Superintegrability on the two-dimensional hyperboloid

In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras

Not all surveillance data are created equal—A multi‐method dynamic occupancy approach to determine rabies elimination from wildlife

1. A necessary component of elimination programmes for wildlife disease is effective surveillance. The ability to distinguish between disease freedom and non‐detection can mean the difference between a successful elimination campaign and new epizootics. Understanding the contribution of different surveillance methods helps to optimize and better allocate effort and develop more effective surveillance programmes. 2. We evaluated the probability of rabies virus elimination (disease freedom) in an enzootic area with active management using dynamic occupancy modelling of 10 years of raccoon rabies virus (RABV) surveillance data (2006–2015) collected from three states in the eastern United States. We estimated detection probability of RABV cases for each surveillance method (e.g. strange acting reports, roadkill, surveillance‐trapped animals, nuisance animals and public health samples) used by the USDA National Rabies Management Program. 3. Strange acting, found dead and public health animals were the most likely to detect RABV when it was present, and generally detectability was higher in fall– winter compared to spring–summer. Found dead animals in fall–winter had the highest detection at 0.33 (95% CI: 0.20, 0.48). Nuisance animals had the lowest detection probabilities (~0.02). 4. Areas with oral rabies vaccination (ORV) management had reduced occurrence probability compared to enzootic areas without ORV management. RABV occurrence was positively associated with deciduous and mixed forests and medium to high developed areas, which are also areas with higher raccoon (Procyon lotor) densities. By combining occupancy and detection estimates we can create a probability of elimination surface that can be updated seasonally to provide guidance on areas managed for wildlife disease. 5. Synthesis and applications. Wildlife disease surveillance is often comprised of a combination of targeted and convenience‐based methods. Using a multi‐method analytical approach allows us to compare the relative strengths of these methods, providing guidance on resource allocation for surveillance actions. Applying this multi‐method approach in conjunction with dynamic occupancy analyses better informs management decisions by understanding ecological drivers of disease occurrence

Temperature Effects on Threshold Counterion Concentration to Induce Aggregation of fd Virus

We seek to determine the mechanism of like-charge attraction by measuring the temperature dependence of critical divalent counterion concentration ($\rm{C_{c}}$) for the aggregation of fd viruses. We find that an increase in temperature causes $\rm{C_c}$ to decrease, primarily due to a decrease in the dielectric constant ($\epsilon$) of the solvent. At a constant $\epsilon$, $\rm{C_c}$ is found to increase as the temperature increases. The effects of $T$ and $\epsilon$ on $\rm {C_{c}}$ can be combined to that of one parameter: Bjerrum length ($l_{B}$). $\rm{C_{c}}$ decreases exponentially as $l_{B}$ increases, suggesting that entropic effect of counterions plays an important role at the onset of bundle formation.Comment: 12 pages, 3 figure

Interpreting the seasonal cycles of atmospheric oxygen and carbon dioxide concentrations at American Samoa Observatory

We present seven years of atmospheric O2/N2 ratio and CO2 concentration data measured from flask samples collected at American Samoa. These data are unusual, exhibiting higher short-term variability, and seasonal cycles not in phase with other sampling stations. The unique nature of atmospheric data from Samoa has been noted previously from measurements of CO2, methyl chloroform, and ozone. With our O2 data, we observe greater magnitude in the short-term variability, but, in contrast, no clear seasonal pattern to this variability. This we attribute to significant regional sources and sinks existing for O2 in both hemispheres, and a dependence on both the latitudinal and altitudinal origins of air masses. We also hypothesize that some samples exhibit a component of "older" air, demonstrating recirculation of air within the tropics. Our findings could be used to help constrain atmospheric transport models which are not well characterized in tropical regions

The Accretion of Lyman Alplha Clouds onto Gas-Rech Protogalaxies; A Scenario for the Formation of Globular Star Clusters

A satisfactory theory for the formation of globular star clusters (GCs) has long been elusive, perhaps because their true progenitors had not yet been guessed. In this paper I propose a causal relationship between the strongly decreasing densities of Lyman alpha (LyA) clouds at high redshift and the formation of GCs - namely that GCs were created by the accretion of LyA clouds onto protogalaxies. I describe a scenario which involves an inherently stable and orderly cycling of compression and cooling in the central cores of clouds during the extended period of dissipation in the outer regins of gas-rich proto galaxies, culminating in a burst of efficient star formation. I demonstrate that the comoving density of GCs is comparable to that of LyA clouds at high redshift, that the energetic requirements for compression to core GC densities can be met, and that the time-scale for cooling is within obvious limits imposed by dynamical stability. This dissipative process requires there to be a large column of dissipated gas about the attractor in order to form GCs. In addition, the energy requirements for compression requires attractor masses greater than that capable of sustaining circular velocities of ~40 km/s. If this scenario is supported by numerical simulations, then by implication, the GCs were formed at modest redshifts of z~1-3. This knowledge could help to break the degeneracy between lookback time and redshift. The model is consistent with a picture of hierarchical galaxy growth over time scales of many billions of years.Comment: 7 pages. Accepted, 10 June 1999 Astrophysical Journa

Generalized Morse Potential: Symmetry and Satellite Potentials

We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schr\"odinger equation with the Laplace equation on the hyperboloid and the Schr\"odinger equation for the P\"oschl-Teller potential, we explain the exact solvability of the problem by an $so(2,2)$ symmetry algebra, and obtain an explicit realization of the latter as $su(1,1) \oplus su(1,1)$. We prove that some of the $so(2,2)$ generators connect among themselves wave functions belonging to different GMP's (called satellite potentials). The conserved quantity is some combination of the potential parameters instead of the level energy, as for potential algebras. Hence, $so(2,2)$ belongs to a new class of symmetry algebras. We also stress the usefulness of our algebraic results for simplifying the calculation of Frank-Condon factors for electromagnetic transitions between rovibrational levels based on different electronic states.Comment: 23 pages, LaTeX, 2 figures (on request). one LaTeX problem settle

Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

Transabdominal ultrasonographic evaluation of fetal well-being in the late-term mare and cow

In the equine practice, attempts have been made to examine the fetus in the second and third trimester of pregnancy but all of the available methods have limitations. Until now, transabdominal ultrasonography has been regarded as the most informative examination. This method allows us to measure fetal heart rate, fetal activity as well as the quality and quantity of the fetal fluids. A modified biophysical profile for horses was used by several researchers in the USA from the 1990s as a gold standard. However, it is not sensitive enough and, in the authors’ experience, professionals can face difficulties during its application (e.g. for measuring aortic diameter and fetal breathing movements). In cows, this method was first used for this purpose by a Canadian research group in 2007. They reported that transabdominal ultrasound was promising but showed low sensitivity in this species. The present studies show that birth weight cannot be predicted from fetal aortic diameter measurement in cows as suggested by other researchers. Transabdominal ultrasound needs special equipment (2–3.5 MHz convex transducer) and basic ultrasonographic knowledge; however, we suggest that in most cases it can be performed with the dam placed in a stock and without shaving the examination area. The method provides useful information within 30–40 minutes, enabling the examiner to determine whether or not the fetus is alive and to recognise placentitis or twins. This technique also allows measuring the combined thickness of the uteroplacental unit, and the authors’ ongoing study showed higher normal values in Lipizzaner mares compared to values in other breeds. In conclusion, with the help of advanced techniques, simple and low-cost methods should be developed for the evaluation of the pregnant dam and its fetus to assess fetal viability in the veterinary practice

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

The Coulomb-Oscillator Relation on n-Dimensional Spheres and Hyperboloids

In this paper we establish a relation between Coulomb and oscillator systems on $n$-dimensional spheres and hyperboloids for $n\geq 2$. We show that, as in Euclidean space, the quasiradial equation for the $n+1$ dimensional Coulomb problem coincides with the $2n$-dimensional quasiradial oscillator equation on spheres and hyperboloids. Using the solution of the Schr\"odinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem.Comment: 15 pages, LaTe