A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term

The properties of a nonlinear oscillator with an additional term $k_g/x^2$, characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, $\kappa$ and $k_g$, in such a way that for $\kappa=0$ all the characteristics of of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form $m(x)=1/(1 - {\kappa} x^2)$, with a $\kappa$-dependent non-polynomial rational potential and with an additional isotonic term. The Schr\"odinger equation is exactly solved and the $(\kappa,k_g)$-dependent wave functions and bound state energies are explicitly obtained for both $\kappa0$.Comment: two figure

Muon Anomalous Magnetic Moment and Lepton Flavor Violating Tau Decay in Unparticle Physics

We study effects of unparticle physics on muon g-2 and LFV tau decay processes. LFV interactions between the Standard Model sector and unparticles can explain the difference of experimental value of muon g-2 from the Standard Model prediction. While the same couplings generate LFV tau decay, we found that LFV coupling can be of O(0.1 ... 1) without conflict with experimental bounds of LFV tau decay if the scaling dimension of unparticle operator d_{U} > 1.6.Comment: 12 pages, 7 figure

Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure

Models of Cosmic Order: Physical Expression of Sacred Space Among the Ancient Maya

The archaeological record, as well as written texts, oral traditions, and iconographic representations, express the Maya perception of cosmic order, including the concepts of quadripartite division and layered cosmos. The ritual act of portioning and layering created spatial order and was used to organize everything from the heavens to the layout of altars. These acts were also metaphors for world creation, world order, and establishing the center as a position of power and authority. This article examines the articulations of these concepts from the level of caches to the level of regions from the past and present in an attempt to understand these ancient perceptions. We emphasize that basic organizational notions of the cosmos permeate all societal levels and argue that scholars should expand their focus to include how the sacred landscape and its related ideology were reproduced in the lives of everyday people

Compound transfer matrices: Constructive and destructive interference

Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the compound barrier is simply given by the product of the transmission probabilities of the individual sub-barriers. In contrast if one is scattering waves (whether we are dealing with either purely classical waves or quantum Schrodinger wavefunctions) each sub-barrier contributes phase information (as well as a transmission probability), and these phases can lead to either constructive or destructive interference, with the transmission probability oscillating between nontrivial upper and lower bounds. In this article we shall study these upper and lower bounds in some detail, and also derive bounds on the closely related process of quantum excitation (particle production) via parametric resonance.Comment: V1: 28 pages. V2: 21 pages. Presentation significantly streamlined and shortened. This version accepted for publication in the Journal of Mathematical Physic

Synergy between HIV-1 Tat and adenovirus E1A is principally due to stabilization of transcriptional elongation

We studied the combined effects of Tat and general trans-activators, such as E1A and phorbol esters, on human immunodeficiency virus-1 (HIV-1) gene expression. Interaction between these two types of trans-activators may be involved in the transition from transcriptional quiesence during viral latency to active gene expression during productive infection. E1A cooperated with Tat to produce a fourfold greater increase in accumulation of full-length, cytoplasmic HIV-1-directed RNA than is expected if they were acting additively to increase RNA accumulation. Similarly, phorbol 12-myristate 13-acetate (PMA) also cooperated with Tat to elevate HIV RNA levels synergistically. Analysis of transcription rates across the HIV-1-directed transcription unit indicated, unexpectedly, that synergy between Tat and E1A could not be accounted for by increased promoter proximal transcription rates that were merely additive. However, Tat and E1A produced a greater than additive increase in transcription rates in the 3' end of the gene. These findings imply that synergy between Tat and E1A (or other general transcriptional activators) is due principally to stabilization of transcriptional elongation. Furthermore, the observation that Tat elicits only a small increase in promoter proximal transcription in the presence of E1A suggests that the magnitude of the effect of Tat on initiation is decreased when the basal level of transcription is increased. These findings underscore the importance of the ability of Tat to stabilize elongation, as well as to stimulate initiation, in an HIV-1-directed transcription unit

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl