Related papers: Borwein-Preiss Vector Variational Principle

The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…

Fix a container polygon $P$ in the plane and consider the convex hull $P_n$ of $n\geq 3$ independent and uniformly distributed in $P$ random points. In the focus of this paper is the vertex number of the random polygon $P_n$. The precise…

One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…

We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…

We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…

We obtain the affine Euler-Poincar\'e equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin…

We apply the borderline Sobolev inequalities of Bourgain-Brezis to the vorticity equation and Navier-Stokes equation in 2D. We take the initial vorticity to be in the space of functions of Bounded variation(BV). We obtain the subsequent…

We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu (1935) and Bhatia and Davis (2000) concerning measures on the line to several dimensions. This is…

Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…

The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…

In this paper we examine an alternative formulation of the gauge principle in which the emphasis is shifted from the symmetry transformations to their generators. We show that the gauge principle can be entirely reformulated in terms of…

We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…

Two classes of fractional type variable weights are established in this paper. The first kind of weights ${A_{\vec p( \cdot ),q( \cdot )}}$ are variable multiple weights, which are characterized by the weighted variable boundedness of…

Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…

All finite element methods, as well as much of the Hilbert-space theory for partial differential equations, rely on variational formulations, that is, problems of the type: find $u\in V$ such that $a(v,u) = l(v)$ for each $v\in L$, where…

We aim to establish Bowen's equations for upper capacity invariance pressure and Pesin-Pitskel invariance pressure of discrete-time control systems. We first introduce a new invariance pressure called induced invariance pressure on…

Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis,…

We introduce the metric space valued in partially ordered groups, and define the convergence of sequences and the multi-valued weak contractions, etc., on the space. We then establish endpoint theorems for the defined maps. Our…

First and second order corrections for the scattering of different types of particles by a weak gravitational field, treated as an external field, are calculated. These computations indicate a violation of the Equivalence Principle: to…

Let $\pi:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted…