Related papers: Symmetric Differentiation on Time Scales

Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

Time scales are a model of time, where the continuous and the discrete time cases are considered and merged into the same framework. In this paper some basic definitions of the time scale calculus are presented. Simultaneously, a package in…

In this paper we considered the most general form of non conformally flat cylindrically symmetric non-static space-times to study proper conformal motions using direct integration technique. We have shown that very special classes for…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue…

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…

The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…

Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…

We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…

Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented.…

Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…

We introduce a more general discrete fractional operator, given by convex linear combination of the delta and nabla fractional sums. Fundamental properties of the new fractional operator are proved. As particular cases, results on delta and…

For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these…

Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…

In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…

With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…

A conformable time-scale fractional calculus of order $\alpha \in ]0,1]$ is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular…