Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems

A new construction using finite dimensional dual grassmannians is developed to study rational and soliton solutions of the KP hierarchy. In the rational case, properties of the tau function which are equivalent to bispectrality of the associated wave function are identified. In particular, it is shown that there exists a bound on the degree of all time variables in tau if and only if the wave function is rank one and bispectral. The action of the bispectral involution, beta, in the generic rational case is determined explicitly in terms of dual grassmannian parameters. Using the correspondence between rational solutions and particle systems, it is demonstrated that beta is a linearizing map of the Calogero-Moser particle system and is essentially the map sigma introduced by Airault, McKean and Moser in 1977.Comment: LaTeX, 24 page

Optimal normal bases in GF(pn)

AbstractIn this paper the use of normal bases for multiplication in the finite fields GF(pn) is examined. We introduce the concept of an optimal normal basis in order to reduce the hardware complexity of multiplying field elements. Constructions for these bases in GF(2n) and extensions of the results to GF(pn) are presented. This work has applications in crytography and coding theory since a reduction in the complexity of multiplying and exponentiating elements of GF(2n) is achieved for many values of n, some prime

Beyond the simple Proximity Force Approximation: geometrical effects on the non-retarded Casimir interaction

We study the geometrical corrections to the simple Proximity Force Approximation for the non-retarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.Comment: 18 pages, 19 figures, 1 tabl

Species differences in the pattern of eicosanoids produced by inflamed and non-inflamed tissue

The synthesis of14C labelled arachidonic acid metabolites was measured in colonic tissues obtained from mice, rats, guinea pigs, rabbits, piglets and in colonic biopsies from humans during colonoscopy. The main eicosanoids formed after stimulation with calcium ionophore A23187 were: in humans, 15-hydroxy-eicosatetraenoic acid (15-HETE); in mice, 12-HETE; in rats, 12-HETE, 12-hydroxy-5,8,10-heptadecatrienoic acid (HHT) and 6-keto-prostaglandine F1α (6kPGF1α); in guinea pigs, PGD2; in rabbits, 6kPGF1α, PGE2 and 15-HETE; and in pigs PGE2 and 12-HETE. In inflamed 15-HETE production was increased in man, HHT and 12-HETE production in rats and overall eicosanoid production in mice

Radiative πρ\pi \rho and πω\pi \omega transition form factors in a light-front constituent quark model

The form factors of the $\pi \rho$ and $\pi \omega$ radiative transitions are evaluated within a light-front constituent quark model, using for the first time the eigenfunctions of a light-front mass operator reproducing the meson mass spectrum and including phenomenological Dirac and Pauli quark form factors in the one-body electromagnetic current operator. The sensitivity of the transition form factors both to the meson wave functions and to the constituent quark form factors is illustrated. It is shown that the measurement of the $\pi \rho$ and $\pi \omega$ radiative transitions could help in discriminating among various models of the meson structure.Comment: 9 pages, latex, 4 figures available as separate .uu file, to appear in Phys. Lett.

Nutrient availability of different batches of wheat distillers dried grains with solubles with and without exogenous enzymes for broiler chickens

Wheat distillers' dried grains with solubles (DDGS) are being used increasingly in the poultry feed industry but their nutritional value is variable. The aim of this experiment was to examine the effect of batch to batch variation of wheat DDGS produced by the same manufacturer on the growth performance, dietary N corrected apparent metabolizable energy (AMEn), energy conversion ratio (ECR), total tract dry matter retention (DMR), nitrogen retention (NR) and fat digestibility (FD) coefficients when fed to broilers in complete diets with and without enzyme supplementation. Six UK wheat DDGS samples, produced by a single manufacturer, were used in a broiler experiment. Six diets containing 150 g/kg of each selected wheat DDGS sample were mixed. Each diet was then split into two batches and one of them was supplemented with commercial enzyme preparation, providing 1220 units xylanase and 152 units of β-glucanase/kg diet, resulting in 12 experimental diets. Each diet was fed ad libitum to five pens of two male Ross 308 broilers from 7 to 21 d old. Enzyme supplementation improved dietary AMEn, DMR, NR (P < 0.001) and FD (P < 0.05) compared to non-supplemented diets. There was DDGS sample by enzyme interaction (P < 0.05) on daily weight gain and ECR. The results suggest that the variability in AMEn of DDGS samples produced from a single manufacturer is greater than expected compared to the variability of whole wheat samples but substantially lower than expected from wheat DDGS samples from different EU manufacturers. This experiment has shown that the variation in feeding value of wheat DDGS may be explained by the variability in polysaccharide contents

Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction

The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra $\widehat{gl}_{pr}\otimes {\Complex}[\lambda, \lambda^{-1}]$. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra $\widehat{gl}_{pr+s}\otimes {\Complex}[\lambda,\lambda^{-1}]$ using the natural embedding $gl_{pr}\subset gl_{pr+s}$ for $s$ any positive integer. The hierarchies obtained admit a description in terms of a $p\times p$ matrix pseudo-differential operator comprising an $r$-KdV type positive part and a non-trivial negative part. This system has been investigated previously in the $p=1$ case as a constrained KP system. In this paper the previous results are considerably extended and a systematic study is presented on the basis of the Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson brackets and makes clear the conformal ($\cal W$-algebra) structures related to the KdV type hierarchies. Discrete reductions and modified versions of the extended $r$-KdV hierarchies are also discussed.Comment: 60 pages, plain TE

Acidity-reactivity relationships in catalytic esterification over ammonium sulfate-derived sulfated zirconia

New insight was gained into the acidity-reactivity relationships of sulfated zirconia (SZ) catalysts prepared via (NH4)2SO4 impregnation of Zr(OH)4 for propanoic acid esterification with methanol. A family of systematically related SZs was characterized by bulk and surface analyses including XRD, XPS, TGA-MS, N2 porosimetry, temperature-programmed propylamine decomposition, and FTIR of adsorbed pyridine, as well as methylbutynol (MBOH) as a reactive probe molecule. Increasing surface sulfation induces a transition from amphoteric character for the parent zirconia and low S loadings <1.7 wt %, evidenced by MBOH conversion to 3-hydroxy-3-methyl-2-butanone, methylbutyne and acetone, with higher S loadings resulting in strong Brønsted-Lewis acid pairs upon completion of the sulfate monolayer, which favored MBOH conversion to prenal. Catalytic activity for propanoic acid esterification directly correlated with acid strength determined from propylamine decomposition, coincident with the formation of Brønsted-Lewis acid pairs identified by MBOH reactive titration. Monodispersed bisulfate species are likely responsible for superacidity at intermediate sulfur loadings

Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct the $W_n^l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.Comment: 41 page

An Analytic Variational Study of the Mass Spectrum in 2+1 Dimensional SU(3) Hamiltonian Lattice Gauge Theory

We calculate the masses of the lowest lying eigenstates of improved SU(2) and SU(3) lattice gauge theory in 2+1 dimensions using an analytic variational approach. The ground state is approximated by a one plaquette trial state and mass gaps are calculated in the symmetric and antisymmetric sectors by minimising over a suitable basis of rectangular states