Related papers: Orbital reducibility and a generalization of lambd…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
Dilution effects on the long-range ordered state of the doubly degenerate $e_g$ orbital are investigated. Quenched impurities without the orbital degree of freedom are introduced in the orbital model where the long-range order is realized…
In this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of $\beta$-reduction in the polymorphic $\lambda$-calculus, to prove the termination of various kinds of rewrite relations on…
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…
Let $(X_n,d_n),\,n\in\Bbb N$ be a sequence of pseudo-metric spaces, $p\ge 1$. For $x,y\in\prod_{n\in\Bbb N}X_n$, let $(x,y)\in E((X_n)_{n\in\Bbb N};p)\Leftrightarrow\sum_{n\in\Bbb N}d_n(x(n),y(n))^p<+\infty$. For Borel reducibility between…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
We discuss the use of group symmetries in optimisation, in particular with respect to the structure of subdifferential and projection operators. This allows us to generalise a classic result of Adrian Lewis regarding the characterisation of…
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations…
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the…
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…
We introduce notions of continuous orbit equivalence and strong (respective, weak) continuous orbit equivalence for automorphism systems of \'{e}tale equivalence relations, and characterize them in terms of the semi-direct product…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
A deformation of the standard prolongation operation, defined on sets of vector fields in involution rather than on single ones, was recently introduced and christened "\sigma-prolongation"; correspondingly one has "\sigma-symmetries" of…
We derive the first-order orbital equation employing a complex variable formalism. We then examine Newton's theorem on precessing orbits and apply it to the perihelion shift of an elliptic orbit in general relativity. It is found that…
We consider rapidly mixing dynamical systems and link the decay of the shortest distance between multiple orbits with the generalized fractal dimension. We apply this result to multidimensional expanding maps and extend it to the realm of…
In this work, a method for solving the constraints of general relativity is presented, where first all geometrical objects are written in terms of a set of orthonormal triads and a flat Weitzenbock connection, which depends on the triads…
Shapiro's notations for natural numbers, and the associated desideratum of acceptability - the property of a notation that all recursive functions are computable in it - is well-known in philosophy of computing. Computable structure theory,…