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Convex Analysisの二,三の進展について

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

http://absimage.aps.org/image/DAMOP06/MWS_DAMOP06-2006-000603.pdf

A quantum Newton's cradle

Thank you very much for downloading a course in functional analysis. As you may know, people have look numerous times for their favorite books like this a course in functional analysis, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they juggled with some harmful virus inside their desktop computer. a course in functional analysis is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the a course in functional analysis is universally compatible with any devices to read.

A Course In Functional Analysis

In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.

Graphs and Matrices

/pdf/dynamics-and-bifurcations-of-nonsmooth-systems-a-survey-1qecz49b7p.pdf

Dynamics and bifurcations of nonsmooth systems: A survey

In this paper we study the existence, uniqueness, and asymptotic stability of the periodic solutions of the Lipschitz system $\dot{x}=\varepsilon g(t,x,\varepsilon)$, where $\varepsilon>0$ is small. Our results extend the classical second Bogoliubov theorem for the existence of stable periodic solutions to nonsmooth differential systems. As an application we prove the existence of asymptotically stable $2\pi$-periodic solutions of the nonsmooth van der Pol oscillator $\ddot{u}+\varepsilon\,(|u|-1)\,\dot{u}+(1+a\varepsilon)u=\varepsilon\lambda\sin t$. Moreover, we construct the so-called resonance curves that describe the dependence of the amplitude of these solutions as a function of the parameters a and $\lambda$. Finally we compare such curves with the resonance curves of the classical van der Pol oscillator $\ddot{u}+\varepsilon\,\bigl(u^2-1\bigr)\,\dot{u}+(1+a\varepsilon)u=\varepsilon\lambda\sin t$.

Asymptotic Stability of Periodic Solutions for Nonsmooth Differential Equations with Application to the Nonsmooth van der Pol Oscillator

Preface: Dynamics and Bifurcations of Nonsmooth Systems

The paper deals with a T -periodically perturbed autonomous system in ℝn of the form




((PS))





with e > 0 small. The main goal of the paper is to provide conditions ensuring the existence of T -periodic solutions to (PS) belonging to a given open set W ⊂ C ([0, T ],ℝn). This problem is considered in the case when the boundary ∂W of W contains at most a finite number of nondegenerate T -periodic solutions of the autonomous system = ϕ (x). The starting point of our approach is the following property due to Malkin: if for any T -periodic limit cycle x 0 of = ϕ (x) belonging to ∂W the so-called bifurcation function f (θ), θ ∈ [0, T ], associated to x0, see (1.11), satisfies the condition f(0) ≠ 0 then the integral operator










does not have fixed points on ∂W for all e > 0 sufficiently small. By means of the Malkin's bifurcation function we then establish a formula to evaluate the Leray–Schauder topological degree of I – Qe on W. This formula permits to state existence results that generalize or improve several results of the existing literature. In particular, we extend a continuation principle due to Capietto, Mawhin and Zanolin where it is assumed that ∂W does not contain any T -periodic solutions of the unperturbed system. Moreover, we obtain generalizations or improvements of some existence results due to Malkin and Loud. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A continuation principle for a class of periodically perturbed autonomous systems

We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer T. 1990 Passive dynamic walking. Int. J. Robot. Res. 9, 6282. (doi:...

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2019.0450

Oleg Makarenkov

Papers

Dynamics and bifurcations of nonsmooth systems: A survey

Asymptotic Stability of Periodic Solutions for Nonsmooth Differential Equations with Application to the Nonsmooth van der Pol Oscillator

Preface: Dynamics and Bifurcations of Nonsmooth Systems

A continuation principle for a class of periodically perturbed autonomous systems

Existence and stability of limit cycles in the model of a planar passive biped walking down a slope.