639 research outputs found
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 on depending
on two parameters . For integers with
this operator extends to a self-adjoint operator on
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, -norms, integral representations and various recurrence
relations.
This fourth order differential operator arises as the
radial part of the Casimir action in the Schr\"odinger model of the minimal
representation of the group , and our "special functions" give
-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 -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
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