Related papers: Redheffer representations and relaxed commutant li…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In modern data analysis, one is frequently faced with statistical inference problems involving massive datasets. Processing such large datasets is usually viewed as a substantial computational challenge. However, if data are a…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with…
In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian…
The Koopman operator framework offers a way to represent a nonlinear system as a linear one. The key to this simplification lies in the identification of eigenfunctions. While various data-driven algorithms have been developed for this…
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with…
We consider the nonlinear Cauchy problem for $ \Psi $- Hilfer fractional differential equations and investigate the existence, interval of existence and uniqueness of solution in the weighted space of functions. The continuous dependence of…
The K-partitioning problem consists of partitioning the vertices of a graph in K sets so as to minimize a function of the edge weights. We introduce a linear mixed integer formulation with edge variables and representative variables. We…
Optimizing Neural networks is a difficult task which is still not well understood. On the other hand, fixed representation methods such as kernels and random features have provable optimization guarantees but inferior performance due to…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
Exhausters are families of compact, convex sets which provide minmax or maxmin representations of positively homogeneous functions and they are efficient tools for the study of nonsmooth function. Upper and lower exhausters of positively…
We refine the understanding of continuous dependence on coefficients of solution operators under the nonlocal $H$-topology viz Schur topology in the setting of evolutionary equations in the sense of Picard. We show that certain components…
The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" method, which…
In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized…
With the help of a useful mathematical tool, the polar decomposition of closed operators, and a simple observation, i.e. the unique relation between tensor-product states and compact operators, we manage to give a compact and coherent…
We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…