Supercongruences of Atkin and Swinnerton-Dyer type for Legendre polynomials

AbstractIn this paper we prove some generalisations of congruences of Atkin and Swinnerton-Dyer type. This is done in the form of congruences for numbers Pn(A√Δ), where Pn(t) are the orthogonal polynomials of Legendre. The proofs are based on complex multiplication of elliptic functions

Use of high-dimensional spectral data to evaluate organic matter, reflectance relationships in soils

Recent breakthroughs in remote sensing technology have led to the development of a spaceborne high spectral resolution imaging sensor, HIRIS, to be launched in the mid-1990s for observation of earth surface features. The effects of organic carbon content on soil reflectance over the spectral range of HIRIS, and to examine the contributions of humic and fulvic acid fractions to soil reflectance was evaluated. Organic matter from four Indiana agricultural soils was extracted, fractionated, and purified, and six individual components of each soil were isolated and prepared for spectral analysis. The four soils, ranging in organic carbon content from 0.99 percent, represented various combinations of genetic parameters such as parent material, age, drainage, and native vegetation. An experimental procedure was developed to measure reflectance of very small soil and organic component samples in the laboratory, simulating the spectral coverage and resolution of the HIRIS sensor. Reflectance in 210 narrow (10 nm) bands was measured using the CARY 17D spectrophotometer over the 400 to 2500 nm wavelength range. Reflectance data were analyzed statistically to determine the regions of the reflective spectrum which provided useful information about soil organic matter content and composition. Wavebands providing significant information about soil organic carbon content were located in all three major regions of the reflective spectrum: visible, near infrared, and middle infrared. The purified humic acid fractions of the four soils were separable in six bands in the 1600 to 2400 nm range, suggesting that longwave middle infrared reflectance may be useful as a non-destructive laboratory technique for humic acid characterization

Behavioral and Genetic Diversity during Dispersal: Analysis of a Polymorphic Esterase Locus in Southern Pine Beetle, Dendroctonus frontalis

Dispersal behavior of the southern pine beetle, Dendroctonus frontalis Zimmermann (Coleoptera: Scolytidae), in response to synthetic aggregating pheromone (frontalin) indicates an exponential decrease in response with distance from the site of emergence. Differential response during dispersal among genotypes at a polymorphic esterase locus was found by using starch gel electrophoresis. These differences produced allelic distributions that predict increased genetic diversity concurrent with increasing dispersal distance from the source population

3D simulations of gas puff effects on edge density and ICRF coupling in ASDEX Upgrade

In recent experiments, a local gas puff was found to be an effective way to tailor the scrape-off layer (SOL) density and improve the ion cyclotron range of frequency (ICRF) power coupling in tokamaks. In order to quantitatively reproduce these experiments, to understand the corresponding physics and to optimize the gas valve positions and rates, simulations were carried out with the 3D edge plasma transport code EMC3-EIRENE in ASDEX Upgrade. An inter-ELM phase of an H-mode discharge with a moderate gas puff rate (1.2 x 10(22) electrons s(-1)) is used in our simulations. We simulated cases with gas puff in the lower divertor, the outer mid-plane and the top of the machine while keeping other conditions the same. Compared with the lower divertor gas puff, the outer mid-plane gas puff can increase the local density in front of the antennas most effectively, while a toroidally uniform but significantly smaller enhancement is found for the top gas puff. Good agreement between our simulations and experiments is obtained. With further simulations, the mechanisms of SOL density tailoring via local gas puffing and the strategies of gas puff optimization are discussed in the paper

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, $\rho^2$(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for~: single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also give attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between $\rho^2$(E0) and isotopic shifts

Modelling of the ICRF induced E x B convection in the scrape-off-layer of ASDEX Upgrade

In magnetic controlled fusion devices, plasma heating with radio-frequency (RF) waves in the ion cyclotron (IC) range of frequency relies on the electric field of the fast wave to heat the plasma. However, the slow wave can be generated parasitically. The electric field of the slow wave can induce large biased plasma potential (DC potential) through sheath rectification. The rapid variation of the rectified potential across the equilibrium magnetic field can cause significant convective transport (E x B drifts) in the scrape-off layer (SOL). In order to understand this phenomenon and reproduce the experiments, 3D realistic simulations are carried out with the 3D edge plasma fluid and kinetic neutral code EMC3-Eirene in ASDEX Upgrade. For this, we have added the prescribed drift terms to the EMC3 equations and verified the 3D code results against the analytical ones in cylindrical geometry. The edge plasma potential derived from the experiments is used to calculate the drift velocities, which are then treated as input fields in the code to obtain the final density distributions. Our simulation results are in good agreement with the experiments

Ionospheric response to the 2009 sudden stratospheric warming over the equatorial, low, and middle latitudes in the South American sector

The present study investigates the ionospheric total electron content (TEC) and F-layer response in the Southern Hemisphere equatorial, low, and middle latitudes due to major sudden stratospheric warming (SSW) event, which took place during January-February 2009 in the Northern Hemisphere. In this study, using 17 ground-based dual frequency GPS stations and two ionosonde stations spanning latitudes from 2.8°N to 53.8°S, longitudes from 36.7°W to 67.8°W over the South American sector, it is observed that the ionosphere was significantly disturbed by the SSW event from the equator to the midlatitudes. During day of year 26 and 27 at 14:00 UT, the TEC was two times larger than that observed during average quiet days. The vertical TEC at all 17 GPS and two ionosonde stations shows significant deviations lasting for several days after the SSW temperature peak. Using one GPS station located at Rio Grande (53.8°S, 67.8°W, midlatitude South America sector), it is reported for the first time that the midlatitude in the Southern Hemisphere was disturbed by the SSW event in the Northern Hemisphere.Fil: Fagundes, P. R.. Universidade do Vale do Paraíba; BrasilFil: Goncharenko, L. P.. Massachusetts Institute of Technology; Estados UnidosFil: De Abreu, A. J.. Universidade do Vale do Paraíba; BrasilFil: Venkatesh, K.. Universidade do Vale do Paraíba; BrasilFil: Pezzopane, M.. Istituto Nazionale Di Geofisica E Vulcanologia; ItaliaFil: De Jesus, R.. Universidade do Vale do Paraíba; BrasilFil: Gende, Mauricio Alfredo. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Coster, A. J.. Massachusetts Institute of Technology; Estados UnidosFil: Pillat, V. G.. Universidade do Vale do Paraíba; Brasi

SU(4) symmetry in the extended proton-neutron interacting boson model: multiplets and symmetry breaking

The manifestation of $SU(4)$ symmetry within an interacting boson model including particle-like and hole-like $\pi$- and $\nu$-bosons is shown for light nuclei around the Z=N=8 shell. We also present a consistent description of the particle-hole (intruder spin or $I$ spin) multiplets in the Extended Interacting Boson Model (EIBM) and of $\pi$-$\nu$ ($F$ spin) multiplets in the IBM-2 as a breaking of this $SU(4)$ symmetry