On the (non)rigidity of the Frobenius Endomorphism over Gorenstein Rings

It is well-known that for a large class of local rings of positive characteristic, including complete intersection rings, the Frobenius endomorphism can be used as a test for finite projective dimension. In this paper, we exploit this property to study the structure of such rings. One of our results states that the Picard group of the punctured spectrum of such a ring $R$ cannot have $p$-torsion. When $R$ is a local complete intersection, this recovers (with a purely local algebra proof) an analogous statement for complete intersections in projective spaces first given in SGA and also a special case of a conjecture by Gabber. Our method also leads to many simply constructed examples where rigidity for the Frobenius endomorphism does not hold, even when the rings are Gorenstein with isolated singularity. This is in stark contrast to the situation for complete intersection rings. Also, a related length criterion for modules of finite length and finite projective dimension is discussed towards the end.Comment: Minor changes in Example 2.2 and Theorem 2.9. Conjecture 1.2 was added

The CP-violating asymmetry in \eta\to\pi^+ \pi^- e^+e^-

We study the CP-violating asymmetry {\cal A}_{\rm CP}, which arises, in \eta\to\pi^+\pi^- e^+e^-, from the angular correlation of the e^+ e^- and \pi^+\pi^- planes due to the interference between the magnetic and electric decay amplitudes. With the phenomenologically determined magnetic amplitude and branching ratio as input, the asymmetry, induced by the electric bremsstrahlung amplitude through the CP-violating decay \eta\to\pi^+\pi^-, and by an unconventional tensor type operator, has been estimated respectively. The upper bound of {\cal A}_{\rm CP} from the former is about 10^{-3}, and the asymmetry from the latter might be up to O(10^{-2}). One can therefore expect that this CP asymmetry would be an interesting CP-violating observable for the future precise measurements in the \eta factories.Comment: LaTeX, 6 pages. One reference corrected, and some new references adde

GEODYN programmer's guide, volume 2, part 2

A computer program for executive control routine for orbit integration of artificial satellites is presented. At the beginning of each arc, the program initiates required constants as well as the variational partials at epoch. If epoch needs to be reset to a previous time, the program negates the stepsize, and calls for integration backward to the desired time. After backward integration is completed, the program resets the stepsize to the proper positive quantity

Optoelectronics of Inverted Type-I CdS/CdSe Core/Crown Quantum Ring

Inverted type-I heterostructure core/crown quantum rings (QRs) are quantum-efficient luminophores, whose spectral characteristics are highly tunable. Here, we study the optoelectronic properties of type-I core/crown CdS/CdSe QRs in the zincblende phase - over contrasting lateral size and crown width. For this we inspect their strain profiles, transition energies, transition matrix elements, spatial charge densities, electronic bandstructure, band-mixing probabilities, optical gain spectra, maximum optical gains and differential optical gains. Our framework uses an effective-mass envelope function theory based on the 8-band k$\cdot$p method employing the valence force field model for calculating the atomic strain distributions. The gain calculations are based on the density-matrix equation and take into consideration the excitonic effects with intraband scattering. Variations in the QR lateral size and relative widths of core and crown (ergo the composition) affect their energy levels, band-mixing probabilities, optical transition matrix elements, emission wavelengths/intensity, etc. The optical gain of QRs is also strongly dimension and composition dependent with further dependency on the injection carrier density causing band-filling effect. They also affect the maximum and differential gain at varying dimensions and compositions.Comment: Published in AIP Journal of Applied Physics (11 pages, 7 figures

Study of intermixing in a GaAs/AlGaAs quantum-well structure using doped spin-on silica layers

The effect of two different dopants, P and Ga, in spin-on glass (SOG) films on impurity-free vacancy disordering (IFVD) in GaAs/AlGaAs quantum-well structures has been investigated. It is observed that by varying the annealing and baking temperatures, P-doped SOG films created a similar amount of intermixing as the undoped SOG films. This is different from the results of other studies of P-doped SiO₂ and is ascribed to the low doping concentration of P, indicating that the doping concentration of P in the SiO₂ layer is one of the key parameters that may control intermixing. On the other hand, for all the samples encapsulated with Ga-doped SOG layers, significant suppression of the intermixing was observed, making them very promising candidates with which to achieve the selective-area defect engineering that is required for any successful application of IFVD.One of the authors (H.H.T.) acknowledges a fellowship awarded to him by the Australian Research Council

Ultrafast trapping times in ion implanted InP

As⁺ and P⁺implantation was performed on semi-insulating (SI) and p-type InP samples for the purpose of creating a material suitable for ultrafast optoelectronic applications. SI InP samples were implanted with a dose of 1×10¹⁶ cm⁻² and p-type InP was implanted with doses between 1×10¹² and 1×10¹⁶ cm⁻². Subsequently, rapid thermal annealing at temperatures between 400 and 700 °C was performed for 30 sec. Hall-effect measurements, double-crystal x-ray diffraction, and time-resolved femtosecond differential reflectivity showed that, for the highest-annealing temperatures, the implanted SI InP samples exhibited high mobility, low resistivity, short response times, and minimal structural damage. Similar measurements on implantedp-type InP showed that the fast response time, high mobility, and good structural recovery could be retained while increasing the resistivity

Thermodynamically stable noncomposite vortices in mesoscopic two-gap superconductors

In mesoscopic two-gap superconductors with sizes of the order of the coherence length noncomposite vortices are found to be thermodynamically stable in a large domain of the $T - H$ phase diagram. In these phases the vortex cores of one condensate are spatially separated from the other condensate ones, and their respective distributions can adopt distinct symmetries. The appearance of these vortex phases is caused by a non-negligible effect of the boundary of the sample on the superconducting order parameter and represents therefore a genuine mesoscopic effect. For low values of interband Josephson coupling vortex patterns with $L_1 \neq L_2$ can arise in addition to the phases with $L_1 =L_2$, where $L_1$ and $L_2$ are total vorticities in the two condensates. The calculations show that noncomposite vortices could be observed in thin mesoscopic samples of MgB$_{2}$.Comment: 5 pages, 3 figures, to be published in Europhysics Letter

Flowering phenology and floral visitors of Piliostigma reticulatum in a tropical dry forest, Burkina Faso

Piliostigma reticulatum is a dioecious species that provides food, fodder and the revenues from the sale of its pods constituted an important resource for sahelian population. During the flowering, flowers are abundant but the fruit set remained very low in spite of a large number of insect visitors. The aim of this work was to study flowering phenology, to identify potential pollinators and visitors, to determine the visitation rate and the synchronism between floral phenology and the insect visitors. The natural population studied is located at Budtenga in the North Sudanian area of Burkina Faso. The phenological study was carried out from July 2009 to December 2009 on 500 inflorescences randomly sampled from inflorescences of 40 male and female individuals. Potentials pollinators were determined using their physical ability to carry pollen in their body and the reference based diets. Our results showed that many orders of insects visit the flowers of P. reticulatum. Nymphalidae (Lepidoptera), Syrphidae (Diptera), Apidae (Hymenoptera) and Sphecidae (Hymenoptera) were regarded as main potential pollinators of P. reticulatum. Apidae (Apis mellifera) was the most abundant and frequent visitor. We found that August was the peak flowering period for both male and female individuals and the peak emergence of potential pollinators. Therefore, the emergence of potential pollinators responsible for pollen dispersal might be punctuated by flowering phenology.Keywords: Caesalpinioideae, P. reticulatum, phenology, visitors, Sudanian fores

Clustering Data of Mixed Categorical and Numerical Type with Unsupervised Feature Learning

Mixed-type categorical and numerical data are a challenge in many applications. This general area of mixed-type data is among the frontier areas, where computational intelligence approaches are often brittle compared with the capabilities of living creatures. In this paper, unsupervised feature learning (UFL) is applied to the mixed-type data to achieve a sparse representation, which makes it easier for clustering algorithms to separate the data. Unlike other UFL methods that work with homogeneous data, such as image and video data, the presented UFL works with the mixed-type data using fuzzy adaptive resonance theory (ART). UFL with fuzzy ART (UFLA) obtains a better clustering result by removing the differences in treating categorical and numeric features. The advantages of doing this are demonstrated with several real-world data sets with ground truth, including heart disease, teaching assistant evaluation, and credit approval. The approach is also demonstrated on noisy, mixed-type petroleum industry data. UFLA is compared with several alternative methods. To the best of our knowledge, this is the first time UFL has been extended to accomplish the fusion of mixed data types