Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance

In a recent article [M. Olshanii, Phys. Rev. Lett. {\bf 81}, 938 (1998)], an analytic solution of atom-atom scattering with a delta-function pseudopotential interaction in the presence of transverse harmonic confinement yielded an effective coupling constant that diverged at a `confinement induced resonance.' In the present work, we report numerical results that corroborate this resonance for more realistic model potentials. In addition, we extend the previous theoretical discussion to include two-atom bound states in the presence of transverse confinement, for which we also report numerical results hereComment: New version with major revisions. We now provide a detailed physical interpretation of the confinement-induced resonance in tight atomic waveguide

Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

RESEARCHES REGARDING THE OBTAINING OF JUICE FROM SUGAR SORGHUM STALK

Sugar sorghum is a technical plant with high energy value due to the high productivity obtained per hectare. By pressing of sugar sorghum strains it can be obtained a juice that can be further used in various forms: alcohol, ethanol, etc

The early evolution of the H-free process

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is formed. Let G be the random maximal H-free graph obtained at the end of the process. When H is strictly 2-balanced, we show that for some c>0, with high probability as $n \to \infty$, the minimum degree in G is at least $cn^{1-(v_H-2)/(e_H-1)}(\log n)^{1/(e_H-1)}$. This gives new lower bounds for the Tur\'an numbers of certain bipartite graphs, such as the complete bipartite graphs $K_{r,r}$ with $r \ge 5$. When H is a complete graph $K_s$ with $s \ge 5$ we show that for some C>0, with high probability the independence number of G is at most $Cn^{2/(s+1)}(\log n)^{1-1/(e_H-1)}$. This gives new lower bounds for Ramsey numbers R(s,t) for fixed $s \ge 5$ and t large. We also obtain new bounds for the independence number of G for other graphs H, including the case when H is a cycle. Our proofs use the differential equations method for random graph processes to analyse the evolution of the process, and give further information about the structure of the graphs obtained, including asymptotic formulae for a broad class of subgraph extension variables.Comment: 36 page

CONSIDERATIONS CONCERNING THE VALORIZATION OF THE JUICE OBTAINED FROM SUGAR SORGHUM STALK FROM ALCOHOL

 With a high production per hectare, sugar sorghum is a high value technical plant for farmers because from an average production of 70-80 t/ha, a high quantity of juice can be obtained, which can be used as such in the food industry (natural sweetener) or processed for the purpose of obtaining alcohol. The alcohol has a higher value/liter, can be stored more easily and its uses are multiple: in the food, pharmaceutical, chemical industry, etc

Spherical Universe topology and the Casimir effect

The mode problem on the factored 3--sphere is applied to field theory calculations for massless fields of spin 0, 1/2 and 1. The degeneracies on the factors, including lens spaces, are neatly derived in a geometric fashion. Vacuum energies are expressed in terms of the polyhedral degrees and equivalent expressions given using the cyclic decomposition of the covering group. Scalar functional determinants are calculated and the spectral asymmetry function treated by the same approach with explicit forms on one-sided lens spaces.Comment: 33 pages, 1 figure. Typos corrected and one reference adde

Исследование микроструктуры безобжиговых периклазоуглеродистых огнеупоров при использовании в качестве заполнителя различного вида периклаза

У статті представлено результати досліджень мікроструктури периклазовуглецевих зразків, у яких в якості наповнювача використовували різні види периклазу. Петрографічні дослідження показали, що зразки щільні та міцні, як на плавленому, так і на спеченому периклазі.In clause the results of researches of microstructure magnesia-carbon refractors are submitted, at which in quality filler used different kind magnesia. Microstructures of samples strong and dense, both on melted, and on sintered periclase have shown, that

Harmonic Sums and Mellin Transforms up to two-loop Order

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ of the momentum fraction $x$ emerging in the quantities of massless QED and QCD up to two--loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.Comment: 44 pages Latex, contract number adde

Feasibility studies of the time-like proton electromagnetic form factor measurements with PANDA at FAIR

The possibility of measuring the proton electromagnetic form factors in the time-like region at FAIR with the \PANDA detector is discussed. Detailed simulations on signal efficiency for the annihilation of $\bar p +p$ into a lepton pair as well as for the most important background channels have been performed. It is shown that precision measurements of the differential cross section of the reaction $\bar p +p \to e^++ e^-$ can be obtained in a wide angular and kinematical range. The individual determination of the moduli of the electric and magnetic proton form factors will be possible up to a value of momentum transfer squared of $q^2\simeq 14$ (GeV/c)$^2$. The total $\bar p +p\to e^++e^-$ cross section will be measured up to $q^2\simeq 28$ (GeV/c)$^2$. The results obtained from simulated events are compared to the existing data. Sensitivity to the two photons exchange mechanism is also investigated.Comment: 12 pages, 4 tables, 8 figures Revised, added details on simulations, 4 tables, 9 figure