Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation

A hidden nonlinear bosonized supersymmetry was revealed recently in Poschl-Teller and finite-gap Lame systems. In spite of the intimate relationship between the two quantum models, the hidden supersymmetry in them displays essential differences. In particular, the kernel of the supercharges of the Poschl-Teller system, unlike the case of Lame equation, includes nonphysical states. By means of Lame equation, we clarify the nature of these peculiar states, and show that they encode essential information not only on the original hyperbolic Poschl-Teller system, but also on its singular hyperbolic and trigonometric modifications, and reflect the intimate relation of the model to a free particle system.Comment: 10 pages, typos corrected; to appear in J. Phys.

A Note on Tachyons in the D3+D3ˉD3+{\bar {D3}} System

The periodic bounce of Born-Infeld theory of $D3$-branes is derived, and the BPS limit of infinite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born--Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3: explanations and references added. Final version to appear in Mod. Phys. Lett.

The Elliptic Billiard: Subtleties of Separability

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem can be solved. A geometric picture is given revealing why levels of a separable system cross. It is shown that the repulsions found by Ayant and Arvieu are computational effects and that the method used by Traiber et al. is related to the present picture which explains the crossings they find. An asymptotic formula for the energy-levels is derived and it is found that the statistical quantities of the spectrum P(s) and \Delta(L) have the form expected for an integrable system.Comment: 10 pages, LaTeX, 3 Figures (postscript). Submitted to European Journal of Physic

Fats and pellets in broiler rations

Published April 1957. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo

Use of corn, barley, and wheat with or without fat in broiler rations

Published January 1957. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo

Use of soybean meal, fish meal, and meat and bone meal as protein supplements in broiler rations

Published February 1959. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo

Effect of soybean meal, extruded soybeans and ground, raw soybeans on the performance of White Leghorn layers

Published December 1975. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo