An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

Causal propagators for algebraic gauges

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so-generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.

ANOTHER QUADRATURE RULE OF HIGHEST ALGEBRAIC DEGREE OF PRECISION

We consider certain quadrature rules of highest algebraic degree of precision that involve strong Stieltjes distributions (i.e., strong distributions on the positive real axis). The behavior of the parameters of these quadrature rules, when the distributions are strong c-inversive Stieltjes distributions, is given. A quadrature rule whose parameters have explicit expressions for their determination is presented. An application of this quadrature rule for the evaluation of a certain type of integrals is also given.

Aquatic humus from an unpolluted Brazilian dark-brown stream: general characterization and size fractionation of bound heavy metals

The main pool of dissolved organic carbon in tropical aquatic environments, notably in dark-coloured streams, is concentrated in humic substances (HS). Aquatic HS are large organic molecules formed by micro-biotic degradation of biopolymers and polymerization of smaller organic molecules. From an environmental point of view, the study of metal-humic interactions is often aimed at predicting the effect of aquatic HS on the bioavailability of heavy metal ions in the environment. In the present work the aquatic humic substances (HS) isolated from a dark-brown stream (located in an environmental protection area near Cubatao city in São Paulo-State, Brazil) by means of the collector XAD-8 were investigated. FTIR studies showed that the carboxylic carbons are probably the most important binding sites for Hg(II) ions within humic molecules. C-13-NMR and H-1-NMR studies of aquatic HS showed the presence of constituents with a high degree of aromaticity (40% of carbons) and small substitution. A special five-stage tangential-flow ultrafiltration device (UF) was used for size fractionation of the aquatic HS under study and for their metal species in the molecular size range 1-100 kDa (six fractions). The fractionation patterns showed that metal traces remaining in aquatic HS after their XAD-8 isolation have different distributions. Generally, the major percentage of traces of Mn, Cd and Ni (determined by ICP-AES) was preferably complexed by molecules with relatively high molecular size. Cu was bound by fractions with low molecular size and Co showed no preferential binding site in the various humic fractions. Moreover, the species formed between aquatic HS and Hg(II), prepared by spiking (determined by CVAAS), appeared to be concentrated in the relatively high molecular size fraction F-1 (> 100 kDa).

Food web structure in a tropical stream ecosystem

This study investigated the structure and properties of a tropical stream food web in a small spatial scale, characterizing its planktonic, epiphytic and benthic compartments. The study was carried out in the Potreirinho Creek, a second-order stream located in the south-east of Brazil. Some attributes of the three subwebs and of the conglomerate food web, composed by the trophic links of the three compartments plus the fish species, were determined. Among compartments, the food webs showed considerable variation in structure. The epiphytic food web was consistently more complex than the planktonic and benthic webs. The values of number of species, number of links and maximum food chain length were significantly higher in the epiphytic compartment than in the other two. Otherwise, the connectance was significantly lower in epiphyton. The significant differences of most food web parameters were determined by the increase in the number of trophic species, represented mainly by basal and intermediate species. High species richness, detritus-based system and high degree of omnivory characterized the stream food web studied. The aquatic macrophytes probably provide a substratum more stable and structurally complex than the sediment. We suggest that the greater species richness and trophic complexity in the epiphytic subweb might be due to the higher degree of habitat complexity supported by macrophyte substrate. Despite differences observed in the structure of the three subwebs, they are highly connected by trophic interactions, mainly by fishes. The high degree of fish omnivory associated with their movements at different spatial scales suggests that these animals have a significant role in the food web dynamic of Potreirinho Creek. This interface between macrophytes and the interconnections resultant from fish foraging, diluted the compartmentalization of the Potreirinho food web.

Yeasts and others parameters of pollution of the Ribeirao Claro stream in Rio Claro, São Paulo

The main water source of the Rio Claro municipal district (DAAE) was analysed for determining the level of organic contamination. Temperature, pH, light penetration, conductivity, dissolved oxygen, total dissolved phosphate, ortophosphate, ammonia, heterotrofic bacteria, total coliforms, fecal coliforms, total yeasts and fermentative yeasts were analysed during one year with samples being collected on a monthly basis. Bathing quality of the water from sites 1, 2 and 3 were classified, respectively, as Satisfactory, Very Good and Improper based on fecal coliform counts. Total yeast counts were appropriate as a complement for the appraisal of fresh water contamination by coliform counts. Seventeen yeast species belonging to genera Candida, Cryptococcus, Kloeckera, Pichia and Rhodotorula were found but none of them could be correlated with a level of contamination. Candida famata, C. robusta-like and C. colliculosa were isolated at all of the sites and between the five species found only at the more polluted site, Rhodotorula mucilaginosa was prevalent.

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Anthropogenic influences on annual flux of cations and anions at meio stream basin, São Paulo State, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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)

Quantum algebraic description of the Moszkowski model

In this paper we investigate the behaviour of the Moukowski model within the mnten of quantum algebras. The Moszkwski Hamiltonian is diagonalized aractly for different numbers of panicles and for various values of the deformalion parameter of the quanlum algebra involved. We also include ranking in our system and observe its variation as a function of the deformation parameters. © 1992 IOP Publishing Ltd.

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.

Distribution of stream macroalgae in the eastern Atlantic Rainforest of São Paulo State, southeastern Brazil

Fifty-two stream segments were sampled from 16 August to 13 September in 1993 in the eastern Atlantic Rainforest of São Paulo State, southeastern Brazil (22°55′-25°00′S, 44°48′-48°03′W). Forty-two macroalgal subgeneric taxa were found and the most widespread species were Audouinella pygmaea (21% of sites), Compsopogon leptoclados and Microcoleus subtorulosus (19%). Macroalgal species number per sampling site ranged from 0 to six (2.6 ± 1.7) and was positively correlated to species abundance, whereas species cover ranged from 0 to 70% of the stream bed (15.5 ± 20.8%). No significant correlation was found among macroalgal species number and abundance with any physical or chemical variable analyzed. Most sites were dominated by one or few macroalgal species, mainly, Audouinella macrospora, C. leptoclados and M. subtorulosus. No significant difference was found between the frequency distribution of variables measured for streams and for total macroalgae but the most widespread species (A. pygmaea) differed significantly for current velocity, specific conductance, turbidity and pH. Overall means for macroalgal occurrence include the following values: temperature (X̄ = 19.9°C), current velocity (X̄ = 45 cm s-1), oxygen saturation (X̄ = 66%), specific conductance (X̄ = 59.6 μS cm-1), turbidity (X̄ = 5 NTU) and pH (X̄ = 7.1). This pattern of patchy distribution and dominance by few species has been suggested as typical of stream macroalgal communities and has been ascribed to the rapid fluctuation of physical and chemical conditions. Total macroalgal species richness as well as mean species number per sampling site were considerably lower than found in similar studies of other regions. The Intermediate Disturbance Hypothesis was applied to explain these results: the same factor (high precipitation) responsible for the maintainance of the high species diversity in the surrounding forest can be, paradoxically, a constraint to the development of a more diverse macroalgal flora in streams. © 1996 Kluwer Academic Publishers.

Phenology of a dioecious population of Batrachospermum delicatulum (Batrachospermales, Rhodophyta) in a stream from southeastern Brazil

The seasonal dynamics of a dioecious population of Batrachospermum delicatulum (Skuja) Necchi and Entwisle was evaluated biweekly during the growth period of the macroscopic gametophyte, from late autumn (May) to early spring (October) in a third-order stream from the northeast region of Sao Paulo State, southeastern Brazil (20°43'S, 49°13'W). The population fluctuated throughout the study period in terms of percentage cover, frequency and chlorophyll content. Percent cover and frequency showed a clear pattern with the lowest values at the initial and final stages of the growth period and the highest in July-August (winter). Gametophyte growth was associated with high illumination and low temperature, which agrees with most observations on Batrachospermales in stream environments. Relatively wide variations in reproductive characteristics were observed during the growth period, which were not correlated with percentage cover, frequency and chlorophyll content. The phenologic pattern observed in this population was characterized by a synchronic development of female/male plant ratio with the number of spermatangia per plant resulting in. (i) a higher proportion of fertilized (carposporophytic) plants associated with more male plants; (ii) higher fertilization rates during the periods with higher production of spermatangia per plant; and (iii) higher production of spermatangia per plant when the population had more male plants. These characteristics were largely associated with water temperature and ion content. In terms of reproductive success, the population studied can be regarded as highly efficient, considering the relatively low proportion of male to female plants and high fertilization rates. These data are consistent with a hypothesis to explain high fertilization rates in dioecious species in lotic habitats consisting of outcrossing among adjacent plants with intermingled male and female branches within an algal cluster. Efficient reproductive strategies have been reported in dioecious, monoecious and even mixed populations of B. delicatulum and can be interpreted as adaptations to successfully colonize streams with different characteristics.

On the Optimality of Finite Constellations from Algebraic Lattices

A construction technique of finite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to find constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and four. © 2001.