Related papers: A generalization of the Ekeland variational princi…
The covariance of the d'Alembert equation for acoustic phenomena -- which is a mechanical wave equation -- under the conventional Galilean transformation is demonstrated without the need to abandon the hypothesis that time is absolute in…
On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
Our purpose is to prove the uniqueness of the representation for $G$-martingales with finite variation.
We establish a large deviation principle for the smallest eigenvalue of a random matrix model composed of the sum of a GOE matrix and a diagonal matrix with an outlier. Our result generalizes and unifies previously studied cases.
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
A variational representation for functionals of G-Brownian motion is established by a finite-dimensional approximate technique. As an application of the variational representation, we obtain a large deviation principle for stochastic flows…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, H\"{o}lder, Maupertuis-Lagrange variational principles of integral style, the…
In this paper, we investigate the concepts of generalized twice differentiability and quadratic bundles of nonsmooth functions that have been very recently proposed by Rockafellar in the framework of second-order variational analysis. These…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
We find some extensions of the Kraft-Russell Generic Equivalence Theorem and using it we obtain a simple proof of a result of Dubouloz and Kishimoto.
We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
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…
Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this…
We consider the classical Inverse Function Theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from Variational Analysis when…
In this paper we prove a version of Lie-B\"acklund theorem for overdetermined systems of scalar PDEs, whose general solution depends on 1 function of 1 variable. This generalizes the case of involutive system of the second order on the…