Convenient parameterizations of matrices in terms of vectors

Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely reviewed, and new ones introduced

Asymptotic solitons of the Johnson equation

We prove the existence of non-decaying real solutions of the Johnson equation, vanishing as $x\to+\infty$. We obtain asymptotic formulas as $t\to\infty$ for the solutions in the form of an infinite series of asymptotic solitons with curved lines of constant phase and varying amplitude and width

A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

Freezing of Nonlinear Bloch Oscillations in the Generalized Discrete Nonlinear Schrodinger Equation

The dynamics in a nonlinear Schrodinger chain in an homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomenon.Comment: LaTeX, 7 pages, 6 figures. Improved version to appear in Phys. Rev.

Complete Wetting of Pits and Grooves

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: (i) one-dimensional periodic arrays of rectangular or parabolic grooves and (ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.Comment: 12 page

Taxa de concepção de cabras inseminadas com sêmen caprino resfriado a 5°C, por 12 ou 24 horas, em meio diluidor à base de gema de ovo.

Avaliou-se a capacidade fecundante do sêmen caprino resfriado a 5°C, por 12 (TI) ou 24 horas (TII), em container especial. Para tanto, utilizaram-se 62 fêmeas e dois reprodutores (B1 e B2) da raça Toggenburg, distribuídos em um esquema fatorial 2x2 (dois reprodutores e dois períodos de estocagem do sêmen). Após a coleta, o sêmen foi diluído em Tris-frutose-gema de ovo a 2,5%, envasado em palhetas de 0,25mL, com 150x106 espermatozoides móveis e resfriado a 5oC. As fêmeas receberam duas doses de 22,5µg de PGF2a, em intervalos de 10 dias para a sincronização do estro. A partir da primeira aplicação de PGF2a, as fêmeas foram monitoradas para ocorrência de estro, três vezes ao dia. Realizou-se uma única inseminação, pela técnica de fixação da cérvice, 12 horas após o início do estro. A motilidade e o vigor, após 12 ou 24 horas de resfriamento, foram de 66,14±0,11% e 62,50±0,05%, e 3,46±0,61 e 3,27±0,50, respectivamente. Não houve influência (P>0,05) do reprodutor, nem do período de armazenamento do sêmen sobre a taxa de concepção das cabras, que foi de 49,1%. Conception rate of goats inseminated with semen cooled in egg yolk diluent at 5 degrees C, for 12 or 24 hours. Abstract: The fertilizing capacity of goat semen cooled in egg yolk diluent at 5 degrees C, for 12 or 24 hours was evaluated. Sixty-two Toggenburg does and two sexually mature Toggenburg bucks were used in a fatorial treatment combination (two bucks and two storage periods). The semen was diluted in 2.5% Tris-frutose-egg yolk; envased in 0.25mL plastic straws, with 150x10(6) mobile spermatozoa; and cooled at 5 degrees C for 12 or 24 hours. The females received two doses of 22.5 mu g of prostaglandine F2 alpha, at each 10-day intervals in order to synchronize the estrous. From the first PGF2 alpha injection, estrous occurrence was monitored three times per day. Only one insemination was used, using the cervix fixation method, 12 hours after the estrous onset. The means of motility and strength, 12 (TI) and 24 hours (TII) after semen cooling at 5 degrees C, were 66.14 +/- 0.11% and 62.50 +/- 0.05%, and 3.46 +/- 0.61 and 3.27 +/- 0.50, respectively. Neither the sire nor the period of semen influenced (P>0.05) the conception rate of the does, which was 49.1%

Progesterona plasmática e fertilidade de fêmeas caprinas submetidas à sincronização do estro com prostaglandina F2?.

Resumo: Avaliou-se a resposta ao protocolo de sincronização do estro com duas doses de prostaglandina F2 (22,5µg) intervaladas de 10 dias, por meio da mensuração da concentração de progesterona plasmática, bem como a taxa de concepção das cabras após a inseminação artificial, de acordo com as diferentes respostas obtidas. Utilizaram-se 23 fêmeas e dois reprodutores da raça Toggenburg. A mensuração da progesterona plasmática foi realizada no dia da primeira aplicação de PGF2? (D0), no D5, no dia da segunda aplicação de PGF2? (D10), no D15, no D20 e no D33. A resposta positiva à PGF2? foi determinada pela queda da concentração de progesterona a valores abaixo de 1,5ng/mL, mensurada nos dias cinco e 15. As fêmeas foram distribuídas em três grupos. O grupo I foi composto por fêmeas que responderam às duas aplicações; o grupo II por fêmeas que não responderam à primeira aplicação e responderam à segunda aplicação; e o grupo III por fêmeas que responderam à primeira aplicação e não responderam à segunda aplicação, foram inseminadas e não conceberam. A presença de um corpo lúteo funcional, no momento das aplicações, determinou a resposta ao protocolo. As diferentes respostas das fêmeas ao protocolo, grupo I e II, não influenciaram as taxas de concepção. Plasmatic progesterone and fertility of goats submitted at estrus synchronization with Prostaglandin F2?. Abstract: Plasmatic progesterone concentrations were evaluated during the synchronization protocol with two doses of 22.5µg of Prostaglandin F2?, 10-day interval, and the conception rate of females in accordance to the reply to the protocol. Twenty-three female goats and two sexually mature Toggenburg bucks were used. Blood was sampled on day 0 (1st PGF2? injection), and on the following days 5, 10 (2nd PGF2? injection), 15, 20, and 33. The positive reply to the PGF2? was determined when the progesterone concentrations fell to values below 1.5ng/mL at days 5 and 15. The females were divided in three groups: Group I: females that responded to the two PGF2? applications; Group II: females that responded only to the second application; Group III: females that responded the first application, did not respond to the second application, were inseminated but did not conceive. The presence of a functional corpus luteum at the moment of the applications determined the reply to the protocol. There was no difference in the conception rates between females that responded to the two PGF2? applications or responded only to the second application