GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

RELATIVE GROWTH OF THE SPECKLED SWIMMING CRAB ARENAEUS-CRIBRARIUS (LAMARCK, 1818) (BRACHYURA, PORTUNIDAE), NEAR UBATUBA, STATE OF SAO-PAULO, BRAZIL

Arenaeus cribrarius is a mainly tropical crab that occurs in the Western Atlantic Ocean, Brazil being its type-locality. The species ranges from Vinevard Sound, Massachusetts, USA to La Paloma, Uruguay. Information about this species is scarce. The relative growth of A. cribrarius was analyzed, based on some morphometric relations, where the carapace width, excluding lateral spines (CW), was used as an independent variable. A total of 403 specimens (189 males and 214 females), was collected in Ubatuba, State of São Paulo, Brazil, with otter-trawls. The animals were sexed and sorted to maturation phase (juvenile or adult). Some measurements were made: carapace (length and width excluding lateral spines), abdomen (greatest width of the fifth somite in females and the sixth in males) and major chela (greatest length, width and height, dactylus length). This study was made by the application of the power function (y=a.x(b)) which was fitted to the data and the pattern of growth established for each parameter by the ''b''-value (constant of allometry), as positive allometry (b>1), negative allometry (b<1) or isometry (b=1). The morphometric relations of the carapace showed a tendency to isometry. In females, the abdominal width grew in positive allometry, higher in juveniles (b=1.33) than in adults (b=1.18). In this case, an overlap and discontinuity was noticed between the phases over a carapace width range of 55 to 70 mm, where the puberty molt occurs. The majority of relationships showed that the major chela of the males grew in positive allometry, however, the greatest allometric difference between the phases was observed towards the propodus length with 1.09 as juvenile and 1.26 as adult ''b''values. In the males, this variable showed an inflection between the CW range of 45' to 55 mm, where the transition to the maturation phase occurs. The relative growth of this species is similar to those of previously studied species. This indicates, that the propodus length and the abdominal width are the morphometric variables most appropriate to estimate the size of the beginning of the sexual maturity for males and females of this species, respectively.

Bethe ansatz solutions for Temperley-Lieb quantum spin chains

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups U-q(X-n) for X-n = A(1), B-n, C-n and D-n. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, bleak quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

THE ALGEBRA OF NONLOCAL CHARGES IN NONLINEAR SIGMA-MODELS

We obtain the exact classical algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, now containing a calculable correction of order one unit lower. The relation with Yangians and the role of the results in the context of Lie-Poisson algebras are also discussed.

Relative growth of spider crab Acanthonyx scutiformis (Dana, 1851) (Crustacea, Decapoda, Majidae)

The dimensions of chelar propodus and abdomen were utilized for the morphometric analysis about the relative growth studies of Acanthonyx scutiformis (Dana, 1851). A total of 297 specimens (114 males and 183 females), was collected in Ubatuba, State of São Paulo, Brazil. The animals were sexed and soarted to maturation phase (immature and mature). The following measurements were made: carapace (length and width), abdomen width and chelar propodus (length and height). In this study was applicated the power function (y= a.x(b)), in which the growth was considered positive allometric with isometric with b=1, and negative allometric with b<1. The alometry becomes isometric, when the results concerning immature and mature females and males are analysed. In the Brachyura male chelipeds are utilized in territorial defense, fight, display and courtship and female abdomens are utilized as a chamber that protect and incubate the eggs.

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

Effects of Incubation Temperature and Relative Humidity on Embryonic Development in Eggs of Red-Winged Tinamou (Rhynchotus rufescens).

This study was conducted to assess the effects of incubation temperature (34 C, 36[degree]C and 38[degree]C) and relative humidity (RH, 50% and 60%) on egg weight loss, embryo mortality, hatchability, incubation time and chick weight in eggs from red-winged tinamou. The eggs were placed in incubators that were operated at 34[degree]C, 36[degree]C, or 38[degree]C and 50% or 60% RH (mean wet bulb temperatures of 28[degree]C and 30[degree]C, respectively) from day 1 to hatching. Each treatment had two replicate groups of 30 eggs each. Hatchability varied with incubation temperature and RH and was highest for eggs incubated at 36[degree]C and 60% RH and lowest for eggs incubated at 38[degree]C. Early, intermediate and late embryo mortality were highest at 38[degree]C, 38[degree]C/50% RH, and 50% RH, respectively. Incubation period was longest at 34[degree]C and shortest at 38[degree]C/50% RH. Present results show the highest hatchability of red-winged tinamou eggs after incubation at 36[degree]C and 60% RH; highest embryo sensitivity to high temperature in the early period of incubation (1 to 7 days), to high temperature and low RH in the second period of incubation (8-14 days) and to low RH in the late period of incubation (after 15 days) and shortest incubation period with increasing temperature and RH.

Inflation and relative prices: the Brazilian experience, 1970/79.

Based on behaviour of output growth and industrial sector prices, it tries to define the several stages comprising the cyclic trends of the Brazilian economy. Analyzes the behaviour of inflation rates and of relative prices, and shows that there is a positive association between the measures of inflation rates and of their variables as well as between both these measures and dispersion of relative price changes. Demonstrates the assymetric behaviour of relative price changes and differentiated behaviour in relative prices of farm produce and industrial products. -from Authors

Amazon fisheries. I. - Variations in the relative abundance of tambaqui ( Colossoma macropomum Cuvier, 1818) based on catch and effort data of the gill-net fisheries.

Adjusted mean catches which are calculated discounting the effect of average fishing effort increase the further the lake is from Manaus, Brazil. -from Author

The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein-Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin-1/2 field. © 1988 American Institute of Physics.

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w∞ algebra) is established.