivariate setting, thus obtaining a class of affine invariant, consistent and easy-to-use goodness-of-fit…
We extend the domain of the Karcher mean $\Lambda$ of positive operators on a Hilbert space to $L^1$-Borel probability measures on the cone of positive operators equipped with the Thompson part metric. We establish existence and uniqueness…