Related papers: Some remarks on cyclization and periodicity
We discuss the conditions for which the non-equilibrium work relation is valid by means of thermodynamic and microscopic arguments.
Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.
$B$-terms are built from the $B$ combinator alone defined by $B\equiv\lambda fgx. f(g~x)$, which is well known as a function composition operator. This paper investigates an interesting property of $B$-terms, that is, whether repetitive…
In this note, we have shown special case on Routh stability criterion, which is not discussed, in previous literature. This idea can be useful in computer science applications.
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
The liftable centralizer for special flows over irrational rotations is studied. It is shown that there are such flows under piecewise constant roof functions which are rigid and whose liftable centralizer is trivial.
Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…
We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…
We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…
Coven and Meyerowitz formulated two conditions which have since been conjectured to characterize all finite sets that tile the integers by translation. By periodicity, this conjecture is reduced to sets which tile a finite cyclic group…
In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance…
It is known that a positive, compactly supported function $f \in L^1(\mathbb R)$ can tile by translations only if the translation set is a finite union of periodic sets. We prove that this is not the case if $f$ is allowed to have unbounded…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin.…
In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function.
We give a sufficient condition for quantising integrable systems.
We collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts from topology and complex analysis. the…
Many colloidal systems display very non-Newtonian and solid-like behaviour when concentrated, a striking feature being the apparition of a yield stress. After recalling some basics about the interactions between colloidal particles, I…