Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we fi nd that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a \balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.

Prevalence and characteristics of periodic leg movements during sleep in the general population : the Hypnolaus study

Objective: The aim of this study was to describe the prevalence and characteristics of periodic legs movements of sleep (PLMS) in theadult general population. Methods: Data from 2162 subjects (51.2% women, mean SD age:58, 11 years, range: 40.5-84.4 years) participating in a population-based cohort study (HypnoLaus, Lausanne, Switzerland) wascollected. They completed a series of sleep related questionnaires and underwent polysomnographic recordings at home. PLMS index(PLMSI) was determined according to AASM 2007 criteria. APLMSI>15/h was considered to be of potential clinical significance. Conclusions: PLMS are highly prevalent in the general population. Age, male gender and RLS are independent predictors of a PLMSIhigher than 15/h. Further studies are needed to evaluate the clinical impact of PLMS.

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

La qualitat informativa de les agències a Catalunya. Comparativa entre EFE, Europa Press y ACN

Anàlisi de la qualitat informativa de les tres agències amb implantació a Catalunya – EFE, Europa Press i ACN – a través d’un estudi de la seva història, dels seus llibres d’estil i d’un anàlisi ortogràfic, gramàtic i lèxic de les notícies que publiquen.

"Periodic crises": Clément Juglar between theories of crises and theories of business cycles

Business cycle theory is normally described as having evolved out of a previous tradition of writers focusing exclusively on crises. In this account, the turning point is seen as residing in Clément Juglar's contribution on commercial crises and their periodicity. It is well known that the champion of this view is Schumpeter, who propagated it on several occasions. The same author, however, pointed to a number of other writers who, before and at the same time as Juglar, stressed one or another of the aspects for which Juglar is credited primacy, including the recognition of periodicity and the identification of endogenous elements enabling the recognition of crises as a self-generating phenomenon. There is indeed a vast literature, both primary and secondary, relating to the debates on crises and fluctuations around the middle of the nineteenth century, from which it is apparent that Juglar's book Des Crises Commerciales et de leur Retour Périodique en France, en Angleterre et aux États-Unis (originally published in 1862 and very much revised and enlarged in 1889) did not come out of the blue but was one of the products of an intellectual climate inducing the thinking of crises not as unrelated events but as part of a more complex phenomenon consisting of recurring crises related to the development of the commercial world - an interpretation corroborated by the almost regular occurrence of crises at about 10-year intervals.

Periodic accumulation of cdc15 mRNA is not necessary for septation in Schizosaccharomyces pombe.

Analysis of Schizosaccharomyces pombe mutants that are defective in septum formation and cytokinesis has identified the product of the cdc15 gene as a key element in formation of a division septum. S. pombe cells lacking cdc15p function cannot assemble a functional medial ring, and do not make a division septum. cdc15 mRNA accumulates periodically during the cell cycle, peaking after entry into mitosis, and increased expression of the gene in G2-arrested cells can promote F-actin ring formation. Here, we have investigated the effects of mutations that block cell division upon the expression of cdc15 in synchronised cell populations, and analysed the expression of cdc15 when septum formation is induced by ectopic activation of the septation signalling network. We concluded the following: (i) the septation signalling network genes are not required for periodic accumulation of cdc15 mRNA; (ii) induction of septum formation in G2-arrested cells by activation of the septation signalling network does not result in accumulation of cdc15 mRNA, which is therefore not a prerequisite for septum formation; (iii) failure to turn off septum formation at the end of mitosis results in continued expression of cdc15; and (iv) periodic accumulation of cdc15 mRNA is mediated by a 97 bp region 5' to the mRNA start site.