Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

The Borsuk-Ulam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.

Cellular decomposition of quaternionic spherical space forms

We obtain an explicit cellular decomposition of the quaternionic spherical space forms, manifolds of positive constant curvature that are factors of an odd sphere by a free orthogonal action of a generalized quaternionic group. The cellular structure gives and explicit description of the associated cellular chain complex of modules over the integral group ring of the fundamental group. As an application we compute the Whitehead torsion of these spaces for any representation of the fundamental group. © 2012 Springer Science+Business Media B.V.

On the curvature ODE associated to the Ricci flow

In the vector space of algebraic curvature operators we study the reaction ODE which is associated to the evolution equation of the Riemann curvature operator along the Ricci flow. More precisely, we give a partial classification of the zeros of this ODE up to suitable normalization and analyze the stability of a special class of zeros of the same. In particular, we show that the ODE is unstable near the curvature operators of the Riemannian product spaces where is an Einstein (locally) symmetric space of compact type and not a spherical space form when .

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Constructing internationally comparable real income aggregates by combining sparse benchmark data with annual national accounts data: A state-space approach

The importance of availability of comparable real income aggregates and their components to applied economic research is highlighted by the popularity of the Penn World Tables. Any methodology designed to achieve such a task requires the combination of data from several sources. The first is purchasing power parities (PPP) data available from the International Comparisons Project roughly every five years since the 1970s. The second is national level data on a range of variables that explain the behaviour of the ratio of PPP to market exchange rates. The final source of data is the national accounts publications of different countries which include estimates of gross domestic product and various price deflators. In this paper we present a method to construct a consistent panel of comparable real incomes by specifying the problem in state-space form. We present our completed work as well as briefly indicate our work in progress.

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Multi-time scale analysis applied to long time simulation of power systems

The results are presented of applying multi-time scale analysis using the singular perturbation technique for long time simulation of power system problems. A linear system represented in state-space form can be decoupled into slow and fast subsystems. These subsystems can be simulated with different time steps and then recombined to obtain the system response. Simulation results with a two-time scale analysis of a power system show a large saving in computational costs.

Almost quarter-pinched Kähler metrics and Chern numbers

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

Dynamic state estimation for identifying earthquake support motions in instrumented structures

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

Relações de poder, currículo e cultura escolar

Esta dissertação, a partir das lentes teórico-metodológicas de Michel Foucault, lança um olhar sobre aspectos da cultura escolar, suas regras, modos de organização, currículo, avaliações que movimentam o processo de escolarização, problematizando as relações de poder envolvidas na produção de subjetividades dos diferentes sujeitos e permeadas por diferentes verdades sobre esses sujeitos. Nessa perspectiva relacional, o poder é entendido como dinâmico, flexível, estratégico, difícil de ser capturado: o sujeito e suas ações são seus efeitos e agentes. Pretendo entender como algumas forças provenientes de diferentes direções vão construindo os cenários nos quais os sujeitos do cotidiano escolar atuam, produzindo relações de poder muito complexas. Nesse exercício, não cabe descrever os efeitos do poder em termos negativos. O poder produz realidades e rituais de verdade. Assim, busco, neste estudo, olhar para essa articulação de forças, de estratégias, de movimentos que, atravessando as relações de poder, produzem o currículo e as subjetividades num determinado espaço educativo. Esses saberes/verdades, extraídos das práticas de objetivação, possibilitam o investimento em ações e intervenções. É nesse sentido que busco olhar as práticas escolares como espaços de objetivação/subjetivação. Ao analisar essas práticas, destaco que os efeitos, no que diz respeito à produção de subjetividades, não se encontram em uma ou outra forma de agir. Percebi que as práticas escolares articulam-se numa rede disciplinar formada por diferentes dispositivos que se relacionam na produção de sujeitos, agindo sobre seus corpos. Relatórios, registros, observações, classificações, controle das atividades, organização do tempo e do espaço formam uma rede de significações e de normalização dos sujeitos no espaço escolar. E aqueles/as que não se enquadram, que se desviam do caminho, são apanhados mais facilmente pelas redes do poder e objetivados são produzidos em sua subjetividade que tenta fazer com que ele/a se perceba e se compreenda de certo jeito para se autogovernar, para melhor aprender e normalizar-se. Nesse processo de normalização dos sujeitos, não descarto a necessidade de se ter determinadas regras de convivência, de se ter a preocupação com que as crianças aprendam os conhecimentos escolares. O que ressalto é que se reflita sobre que tipo de normas estabelece o que é normal e anormal, que tipo de saberes é valorizado, com que propósito se investe sobre os corpos das crianças, que subjetividades estão sendo produzidas no espaço da escola.

云南抚仙湖的鱼类及其在进化过程中的生物学表达

本文依据生物与环境相统一、生物的演化必然在其生态学特性上表达出来，从进化的观点出发，以生态学作为一种手段，结合湖泊的地质变迁，借以阐明抚仙湖的鱼类区系在漫长的演化过程中是怎样形成的。全文分八部分。着重介绍区系的概貌、起源及鱼类演化的生物学表达。经鉴定，抚仙湖共有土著鱼类23种，根据属的分布中心可把它们分为四个分布型，即广泛分布型、云南弧分布型、南亚分布型和青藏高原分布型。它们从宏观上反映了抚仙湖鱼类区系起源的背景和演化的阶段性。研究结果表明，抚仙湖鱼类的演化是从时间(time)、空间(space)、形式(form)三个方面展开的。具体表现在鱼类物种和区系两个层次的生物学特点均源自对抚仙湖由浅变深的时、空演变过程的适应。随着湖泊由浅变深和贫营养化，抚仙湖的鱼类区系产生了一系列相应的变化：鱼类区系的空间分布由古抚仙湖的广泛性浅水生活类型分化为目前的沿岸浅水区生活类型、敞水区中上层生活类型、深水区中下层生活类型；种间食性出现多种多样的分歧；生长的演化表现为生长速度减慢，体型趋向细长；繁殖期延长，而且每两个产卵批次之间有一定的时间间隔，个体的繁殖力趋向降低，种群性比趋向悬殊，雌性增多。这些综合分化的结果就形成了今天抚仙湖鱼类的多样性。它们各得其所，各就其位，保持一个相对稳定而复杂的网络关系。文中还记述了2新种和1新亚种，它们是抚仙高原鳅(Triplophysa fuxianensis)、后鳍云南鳅(Yunnanilus opisthopterus)和小鳔长身 (Acheilognathus elongatus elongatus)。这进一步反映了云南高原湖泊鱼类区域化较突出的特点。抚仙湖鱼类区是云南高原湖泊鱼类区系的典型代，而且是云南众多湖泊中唯一仍基本保持其自然而貌的湖泊，因此，发展抚仙湖渔业生产的方针应不同于其它湖泊，即有选择地增殖土著鱼类，首先是增殖鱇 白鱼和云南倒刺鲃；谨慎引入外来种。同时还要兼顾湖泊的多功能性加以综合利用，不可就某一功能就满打满算。

Identification of dynamic systems under closed-loop control

This paper introduces a novel modelling framework for identifying dynamic models of systems that are under feedback control. These models are identified under closed-loop conditions and produce a joint representation that includes both the plant and controller models in state space form. The joint plant/controller model is identified using subspace model identification (SMI), which is followed by the separation of the plant model from the identified one. Compared to previous research, this work (i) proposes a new modelling framework for identifying closed-loop systems, (ii) introduces a generic structure to represent the controller and (iii) explains how that the new framework gives rise to a simplified determination of the plant models. In contrast, the use of the conventional modelling approach renders the separation of the plant model a difficult task. The benefits of using the new model method are demonstrated using a number of application studies.