THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

Ticks (Acari : Ixodidae) parasitizing humans in an Atlantic rainforest reserve of Southeastern Brazil with notes on host suitability

While conducting projects on ticks from deer and on tick ecology in animal trails in an Atlantic rainforest reserve in Southeastern Brazil, researchers of our group were bitten by ticks several times. Some of these episodes were recorded. Three species of adult ticks attached to humans: Amblyomma brasiliense Aragauo, Amblyomma incisum Neumann, and Amblyomma ovale Koch. Eight nymphal attachments with engorgement on humans were recorded. From these, six molted to adults of A. incisum, one to an adult of A. brasiliense, and one had an anomalous molting, therefore the adult tick could not be properly identified. Local reactions to tick attachment varied among individual hosts from almost imperceptible to intense. Especially itching, but hyperemia and swelling as well, were prominent features of the reaction. Overall it can be affirmed that human beings can be a physiologically suitable host species for ticks in the Atlantic rainforest and that itching was an important if not the major component of the resistance to tick bite.

Insights into the concept of fish welfare

Fish welfare issues are predicated on understanding whether fish are sentient beings. Therefore, we analyzed the logic of the methodologies used for studying this attribute. We conclude that empirical science is unable to prove or to disprove that fish are sentient beings. Thus, we propose a combined ethical-scientific approach for considering fish as sentient beings. The most difficult ongoing question is to determine which conditions fish prefer. Approaches to assess fish preferences should be rigorously and cautiously employed. In light of these considerations, attempts to establish physiological standards for fish welfare are discouraged, and a preference-based definition of fish welfare is proposed.

Toda lattice realization of integrable hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudo-differential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld-Sokolov realization.

Canine bartonellosis: serological and molecular prevalence in Brazil and evidence of co-infection with Bartonella henselae and Bartonella vinsonii subsp berkhoffii

The purpose of this study was to determine the serological and molecular prevalence of Bartonella spp. infection in a sick dog population from Brazil. At the São Paulo State University Veterinary Teaching Hospital in Botucatu, 198 consecutive dogs with clinicopathological abnormalities consistent with tick-borne infections were sampled. Antibodies to Bartonella henselae and Bartonella vinsonii subsp. berkhoffii were detected in 2.0% ( 4/197) and 1.5% ( 3/197) of the dogs, respectively. Using 16S-23S rRNA intergenic transcribed spacer ( ITS) primers, Bartonella DNA was amplified from only 1/198 blood samples. Bartonella seroreactive and/or PCR positive blood samples ( n = 8) were inoculated into a liquid pre-enrichment growth medium ( BAPGM) and subsequently sub-inoculated onto BAPGM/blood-agar plates. PCR targeting the ITS region, pap31 and rpoB genes amplified B. henselae from the blood and/or isolates of the PCR positive dog ( ITS: DQ346666; pap31 gene: DQ351240; rpoB: EF196806). B. henselae and B. vinsonii subsp. berkhoffii ( pap31: DQ906160; rpoB: EF196805) co-infection was found in one of the B. vinsonii subsp. berkhoffii seroreactive dogs. We conclude that dogs in this study population were infrequently exposed to or infected with a Bartonella species. The B. henselae and B. vinsonii subsp. berkhoffii strains identified in this study are genetically similar to strains isolated from septicemic cats, dogs, coyotes and human beings from other parts of the world. To our knowledge, these isolates provide the first Brazilian DNA sequences from these Bartonella species and the first evidence of Bartonella co-infection in dogs.

AGONISTIC PROFILE AND METABOLISM IN ALEVINS OF THE NILE TILAPIA

Metabolic differences derived from social stress usually show data with high variance that may hinder the finding of important differences. Since such high variance may be caused by agonistic variability occurring during social interactions, this work tested whether metabolism is associated with agonistic profile in the cichlid fish Nile tilapia, Oreochromis niloticus (L.). Metabolism was inferred from oxygen consumption, resistance to progressive hypoxia and ventilatory rate. Fifteen pairs of alevins were used for each metabolic and behavioral series. An ethogram based on 8 types of agonistic interactions was employed. Agonistic profiles were determined and associated with the physiological parameters later on. The test of canonical correlation showed significant association between some agonistic profiles and metabolism. Ventral nipping and lateral fight appeared as the two most important in promoting association with metabolism.

The correlation between subordinate fish eye colour and received attacks: a negative social feedback mechanism for the reduction of aggression during the formation of dominance hierarchies

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cholangiocarcinoma and Squamous Cell Carcinoma of the Stratified Epithelial Portion of the Stomach in a Horse: A Case Report

Both cholangiocarcinoma and squamous cell carcinoma of the stomach stratified squamous epithelial portion are rarely found in equine medicine despite being more common in human beings, dogs, and cats. The objective of the present article was to report the simultaneous occurrences of these two types of neoplasias in an 11-year-old mare. Numerous firm, whitish nodules were distributed throughout the liver parenchyma and those protruding over its surface were umbilicated in their appearance. It was verified that the nodules adhered to the peritoneum and omentum, diaphragm, spleen, and stomach serosa compressed the adjacent structures. The stomach stratified squamous epithelial portion, particularly originating in the margo plicatus toward the cardia, was covered by numerous smooth, whitish spherules. Microscopic examination allowed the liver, tumor, and the abdominal implants to be identified as a cholangiocarcinoma, and the stomach neoplasia as a carcinoma of its stratified squamous epithelial portion. Considering this as an uncommon finding, although when considered individually, the presence of a cholangiocarcinoma and a squamous cell carcinoma of the stratified squamous epithelial portion of the equine stomach in the same specimen is worthy of reporting. (C) 2011 Elsevier B.V. All rights reserved.

On non-linear W-infinity symmetry of generalized Liouville and conformal Toda models

Invariance under non-linear Ŵ∞ algebra is shown for the two-boson Liouville type of model and its algebraic generalizations, the extended conformal Toda models. The realization of the corresponding generators in terms of two boson currents within KP hierarchy is presented.

Toda and Volterra lattice equations from discrete symmetries of KP hierarchies

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation

By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.

Estimation of crowd density using image processing

Human beings perceive images through their properties, like colour, shape, size, and texture. Texture is a fertile source of information about the physical environment. Images of low density crowds tend to present coarse textures, while images of dense crowds tend to present fine textures. This paper describes a new technique for automatic estimation of crowd density, which is a part of the problem of automatic crowd monitoring, using texture information based on grey-level transition probabilities on digitised images. Crowd density feature vectors are extracted from such images and used by a self organising neural network which is responsible for the crowd density estimation. Results obtained respectively to the estimation of the number of people in a specific area of Liverpool Street Railway Station in London (UK) are presented.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.