Related papers: New Interval Calculus with Application to Interval…
In the present paper we extend the multiplicative integral to complex-valued functions of complex variable. The main difficulty in this way, that is the multi-valued nature of the complex logarithm, is avoided by division of the interval of…
We introduce the volume function for hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence,…
In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…
In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms. Using a one parameter family of index functions based on the dilations of a given index function, a new class of scales…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
Inequalities play an important role in pure and applied mathematics. In particular, Opial inequality plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. It has…
This article develops sufficient conditions of local optimality for the scalar and vectorial cases of the calculus of variations. The results are established through the construction of stationary fields which keep invariant what we define…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new approach for change-point detection, which is an important field of investigation in various areas of applied sciences and…
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
In this work we extend to the interval-valued setting the notion of an overlap functions and we discuss a method which makes use of interval-valued overlap functions for constructing OWA operators with interval-valued weights. . Some…
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…