Related papers: Variational principles using a non-symmetric non-t…
Elaboration of some fundamental relations in three dimensional quantum mechanics is considered taking into account the restricted character of areas in radial distance. In such cases the boundary behavior of the radial wave function and…
We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators. As an application, we explore some consequences of our…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
Nonlinear energy-conserving drift-fluid equations that are suitable to describe self-consistent finite-beta low-frequency electromagnetic (drift-Alfven) turbulent fluctuations in a nonuniform, anisotropic, magnetized plasma are derived from…
We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincar\'e equations that naturally includes…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such…
I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
This paper completes and comments on some aspects of our previous publications. In ref [1], we have derived a set of space-time transformations referred to as the extended space-time transformations. These transformations, which assume the…
We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…
We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order p for any p $\ge$ 1, and we give some…
We prove a quenched almost sure invariance principle for certain classes of random distance expanding dynamical systems which do not necessarily exhibit uniform decay of correlations.
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a…
We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogous to Bernstein's theorem on non-parametric minimal surfaces.…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…
In this note, we prove a new uncertainty principle for functions with radial symmetry by differentiating a radial version of the Stein-Weiss inequality. The difficulty is to prove the differentiability in the limit of the best constant…