Newton`s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton`s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Improved Prediction of Hydrocarbon Flash Points from Boiling Point Data

Flash points (T(FP)) of hydrocarbons are calculated from their flash point numbers, N(FP), with the relationship T(FP) (K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 In turn, the N(FP) values can be predicted from experimental boiling point numbers (Y(BP)) and molecular structure with the equation N(FP) = 0.987 Y(BP) + 0.176D + 0.687T + 0.712B - 0.176 where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. For a data set consisting of 300 diverse hydrocarbons, the average absolute deviation between the literature and predicted flash points was 2.9 K.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Simple Method to Evaluate and to Predict Flash Points of Organic Compounds

Flash points (T(FP)) of organic compounds are calculated from their flash point numbers, N(FP), with the relationship T(FP) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901. In turn, the N(FP) values can be predicted from boiling point numbers (Y(BP)) and functional group counts with the equation N(FP) = 0.974Y(BP) + Sigma(i)n(i)G(i) + 0.095 where G(i) is a functional group-specific contribution to the value of N(FP) and n(i) is the number of such functional groups in the structure. For a data set consisting of 1000 diverse organic compounds, the average absolute deviation between reported and predicted flash points was less than 2.5 K.

Reglerad miljöredovisning : Tillståndspliktiga företag i Dalarna 2013

Bakgrund: De verksamheter som bedriver miljöfarlig verksamhet enligt miljöbalkenär anmälnings- eller tillståndspliktiga. Dessa företag ska lämnamiljöinformation i förvaltningsberättelsen. Tidigare studier visar attföretagen inte följer denna regel fullt ut. Som förklaring till företagensval av att miljöredovisa eller att inte redovisa sin miljöpåverkan användervi oss av legitimitetsteorin och intressentteorin.Syfte: Syftet med undersökningen är att för år 2013 se hur väl detillståndspliktiga företagen i Dalarna följer lagen om miljöredovisningoch vilka faktorer som kan förklara deras tillämpning av lagen.Metod: Studien bygger huvudsakligen på kvantitativ metod med inslag avkvalitativ metod. Vi använder en deduktiv ansats för att skapa fyrahypoteser om omsättning, branschtillhörighet, revisionsbyrå ochskuldsättningsgrad. Urvalet är de tillståndspliktiga företagen i Dalarna.Varje företag kan ha flera enheter som är tillståndspliktiga och vårt urval,Dalarna, blir 209 enheter varav 116 är stora enheter.Slutsats: Företagen i Dalarna uppfyller inte lagen om reglerad miljöredovisning tillfullo. Endast 18 av 116 stora enheter uppfyller alla fyra punkterna.Däremot är det 61,2 procent av de stora enheterna som får tre poäng.Som en jämförelse med Ljungdahls studie där nästan 27 procent når trepoäng ser vi en klar förbättring. De faktorer som kan förklara företagenstillämpning av lagen i vår undersökning är omsättning, de som anlitarrevisionsbyrån PwC samt branschtillhörighet avlopp och avfall. Av defyra hypoteser som vi använder är det en som stämmer, två som förkastasoch en som vi inte med säkerhet kan avgöra om den ska vara kvar ellerförkastas.

Brazil: the pressure points in labor legislation

Brazil’s experience shows that the economic and political history of a country is a critical determinant of which labor laws influence wages and employment, and which are not binding. Long periods of high inflation, illiteracy of the workforce, and biases in the design and enforcement of labor legislation bred by the country’s socioeconomic history are all important in determining the reach of labor laws. Defying conventional wisdom, these factors are shown to affect labor market outcomes even in the sector of employment regarded as unregulated. Following accepted practice in Brazil, we distinguish regulated from unregulated employment by determining whether or not the contract has been ratified by the Ministry of Labor, viz., groups of workers with and without signed work booklet. We then examine the degree of adherence to labor laws in the formal and informal sectors, and finds “pressure points” – viz., evidence of the law on minimum wage, work-hours, and payment timing being binding on outcomes – in both the formal and informal sectors of the Brazilian labor market. The findings of the paper imply that in terms of the design of legislation, informality in Brazil is mainly a fiscal, and not a legal phenomenon. But the manner in which these laws have been enforced is also critical determinant of informality in Brazil: poor record-keeping has strengthened the incentives to stay informal that are already built into the design of the main social security programs, and ambiguities in the design of labor legislation combined with slanted enforcement by labor courts have led to workers effectively being accorded the same labor rights whether or not they have ratified contracts. The incentives to stay informal are naturally higher for workers who are assured of protection under labor legislation regardless of the nature of their contract, which only alters their financial relationship with the government. The paper concludes that informality in Brazil will remain high as long as labor laws remain ambiguous and enforced with a clear pro-labor bias, and social security programs lack tight benefitcontribution linkages and strong enforcement mechanisms.

Impacto da emissão dual-class na estrutura de capital

A tese propõe que empresas que emitem apenas ações com direitos de voto utilizam mais capitais de terceiros do que empresas que emitem tanto ações votantes quanto não votantes. No desenvolvimento do trabalho, foi demonstrada a relevância de relacionar endividamento ao fato de uma empresa emitir ou não ações sem direito a voto, considerando as principais teorias de estrutura de capital e a realidade brasileira. Como os modelos teóricos que explicam o nível de endividamento das empresas ainda carecem de capacidade explicativa, a busca por novos determinantes está presente na literatura de estrutura de capital. A ocorrência da emissão de ações em classes diferenciadas (dual-class) como fator impactante no nível de endividamento foi analisada sob três prismas: de mercado, dos setores e das empresas que unificaram suas ações. Pelas três investigações ficou evidenciada a perspectiva de que o endividamento seja menor nos casos de emissão de ações preferenciais, considerando o ambiente de negociação e regulamentação do Brasil. A aceitação da tese tem reflexos teóricos na identificação de um fator que deve ser levado em consideração nos modelos de estrutura de capital, bem como suscita a importância de gestores, investidores e credores reconhecerem que o fato de uma empresa ser dual-class impacta não apenas na sua estrutura de controle, mas principalmente em sua estrutura de capital. Entre as considerações da aceitação da tese, estaria o reconhecimento de que empresas que ingressam no Novo Mercado na prática estão, no longo prazo, trocando o uso de ações preferenciais como forma de financiamento pela emissão de dívida.