Related papers: New Interval Calculus with Application to Interval…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
We introduce the interval Darboux delta integral (shortly, the $ID$ $\Delta$-integral) and the interval Riemann delta integral (shortly, the $IR$ $\Delta$-integral) for interval-valued functions on time scales. Fundamental properties of…
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…
In this article, we study the notion of gH-Hadamard derivative for interval-valued functions (IVFs) and its applications to interval optimization problems (IOPs). It is shown that the existence of gH-Hadamard derivative implies the…
We consider a general problem of the calculus of variations on time scales with a cost functional that is the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange delta-nabla…
Because of its ineffectiveness, the usual arithmetic Hilbert-Samuel formula is not applicable in the context of Diophantine Approximation. In order to overcome this difficulty, the present paper presents explicit estimates for arithmetic…
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
In this paper, we propose a numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval, that is, a finite value assigned to a divergent integral with an…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish…
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on…
This article proposes a new approach in the treatment of the Hilbert transform and some cases of the Fourier transform whose improper integrals are principal values. This approach may be useful for teaching these issues to undergraduate…
We propose a new, nonparametric approach to estimating the value function in reinforcement learning. This approach makes use of a recently developed representation of conditional distributions as functions in a reproducing kernel Hilbert…
Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some…
In this paper, we develop a novel approach to the Weingarten calculus by employing the notion of virtual isometries. Traditionally, Weingarten calculus provides explicit formulas for integrating polynomial functions over compact matrix…
We develop the calculus of variations on time scales for a functional that is the composition of a certain scalar function with the delta and nabla integrals of a vector valued field. Euler-Lagrange equations, transversality conditions, and…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…