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This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…
This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has…
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…
We provide a theory to establish the existence of nonzero solutions of perturbed Hammerstein integral equations with deviated arguments, being our main ingredient the theory of fixed point index. Our approach is fairly general and covers a…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
The main purpose of this note is to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we derive the existence theorems on a…
This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…
In this work we present an a posteriori analysis for classes of inconsistent, nonconforming schemes approximating elliptic problems. We show the estimates coincide with existing ones for interior penalty type discontinuous Galerkin…
A theorem is proved on the uniform estimation of the residual term of the asymptotic expansion with respect to a small parameter of the solution of the initial problem for a singularly perturbed differential operator weakly nonlinear…
While for deterministic systems, a counterexample to a property can simply be an error trace, counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative…
Let $G$ be a semisimple algebraic group. We develop a machinery for manipulation and manufacture of well-rounded families $\left\{ \mathcal{B}_{T}\right\} _{T>0}\subset G$ as they were defined in a work by A. Gorodnik and A. Nevo. The…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
The Erd\H{o}s discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem,…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
In this thesis, we explore several related topics broadly regarding the symmetry and geometric properties of nonlocal partial differential equations (PDE). This thesis is split into three parts. In the first part, we study two…
The $N$-color Ashkin-Teller model corresponds to $N$ Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the…