Related papers: The Rise-Contact involution on Tamari intervals

In this contribution we discuss the occurrence of first-order transitions in temperature in various short-range lattice models with a rotation symmetry. Such transitions turn out to be widespread under the condition that the interaction…

We argue that for Fermi systems on lattices or the continuum with interaction invariant under a kind of Galilei transformation the time evolution is either weakly asymptotically abelian or at least $\eta$-abelian in the tracial state but…

We discuss the evolution of quantum correlations for a system of two two-level atoms interacting with a common reservoir. The Markovian master equation is used to describe the evolution of various measures of quantum correlations.

Baxter numbers are known to count several families of combinatorial objects, all of which come equipped with natural involutions. In this paper, we add a combinatorial family to the list, and show that the known bijections between these…

Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori. This knowledge is significantly increased…

We prove that any over-twist pattern is conjugate to an interval exchange transformation with bounded number of segments of isometry, restricted on one of its cycles. The bound is independent of the period and over-rotation number of the…

We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the…

The study of patterns in permutations associated with forests of binary shrubs was initiated by D. Bevan et al.. In this paper, we study five different types of rise statistics that can be associated with such permutations and find the…

We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lagrangian multiforms" and "Pluri-Lagrangian systems", which…

Context. As a star evolves, the planet orbits change with time due to tidal interactions, stellar mass losses, friction and gravitational drag forces, mass accretion and evaporation on/by the planet. Stellar rotation modifies the structure…

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type…

Sources of uncertainties in perturbative calculations, tadpole improvement and its role in lattice perturbation theory, and six recent calculations are discussed.

We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just…

Finding a comprehensive and general description of the collective Lamb shift and cooperative broadening in a radiatively interacting system is a long-standing open question. Both energy levels and linewidth of individual atoms are modified…

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…

In this paper, we revisit some classical and recent works on modelling slide-contact with wear and propose their generalisation. Namely, we upgrade the relation between the pressure and the wear rate by incorporating some non-local…

In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites. We only consider the case of a single spin degree of…

Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r^{\alpha} with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction…

We present a detailed multi-wavelength analysis and interpretation of the evolution of an M7.6 flare on October 24, 2003. The X-ray observations of the flare taken from the RHESSI spacecraft reveal two phases of the flare evolution. The…