Related papers: Generalized Leibniz rules and Lipschitzian stabili…
Let $X$ be a compact strictly pseudoconvex embeddable Cauchy-Riemann manifold and let $T_P$ be the Toeplitz operator on $X$ associated with a first-order pseudodifferential operator $P$. In our previous work we established the asymptotic…
Khasminski's \cite{chas1980stochastic} showed that many of the asymptotic stability and the integrability properties of the solutions to the Stochastic Differential Equations (SDEs) can be obtained using Lyapunov functions techniques. These…
In this paper, our focus lies on the study of the second-order variational analysis of orthogonally invariant matrix functions. It is well-known that an orthogonally invariant matrix function is an extended-real-value function defined on…
We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…
The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.
Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are…
Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials,…
It is hereby established that the set of Lipschitz functions $f:\mathcal{U}\rightarrow \mathbb{R}$ ($\mathcal{U}$ nonempty open subset of $\ell_{d}^{1}$) with maximal Clarke subdifferential contains a linear subspace of uncountable…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
The Strang-Fix conditions are necessary and sufficient to reproduce spaces of algebraic polynomials up to some degree by integer shifts of compactly supported functions. W. Dahmen and Ch. Micchelli (Linear Algebra Appl. 52/3:217-234, 1983)…
In this paper, we study the properties of integral functionals induced on $L^1_E (S,\mu)$ by closed convex functions on a Euclidean space $E$. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We…
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
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…
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…
Given a multimodal interval map $f:I \to I$ and a H\"older potential $\phi:I \to \mathbb{R}$, we study the dimension spectrum for equilibrium states of $\phi$. The main tool here is inducing schemes, used to overcome the presence of…