Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two dimensions. In the case of motion in the vicinity of an attractive fixed point, it is shown how the solution of this equation can be developed as a power series. The coefficients are determined exactly by using algebraic properties of a system of annihilation and creation operators.Comment: 7 pages, 0 figure

Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors

Roentgen cephalometric analysis of ridge resorption and changes in jaw and occlusal relationships in immediate complete denture wearers

In eighteen subjects assigned for immediate complete upper and lower dentures, roentgen cephalometric recordings were made before extraction of the residual anterior dentition and 3 weeks, 3 months, 6 months and 1 year after denture insertion. The cephalometric analysis was based on electronic measurements of linear and angular morphological variables and computer head plots generated from 177 reference points (Walker, 1967), derived for each subject for each of the five observation stages. The reduction of the alveolar ridges was most rapid during the first 3 months of denture wear and particularly during the post-extraction period of 3 weeks. The reduction in anterior height of the lower ridge was on average twice as great as that of the upper ridge. The ridge resorption and the accompanying settling of the dentures on the basal seats, measured from lead shots inserted in the dentures, brought about an upward rotation of the mandible with a resulting decrease in occlusal vertical dimension and reduction in overjet of the dentures. In accordance with the amount of ridge reduction, these changes showed great individual variation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73577/1/j.1365-2842.1980.tb01466.x.pd

On manifolds with nonhomogeneous factors

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces

Using VR to investigate the relationship between visual acuity and severity of simulated oscillopsia

Purpose: Oscillopsia is a debilitating symptom resulting from involuntary eye movement most commonly associated with acquired nystagmus. Investigating and documenting the efects of oscillopsia severity on visual acuity (VA) is challenging. This paper aims to further understanding of the efects of oscillopsia using a virtual reality simulation. Methods: Fifteen right-beat horizontal nystagmus waveforms, with diferent amplitude (1°, 3°, 5°, 8° and 11°) and frequency (1.25 Hz, 2.5 Hz and 5 Hz) combinations, were produced and imported into virtual reality to simulate diferent severities of oscillopsia. Fifty participants without ocular pathology were recruited to read logMAR charts in virtual reality under stationary conditions (no oscillopsia) and subsequently while experiencing simulated oscillopsia. The change in VA (logMAR) was calculated for each oscillopsia simulation (logMAR VA with oscillopsia – logMAR VA with no oscillopsia), removing the inluence of diferent baseline VAs between participants. A one-tailed paired t-test was used to assess statistical signiicance in the worsening in VA caused by the oscillopsia simulations. Results: VA worsened with each incremental increase in simulated oscillopsia intensity (frequency x amplitude), either by increasing frequency or amplitude, with the exception of statistically insigniicant changes at lower intensity simulations. Theoretical understanding predicted a linear relationship between increasing oscillopsia intensity and worsening VA. This was supported by observations at lower intensity simulations but not at higher intensities, with incremental changes in VA gradually levelling of. A potential reason for the diference at higher intensities is the inluence of frame rate when using digital simulations in virtual reality. Conclusions: The frequency and amplitude were found to equally afect VA, as predicted. These results not only consolidate the assumption that VA degrades with oscillopsia but also provide quantitative information that relates these changes to amplitude and frequency of oscillopsia

Carotenoid content and reflectance of yellow and red nuptial plumages in widowbirds (Euplectes spp.)

1. Ornamental carotenoid coloration is commonly based on several different pigments with different nutritional and metabolic constraints. The identification and quantification of carotenoid pigments is therefore crucial to the understanding of signal content and signal evolution. 2. In male widowbirds (Euplectes spp.), the striking yellow and red carotenoid colours have been measured by reflectance spectrometry and studied with respect to sexual selection through male contest competition, but their biochemical mechanisms have not been analysed. 3. Here we use reflectance analysis and high performance liquid chromatography (HPLC) to describe the species-specific colours and plumage carotenoids in three widowbird species: yellow-mantled widowbird (YMW) Euplectes macrourus, red-shouldered widowbird (RSW) E. axillaris and red-collared widowbird (RCW) E. ardens. 4. YMW yellow (‘hue’ colorimetric λR50 = 522 nm) derives from the two ‘dietary yellow’ xanthophylls lutein and zeaxanthin, together with small amounts of ‘derived yellow’ pigments (3′-dehydrolutein and canary xanthophylls). 5. RCW red (λR50 = 574 nm) is achieved by the addition of low concentrations of ‘derived red ’ 4-keto-carotenoids, notably α- and β-doradexanthin and canthaxanthin. 6. RSW red (λR50 = 589 nm) is, in contrast, created by high concentrations of ‘dietary yellow ’ pigments (lutein, zeaxanthin) and ‘derived yellow ’ anhydrolutein, the latter only recently described in birds. 7. The two different mechanisms of producing red plumage are compared with other bird species and discussed with regard to costs and signal ‘honesty’

Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Massive stars as thermonuclear reactors and their explosions following core collapse

Nuclear reactions transform atomic nuclei inside stars. This is the process of stellar nucleosynthesis. The basic concepts of determining nuclear reaction rates inside stars are reviewed. How stars manage to burn their fuel so slowly most of the time are also considered. Stellar thermonuclear reactions involving protons in hydrostatic burning are discussed first. Then I discuss triple alpha reactions in the helium burning stage. Carbon and oxygen survive in red giant stars because of the nuclear structure of oxygen and neon. Further nuclear burning of carbon, neon, oxygen and silicon in quiescent conditions are discussed next. In the subsequent core-collapse phase, neutronization due to electron capture from the top of the Fermi sea in a degenerate core takes place. The expected signal of neutrinos from a nearby supernova is calculated. The supernova often explodes inside a dense circumstellar medium, which is established due to the progenitor star losing its outermost envelope in a stellar wind or mass transfer in a binary system. The nature of the circumstellar medium and the ejecta of the supernova and their dynamics are revealed by observations in the optical, IR, radio, and X-ray bands, and I discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry" Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure