Chemical composition of oysters from São Paulo and Paraná, Brazil

During the years 1966/67 a comparative study of the chemical composition of oysters was performed on protein, water, ash, trimethylamine oxide, trimethylamine, crude glycogen, iron (Fe+ + +) , calcium, magnesium, total and inorganic phosphorus, with oysters coming from the lagoon regions of the State of São Paulo, namely Cananéia and Bertioga Channel (Santos), and from the State of Paraná. The oyster discussed here is the species found on mangrove tree stilt roots. It was determined as Ostrea arborea Chemnitz, by Dr. Hugo de Souza Lopes, Museu Nacional do Rio de Janeiro. Other zoologists have placed the present species in the genus Crassostrea. Appraisal of the analytical results of the oysters was made taking into consideration the reproductive cycle and the meteorological conditions of the three regions under study. A seasonal variation was observed regarding fat, crude glycogen, dry matter and energy content when related to fresh and dry matter, and of protein when expressed in relation to dry matter. The seasonal variation are related to the reproductive cycle of oysters and is probably influenced by water temperature variations which depend on the solar radiation incidence, and also by phytoplankton abundance. We endeavoured to determine the season when distinct phases of the oyster reproductive cycle occurs, fattening, ripening, gonadal and sexual products discharge, for each one of the three regions studied, as well as the most favorable time of the year for comsumption (winter and spring). This paper shows that oysters are a complementary source of food and income, that their production must be managed for an optimum return to the population inhabiting the lagoon regions of Brazil southern coast.Durante 1966-1967, foi efetuado um estudo comparativo da variação da composição química da ostra (proteína, matéria graxa, água, cinza, óxido de trimetilamina, glicogênio cru, cálcio, magnésio, ferro (Fe+ + + ), fósforo total e inorgânico), proveniente de regiões lagunares do Estado de São Paulo: Cananéia e Canal da Bertioga (Santos), e do Estado do Paraná: Paranaguá. A análise dos resultados foi efetuada, levando-se em consideração o ciclo reprodutivo da ostra e as condições meteorológicas das três regiões em estudo. Com base no observado pode-se considerar o seguinte: 1 - Os teores de umidade das ostras analisadas estão mais próximos dos obtidos por outros autores no gênero Crassostrea do que no gênero Ostrea; 2 - Os teores de magnésio mais elevados que os de cálcio, divergem da maioria dos dados de outros autores, concordando somente com os de NELSON & COULSON (1939), para Crassostrea gigas da costa do Pacífico, Estados Unidos. 3 - Os teores de proteína e cinzas, são em geral mais baixos que os constatados por outros autores; 4 - Foi constatada em 19 análises, dentre 32, a presença de óxido de trimetilamina (TMO), divergindo das observações de ausência total de TMO feita por NORRIS & BERNOIT (1945), para O. japonica, no Pacífico, e DYER (1952), para O. virginica, no Atlântico, únicos que citam trabalhos de TMO em ostra; 5 - Os valores energéticos observados se revelaram mais baixos que os constatados por RUSSEL (1923), TULLEY (1935) e KRVARIC (1953); 6 - Foi observada uma variação sazonal nos teores energéticos das ostras: inverno e primavera, elevados; verão e outono, baixos, concordando com RUSSEL, TULLEY e KRVARIC (op. cit.); 7 - Foi constatada variação sazonal correspondente entre si para os teores de glicogênio, matéria graxa e matéria seca, para a expressão em função da matéria fresca e seca; 8 - A proteína somente apresentou variação sazonal quando expressa em função da matéria seca, sendo oposta à de glicogênio e matéria graxa; 9 - As variações de glicogênio, matéria graxa e matéria seca, estão relacionadas com o ciclo reprodutivo das ostras, sugerindo os seguintes períodos propostos por MATSUMOTO et al. (1934) e analisados para as nossas condições: a) "Fattening": Paranaguá - julho à agosto/66; fevereiro à abril/67; Cananéia - maio à julho/66; março à abril/67; Santos - março à maio/66; julho à agosto/66; março à abril/67. b) "Gonadal ripening": Paranaguá - agosto à outubro/66; Santos - agosto à setembro/66; novembro à dezembro/66. c) "Discharge of sexual products": Paranaguá - maio à julho/66; outubro a dezembro/66; janeiro à fevereiro/67; Cananéia - julho/66 à março/67; abril à julho/67; Santos - maio à junho/66; setembro à outubro/66; dezembro/66 à março/67. 10 - As variações do ciclo reprodutivo são evidenciadas pela variações dos teores de glicogênio, matéria graxa e matéria seca, estando possivelmente relacionadas com a temperatura da água e esta com a radiação solar recebida (Q); 11 - Observou-se uma relação inversa da energia solar recebida (Q) e os teores de glicogênio e de matéria seca das ostras analisadas; 12 - As semelhanças observadas entre a composição química das ostras procedentes de Paranaguá, Cananéia e Canal da Bertioga (Santos), poderão ser consequentes da semelhança dos fatores meteorológicos atuantes, temperatura da água e do ar, precipitação e radiação solar; 13 - É possível que as variações da composição química e portanto o ciclo reprodutivo, observados para 1966/67, influenciados pelas condições meteorológicas desse período, sejam representativos para cada região em virtude da concordância deste período com o representativo da região; 14 - As ostras apresentam melhores características para o consumo, sob o ponto de vista energético e aceitabilidade durante o inverno e primavera; 15 - A determinação da matéria seca poderá ser usada, nas nossas condições, como indicadores das variações dos teores de glicogênio e matéria graxa e, conseqüentemente, do ciclo de reprodução

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

The Dirac-Dowker Oscillator

The oscillator-like interaction is introduced in the equation for the particle of arbitrary spin, given by Dirac and re-written to a matrix form by Dowker.Comment: LaTeX file, 4pp. Preprint EFUAZ 94-0

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and $\gamma^5$ chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry related problems have the same spectrum, but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.Comment: 33 pages, 10 figures, uses revtex macro

Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes

Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The analysis of the fractional version (of order $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ with real sign-varying density is constructed and some of its properties examined. The equation of vibrations of plates is considered and the case of circular vibrating disks $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure

Comment on ``the Klein-Gordon Oscillator''

The different ways of description of the $S=0$ particle with oscillator-like interaction are considered. The results are in conformity with the previous paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p

Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size $t$. We compute the disorder average distributions of the local time, the inverse local time, the occupation time and the inverse occupation time, and show that in many cases disorder modifies the behavior drastically.Comment: Revtex two column 27 pages, 10 figures, 3 table

Brownian Simulations and Uni-Directional Flux in Diffusion

Brownian dynamics simulations require the connection of a small discrete simulation volume to large baths that are maintained at fixed concentrations and voltages. The continuum baths are connected to the simulation through interfaces, located in the baths sufficiently far from the channel. Average boundary concentrations have to be maintained at their values in the baths by injecting and removing particles at the interfaces. The particles injected into the simulation volume represent a unidirectional diffusion flux, while the outgoing particles represent the unidirectional flux in the opposite direction. The classical diffusion equation defines net diffusion flux, but not unidirectional fluxes. The stochastic formulation of classical diffusion in terms of the Wiener process leads to a Wiener path integral, which can split the net flux into unidirectional fluxes. These unidirectional fluxes are infinite, though the net flux is finite and agrees with classical theory. We find that the infinite unidirectional flux is an artifact caused by replacing the Langevin dynamics with its Smoluchowski approximation, which is classical diffusion. The Smoluchowski approximation fails on time scales shorter than the relaxation time $1/\gamma$ of the Langevin equation. We find the unidirectional flux (source strength) needed to maintain average boundary concentrations in a manner consistent with the physics of Brownian particles. This unidirectional flux is proportional to the concentration and inversely proportional to $\sqrt{\Delta t}$ to leading order. We develop a BD simulation that maintains fixed average boundary concentrations in a manner consistent with the actual physics of the interface and without creating spurious boundary layers

Maximum likelihood drift estimation for a threshold diffusion

We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold diffusion is called drifted Oscillating Brownian motion.For this continuously observed diffusion, the maximum likelihood estimator coincide with a quasi-likelihood estimator with constant diffusion term. We show that this estimator is the limit, as observations become dense in time, of the (quasi)-maximum likelihood estimator based on discrete observations. In long time, the asymptotic behaviors of the positive and negative occupation times rule the ones of the estimators. Differently from most known results in the literature, we do not restrict ourselves to the ergodic framework: indeed, depending on the signs of the drift, the process may be ergodic, transient or null recurrent. For each regime, we establish whether or not the estimators are consistent; if they are, we prove the convergence in long time of the properly rescaled difference of the estimators towards a normal or mixed normal distribution. These theoretical results are backed by numerical simulations

Relativistic quantum mechanics of a Dirac oscillator

The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in quantum chromodynamics. These considerations should be enough for demonstrating that the Dirac oscillator can be an excellent example in relativistic quantum mechanics. In this paper we offer a solution to the problem and discuss some of its properties. We also discuss a physical picture for the Dirac oscillator's non-standard interaction, showing how it arises on describing the behaviour of a neutral particle carrying an anomalous magnetic moment and moving inside an uniformly charged sphere.Comment: 19 pages, 1 figur