Related papers: Symmetric Differentiation on Time Scales
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along…
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…
Different symmetry formalisms for difference equations on lattices are reviewed and applied to perform symmetry reduction for both linear and nonlinear partial difference equations. Both Lie point symmetries and generalized symmetries are…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
We introduce the $\alpha,\beta$-symmetric difference derivative and the $\alpha,\beta$-symmetric N\"orlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward…
Let X be a topological space. The closure of \Delta = {(x, x) : x \in X} in X \times X is a symmetric relation on X. We characterise those equivalence relations on an infinite set that arise as the closure of the diagonal with respect to a…
Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. In a recent series of papers, we have studied methods to break value symmetries. Our results…
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…
It is shown that a contraction on a Hilbert space is complex symmetric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications are given to the description of complex…
Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over…
Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar…
As an efficient mathematical tool, monotonicity rules play an extremely crucial role in the real analysis field. In this paper, we explore some monotonicity rules for quotient of Delta, Nabla and Diamond-Alpha integrals with variable upper…
Perusal of research articles that deal with the topic of matrix calculus reveal two different approaches to calculation of the gradient of a real-valued function of a symmetric matrix leading to two different results. In the mechanics and…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
This letter investigates the Lie point symmetries and conserved quantities of the Lagrangian systems on time scales, which unify the Lie symmetries of the two cases for the continuous and the discrete Lagrangian systems. By defining the…