Related papers: On Lipschitzian properties of implicit multifuncti…
Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning…
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…
The artefact is dedicated towards the inspection of nonlinear fractional differential systems involving Riemann-Liouville derivative with higher order and fixed lower limit, including non-instantaneous impulses for existence and uniqueness…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
We study the presence of abelian discrete symmetries in globally consistent orientifold compactifications based on rational conformal field theory. We extend previous work [1] by allowing the discrete symmetries to be a linear combination…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
The classical as well as non commutative Korovkin-type theorems deal with convergence of positive linear maps with respect to modes of convergences such as norm convergence and weak operator convergence. In this article, Korovkin-type…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan-K\"ahler theorem. Guillemin normal form establishes that the…
In this paper, by modifying significantly the Friedrichs-Gross mollifier technique and/or using the Lasry-Lions regularization technique together with some carefully chosen cut-off functions, for the first time we construct explicitly…
We prove some fundamental properties of mu-differentiable functions. A new notion of local minimizer and maximizer is introduced and several extremum conditions are formulated using the language of nonstandard analysis.
We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
We show subellipticity of the d-bar Neumann problem on domains with Lipschitz boundary in the presence of plurisubharmonic functions with Hessians of algebraic growth. In particular, a subelliptic estimate holds near a point where the…
In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed…
We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary…
Special exotic class of dynamical systems~ -- the implicit maps~ -- is considered. Such maps, particularly, can appear as a result of using of implicit and semi-implicit iterative numerical methods. In the present work we propose the…