Penrose Limit and String Theories on Various Brane Backgrounds

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.Comment: 41 pages, Latex, minor correction

Nonlocal symmetries of Riccati and Abel chains and their similarity reductions

We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our results show that all the equations in Riccati chain share the same form of nonlocal symmetry. The similarity reduced $N^{th}$ order ordinary differential equation (ODE), $N=2, 3,4,...$, in this chain yields $(N-1)^{th}$ order ODE in the same chain. All the equations in the Abel chain also share the same form of nonlocal symmetry (which is different from the one that exist in Riccati chain) but the similarity reduced $N^{th}$ order ODE, $N=2, 3,4,$, in the Abel chain always ends at the $(N-1)^{th}$ order ODE in the Riccati chain. We describe the method of finding general solution of all the equations that appear in these chains from the nonlocal symmetry.Comment: Accepted for publication in J. Math. Phy

Integral D-Finite Functions

We propose a differential analog of the notion of integral closure of algebraic function fields. We present an algorithm for computing the integral closure of the algebra defined by a linear differential operator. Our algorithm is a direct analog of van Hoeij's algorithm for computing integral bases of algebraic function fields

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by PT-symmetric interactions composed of imaginary delta functions which mimic creation/annihilation processes.Comment: Int. Worskhop "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (June 20 - 22, 2005, Koc Unversity, Istanbul(http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.htm) a part of talk (9 pages

MHD Memes

The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics.Comment: Submitted for publication in IOP Journal of Physics: Conference Series for publication in "Plasma Theory, Wave Kinetics, and Nonlinear Dynamics", Proceedings of KaufmanFest, 5-7 October 2007, University of California, Berkeley, US

Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use perturbation theory to obtain their evolution away from the bifurcation points. As an application, we derive an analytical semiclassical trace formula for the density of states in the separable case, using a uniform approximation for the pitchfork bifurcations occurring there, which allows for full semiclassical quantization. For the non-integrable situations, we show that the uniform contribution of the bifurcating period-one orbits to the coarse-grained density of states competes with that of the shortest isolated orbits, but decreases with increasing chaoticity parameter $\alpha$.Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear in J. Phys. A final version 3; error in eq. (33) corrected and note added in prin

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain

Proteomic analysis of Glossina pallidipes salivary gland hypertrophy virus virions for immune intervention in tsetse fly colonies

Many species of tsetse flies (Diptera: Glossinidae) can be infected by a virus that causes salivary gland hypertrophy (SGH). The viruses isolated from Glossina pallidipes (GpSGHV) and Musca somestica (MdSGHV) have recently been sequenced. Tsetse flies with SGH have a reduced fecundity and fertility which cause a serious problem for mass rearing in the frame of sterile insect technique (SIT) programs to control and eradicate tsetse populations in the wild. A potential intervention strategy to mitigate viral infections in fly colonies is neutralizing of the GpSGHV infection with specific antibodies against virion proteins. Two major GpSGHV virion proteins of about 130 kDa and 50 kDa, respectively, were identified by Western analysis using polyclonal rabbit antibody raised against whole GpSHGV virions. The proteome of GpSGHV, containing the antigens responsible for the immune-response, was investigated by liquid chromatography tandem mass spectrometry (LC-MS/MS) and 61 virion proteins were identified by comparison with the genome sequence. Specific antibodies were produced in rabbits against seven candidate proteins including the ORF10 / C-terminal fragment, ORF47 and ORF96 as well as proteins involved in peroral infectivity PIF-1 (ORF102), PIF-2 (ORF53), PIF-3 (ORF76) and P74 (ORF1). Antiserum against ORF10 specifically reacted to the 130 kDa protein in a Western blot analysis and to the envelope of GpSGHV using immunogold-EM. This result suggests that immune intervention of viral infections in colonies of G. pallidipes is a realistic optio

The Pseudothreshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

The values at pseudothreshold of two loop sunrise master amplitudes with arbitrary masses are obtained by solving a system of differential equations. The expansion at pseudothreshold of the amplitudes is constructed and some lowest terms are explicitly presented.Comment: 1+22 pages, Latex, no figures, changes in Eq.(41),(44),(47