Related papers: Double Calculus
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we…
We introduce a two state vector formalism of quantum mechanics by generalizing Bell hidden variable model to higher dimensions and by attributing a physical significance, a state evolving backward in time, to the hidden variable. A simple…
Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R,C) to give a new proof of classical Montel's theorem, about continuous solutions of Fr\'{e}chet's functional equation…
We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.
After an elementary derivation of Bell's inequality, several forms of expectation functions for two-valued observables are discussed. Special emphasis is given to hypothetical stronger-than quantum expectation functions which give rise to a…
The Euler-Gauss linear transformation formula for the hypergeometric function was extended by Goursat for the case of logarithmic singularities. By replacing the perturbed Bessel differential equation by a monodromic functional equation,…
We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…
In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and study certain operators generalizing the classical umbral…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak…
We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated,…
This study addresses the often-overlooked issue of measurability at intermediate points when applying Taylor's theorems to random functions and random vectors (e.g., likelihood functions with respect to estimators) in statistics. Classical…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ f\left( x\right) $ is a sum of two functions $f\left( x\right) =f_{1}\left( x\right)…
The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and…
We study two techniques to obtain new families of classical and general Dual-Feasible Functions: A conversion from minimal Gomory--Johnson functions; and computer-based search using polyhedral computation and an automatic maximality and…
A very small amount of K\"ahler algebra (i.e. Clifford algebra of differential forms) in the real plane makes x + ydxdy emerge as a factor between the differentials of the Cartesian and polar coordinates, largely replacing the concept of…
The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.