Related papers: A partial order principle and vector variational p…

Vector operators based on robust order statistics have proved successful in digital multichannel imaging applications, particularly color image filtering and enhancement, in dealing with impulsive noise while preserving edges and fine image…

In this paper we prove some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on $\mathbb R^n$, which is a further study of the results in \cite{Dang-Deng-Qian}. In…

Pade Approximants can be used to go beyond Vector Meson Dominance in a systematic approximation. We illustrate this fact with the case of the pion vector form factor and extract values for the first two coefficients of its Taylor expansion.…

Let $h$ be a three times partially differentiable function on $R^n$, let $X=(X_1,\dots,X_n)$ be a collection of real-valued random variables and let $Z=(Z_1,\dots,Z_n)$ be a multivariate Gaussian vector. In this article, we develop Stein's…

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…

We prove several optimal-order error estimates for a finite-element method applied to an inhomogeneous Robin boundary value problem (BVP) for the Poisson equation defined in a smooth bounded domain in $\mathbb{R}^n$, $n=2,3$. The boundary…

We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal…

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…

To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…

The margin of victory of an election is a useful measure to capture the robustness of an election outcome. It also plays a crucial role in determining the sample size of various algorithms in post election audit, polling etc. In this work,…

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of…

This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…

In this paper we investigate a class of $2$-Hessian equations and establish a minimum principle for a $P$-function in the sense of L.E. Payne (see R. Sperb \cite{Sp81}). The analysis is based on a sharp matrix inequality providing an…

A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.

To improve convergence results obtained using a framework for unsymmetric meshless methods due to Schaback (Preprint G\"ottingen 2006), we extend, in two directions, the Sobolev bound due to Arcang\'eli et al. (Numer Math 107, 181-211,…

The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…

In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different…

This paper settles an open and challenging question pertaining to the design of simple and optimal high-order methods for solving smooth and monotone variational inequalities (VIs). A VI involves finding $x^\star \in \mathcal{X}$ such that…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

The ability to deal with complex geometries and to go to higher orders is the main advantage of space-time finite element methods. Therefore, we want to develop a solid background from which we can construct appropriate space-time methods.…