Discussion on the geometric structure of strange attractor

We discuss the transversal heteroclinic cycle formed by hyperbolic periodic pointes of diffeomorphism on the differential manifold. We point out that every possible kind of transversal heteroclinic cycle has the Smalehorse property and the unstable manifolds of hyperbolic periodic points have the closure relation mutually. Therefore the strange attractor may be the closure of unstable manifolds of a countable number of hyperbolic periodic points. The Henon mapping is used as an example to show that the conclusion is reasonable.

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.

The geometric structure and dynamic properties of lauwerier attractor

 Introduction The strange chaotic attractor (ACS) is an important subject in the nonlinear field. On the basis of the theory of transversal heteroclinic cycles, it is suggested that the strange attractor is the closure of the unstable manifolds of countable infinite hyperbolic periodic points. From this point of view some nonlinear phenomena are explained reasonably. 更多还原

Pulse vs. Optimal Stationary Fishing: The Northern Stock of Hake

Pulse fishing may be a global optimal strategy in multicohort fisheries. In this article we compare the pulse fishing solutions obtained by using global numerical methods with the analytical stationary optimal solution. This allows us to quantify the potential benefits associated with the use of periodic fishing in the Northern Stock of hake. Results show that: first, management plans based exclusively on traditional reference targets as Fmsy may drive fishery economic results far from the optimal; second, global optimal solutions would imply, in a cyclical manner, the closure of the fishery for some periods and third, second best stationary policies with stable employment only reduce optimal present value of discounted profit in a 2%.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

Representing measures on the Royden boundary for solutions of Δu=Pu on a Riemannian manifold

Consider the Royden compactification R* of a Riemannian n-manifold R, Γ = R*\R its Royden boundary, Δ its harmonic boundary and the elliptic differential equation Δu = Pu, P ≥ 0 on R. A regular Borel measure m^P can be constructed on Γ with support equal to the closure of Δ^P = {q ϵ Δ : q has a neighborhood U in R* with _U^ʃ_ᴖR^{P ˂ ∞} }. Every enegy-finite solution to u (i.e. E(u) = D(u) + ^ʃ_Ru²P ˂ ∞, where D(u) is the Dirichlet integral of u) can be represented by u(z) = ^ʃ_Γu(q)K(z,q)dm^P(q) where K(z,q) is a continuous function on ^Rx Γ . A _P^~_E-function is a nonnegative solution which is the infimum of a downward directed family of energy-finite solutions. A nonzero _P^~_E-function is called _P^~_E-minimal if it is a constant multiple of every nonzero _P^~_E-function dominated by it. THEOREM. There exists a _P^~_E-minimal function if and only if there exists a point in q ϵ Γ such that m^P(q) > 0. THEOREM. For q ϵ Δ^P , m^P(q) > 0 if and only if m⁰(q) > 0 .

Multiplication in Riesz spaces

A.G. Vulih has shown how an essentially unique intrinsic multiplication can be defined in certain types of Riesz spaces (vector lattices) L. In general, the multiplication is not universally defined in L, but L can always be imbedded in a large space L^# in which multiplication is universally defined.

If ф is a normal integral in L, then ф can be extended to a normal integral on a large space L₁(ф) in L^#, and L₁(ф) may be regarded as an abstract integral space. A very general form of the Radon-Nikodym theorem can be proved in L₁(ф), and this can be used to give a relatively simple proof of a theorem of Segal giving a necessary and sufficient condition that the Radon-Nikodym theorem hold in a measure space.

In another application, the multiplication is used to give a representation of certain Riesz spaces as rings of operators on a Hilbert space.

The impact of Cow Green Reservoir on invertebrate populations in the River Tees

Cow Green is a new reservoir situated in Pennine moorland. It has an area of 312 ha, a capacity of 40 . 9 x 10 SUP-6 m SUP-3 and a maximum depth of 22 . 8 m. The function of the reservoir is to regulate flow in the River Tees to provide industrial Teesside with sufficient water during the dry spells. Invertebrate studies were carried out in the Tees to monitor changes resulting from the construction of the reservoir both in the flooded basin and below the dam. The overall effect of the reservoir on the Tees has been to increase the numbers and biomass of certain taxa, but generally not at the expense of previous fauna. Some of the positive effects, ie. increase in number and biomass, and maintenance of faunal diversity, may in part be attributable to the presence of the rapids and waterfall. Turbulence resulting from this rapid flow over heterogeneous bottom is sufficient to prevent clogging of interstitial spaces by silt and to maintain the variety of ecological niches necessary for a diverse fauna.

A cidade dos Meninos: educação e política na Baixada Flulminense/RJ

O presente trabalho tem como objetivo analisar alguns dos ideários sócio moralizantes que foram repercutidos na construção do pensamento social brasileiro, através das políticas pró-educação implementadas na década de 1940. O processo histórico que culminou com a edificação da Cidade dos Meninos, em Duque de Caxias no Rio Janeiro, surge, portanto, como um locus privilegiado para a investigação deste modelo educacional. Nesse contexto, as reflexões da intelectualidade à época, eram revestidas de uma expectativa moralizadora: "salvação pelo trabalho". Desta forma, surgiram espaços escolares que funcionavam em regime de internato e semi-internato, como a Cidade dos Meninos. Tratava-se de uma instituição destinada para essas populações "desvalidas", que seriam alvo de uma política educacional direcionada para a oferta do ensino "das letras" e do ensino profissionalizante de caráter elementar. Contudo, em 1950, ao ter uma fábrica de pesticidas instalada em seu interior, e com o posterior abandono desta, em virtude da mesma ter se tornado inviável economicamente em 1960, esse espaço foi alvo de uma contaminação ambiental e humana. Somente cerca de 30 anos depois, a referida contaminação foi trazida a público a partir de denúncias jornalísticas. A principal conseqüência foi o fechamento das escolas e a interrupção dos projetos de assistência social prejudicando muitos dos assistidos e antigos funcionários que assentaram residência na localidade, fazendo com que o problema social e de saúde pública se desdobrasse também numa questão fundiária. Todo esse movimento parece ter levado os atores sociais envolvidos no processo à uma elaboração pragmática sobre o papel da educação, do Estado, da pesquisa científica e do tipo de política que se destina a populações em situação de "periculosidade". A análise das memórias e das "trajetórias exemplares" de alguns moradores contribuíram para a compreensão da relação entre as políticas sociais e a perspectiva dos assistidos. Esse fato denota a possibilidade, na atualidade, de que os pressupostos que idealizaram tais políticas "sócio moralizantes" ainda apresentem vestígios no discurso e na ação tanto das autoridades, quanto dos próprios pesquisadores, desqualificando seus interlocutores e obscurecendo a solução do problema no referido local

From social to political. New forms of mobilization and democratization. Conference proceedings

In the recent evolution of contemporary social movements three phases can be identified. The first phase is marked by the labour movement and the systemic importance attributed to the labour conflict in industrial societies. This conflict has been interpreted as a consequence of the shortcoming of social integration mechanisms by Emile Durkheim, as a rational conflict by entrepreneurs’ and workers’ interests by Max Wener, and as a central class struggle for the transformation of society by Karl Marx. The second phase in this development was led by the new social movements of the post-industrial society of the 1960s and 1970s’ students, women and environmentalist movements. Two new analytical perspectives have explained these movements’ meaning and actions. Resource mobilization theory (McAdam and Tilly) has focuses on rational attitudes and conflicts. Actionalist sociology, in turn, has identified the new protagonists of social conflicts that replaced the labour movement in postindustrial societies. The third phase emerges in a world characterized by the ascendance of markets, the increasingly prominent role of financial capital flows, the closure of communities, and fundamentalism. In this context, human rights and pro-democratization movements constitute alternatives to global domination and the systemic conditioning of individual and groups.

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Learning to perceive in the sensor motor approach: Piaget's theory of equilibration interpreted dynamically

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the "laws" of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget's theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget's theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level.

Fishery Management and Local Communities: The Case of Madeira Beach, Florida

This paper uses an industrial organization approach to trace the impact on Madeira Beach, Fla., and surrounding areas of a 1-month closure of the grouper fishery from 15 February 2001 to 15 March 2001. A proposed 2-month closure is also evaluated. This approach identifies the economic relationships in the industry based on both product and place. The empirical analysis measures the losses in employment and income, information that enriches social and anthropological research on fishery-dependent communities. The 1-month closure is estimated to have reduced annual catches landed in Madeira Beach by 9.7–10.1% and annual revenues by 9.3–11.5%. These reductions are associated with a direct loss of about 33 full-time (annualized) jobs and personal income losses between $8 and 12 million in Madeira Beach and Pinellas County over a 10-year period. If the closure occurs for 2 months, annual landings and revenues will be reduced an estimated 17–21% and 20–23%, respectively.

The role of substrate, flow and larval supply to recruitment of the red abalone (Haliotis rufescens)

Precipitous declines in wild populations of the red abalone Haliotis rufescens and the eventual closure of the commercial and southern recreational fishery have led to renewed interest in supplementing wild stocks with hatchery-raised individuals. Most work to date has focused on releasing small juveniles and has had limited success. Although much is known about larval settlement, juvenile survivorship and growth of abalone, there is scanty information on natural processes in the field. The failure of many regulated fisheries worldwide suggests that both the larval and juvenile stages may be important in determining the future population, and that early juvenile mortality is more important than previously believed. This paper presents a series of experiments designed to examine factors and mechanisms that could affect settlement, survivorship, and growth of larvae and early post-settlers in the field. Laboratory trials under different flow regimes showed that red abalone larvae settled preferentially on substrates encrusted with coralline algae, and that settlement was rapid when exposed to crusts compared to other surfaces. Urchin grazing of films appeared to facilitate abalone settlement but only when urchins were removed. Initial field experiments showed that released larvae settled on natural cobble rock, and that settlement was at least one order of magnitude greater when settlement habitats were tented. I then examined post-settlement survivorship at one and two days after settlement, and found that although there was a large amount of variation, on average 10% of released larvae were found as newly-settled recruits after 1 day. Survivorship and growth of recruits were followed over at least one month in both Spring and Fall. Abalone settled at higher densities, survived better and grew faster in the warmer Fall months than in the Spring. The density of month-old abalone recruits was correlated with density of naturally-occurring gastropods in the Spring, but not in the Fall. These results suggest that settlement and survivorship can be extremely variable across space and time, and that oceanographic and local biotic conditions play a role and should be considered when planning larval seeding.

Shifts in the estuarine demersal fish community after a fishery closure in Puget Sound, Washington

Puget Sound is one of the largest and most ecologically significant estuaries in the United States, but the status and trends of many of its biological components are not well known. We analyzed a 21-year time series of data from standardized bottom trawl sampling at a single study area to provide the first assessment of population trends of Puget Sound groundfishes after the closure of bottom trawl fisheries. The expected increase in abundance was observed for only 3 of 14 species after this closure, and catch rates of most (10) of the abundant species declined through time. Many of these changes were stepwise (abrupt) rather than gradual, and many stocks exhibited changes in catch rate during the 3-year period from 1997 through 2000. No detectable change was recorded for either temperature or surface salinity over the entire sampling period. The abrupt density reductions that were observed likely do not reflect changes in demographic rates but may instead represent distributional shifts within Puget Sound.