Related papers: Multidimensional Lambert-Euler inversion and vecto…

We study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The L-M method transforms the Tikhonov regularized…

We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms…

A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…

We found a new formulation to the Euler-Lagrange equation of the Willmore functional for immersed surfaces in ${\R}^m$. This new formulation of Willmore equation appears to be of divergence form, moreover, the non-linearities are made of…

The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\lambda \phi^4_2$-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for…

This paper investigates the generalized convexity properties of the Lambert $W$ function, defined as the solution to $W(z)e^{W(z)}=z$. Focusing on $H_{p,q}$-convexity and concavity with respect to H\"older means, we derive necessary and…

Let $\Omega$ be a bounded, smooth domain of $\mathbb{R}^n, n \ge 3$ and $\lambda \ge 0$. We consider the celebrated Br\'ezis-Nirenberg problem: \begin{equation}\label{eq:critlambda:abs} \tag{*} \left\{\begin{aligned} -\Delta u -\lambda u &…

We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, namely, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM$_{01}$ mode) in a cylindrical metallic…

A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…

We prove existence of radially symmetric solutions and validity of Euler-Lagrange necessary conditions for a class of variational problems such that neither direct methods nor indirect methods of Calculus of Variations apply. We obtain…

{We consider alternating minimization procedures for convex optimization problems with variable divided in many block, each block being amenable for minimization with respect to its variable with freezed other variables blocks. In the case…

We derive formulas for the Coulomb matrix within the full-potential linearized augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central ingredient in implementations of many-body perturbation theory, such as the Hartree-Fock and…

Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main goal are…

The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…

Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…

We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stochastic coefficients, and certain terms in the expansion…

We study the Euler-Lagrange equation of the dynamical Boulatov model which is a simplicial model for 3d Euclidean quantum gravity augmented by a Laplace-Beltrami operator. We provide all its solutions on the space of left and right…

This article study the fractional Hamiltonian systems \begin{eqnarray}\label{00} {_{t}}D_{\infty}^{\alpha}({_{-\infty}}D_{t}^{\alpha}u) + \lambda L(t)u = \nabla W(t, u), \;\;t\in \mathbb{R}, \end{eqnarray} where $\alpha \in (1/2, 1)$,…

This paper deals with new continuous and compact embedding theorems for the fractional Musielak-Sobolev spaces in $\mathbb{R}^d$. As an application, using the variational methods, we obtain the existence of nontrivial weak solution for the…

In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…