Related papers: New examples of period collapse
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We propose a model to describe an evolution of a bubble cluster with rupture. In a special case, the equation is reduced to a single parabolic equation with evaporation for the thickness of a liquid layer covering bubbles. We postulate that…
We study the time evolution of the entropy of a collapsing spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. domain wall and radiation) and induced radiation…
Collapse models describe the breakdown of the quantum superposition principle when moving from microscopic to macroscopic scales. They are among the possible solutions to the quantum measurement problem and thus describe the emergence of…
If P is a rational polytope in R^d, then $i_P(t):=#(tP\cap Z^d)$ is a quasi-polynomial in t, called the Ehrhart quasi-polynomial of P. A period of i_P(t) is D(P), the smallest positive integer D such that D*P has integral vertices. Often,…
We investigate numerically the dynamical behaviour of a polymer chain collapsing in a dilute solution. The rate of collapse is measured with and without the presence of hydrodynamic interactions. We find that hydrodynamic interactions both…
In this paper, we study the collapsing behaviour of negative K\"{a}hler-Einstein metrics along degenerations of canonical polarized manifolds. We prove that for a toroidal degeneration of canonical polarized manifolds with the total space…
The purpose of this paper is to extend the scope of the Ehrhart theory to periodic graphs. We give sufficient conditions for the growth sequences of periodic graphs to be a quasi-polynomial and to satisfy the reciprocity laws. Furthermore,…
Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if…
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and…
Possible periods of Herman rings are studied for general meromorphic functions with at least one omitted value. A pole is called $H$-relevant for a Herman ring $H$ of such a function $f$ if it is surrounded by some Herman ring of the cycle…
It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann {\zeta} function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from…
We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $\Lambda$. The formalism is used for numerical simulations of…
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z^d}$ which tiles that lattice by translations, in fact tiles periodically. We announce here a disproof of this conjecture for sufficiently large $d$, which…
We derive lower und upper bounds for the degree of regularity of an overdetermined, zero-dimensional and homogeneous quadratic semi-regular system of polynomial equations. The analysis is based on the interpretation of the associated…
We explain the collapse of the wavefunction with the notion that, in a measurement, the system observed nucleates a first order phase transition in the measuring device. The possible final states differ by the values of macroscopic…
Everybody knows what the classical black holes are. In short, this is a spacetime region beyond the so-called event horizon. The notion of the event horizon is mathematically well defined. The situation with a definition of quantum black…
We define a completely new space-time starting from the well known Schwarzschild Space time by defining a new polar angle $\phi '= \phi - \omega t$ and then redefining the periodicity: instead of demanding that the original angle be…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…