Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case

We consider the minimal discrete and continuous energy problems on the unit sphere $\mathbb{S}^d$ in the Euclidean space $\mathbb{R}^{d+1}$ in the presence of an external field due to finitely many localized charge distributions on $\mathbb{S}^d$, where the energy arises from the Riesz potential $1/r^s$ ($r$ is the Euclidean distance) for the critical Riesz parameter $s = d - 2$ if $d \geq 3$ and the logarithmic potential $\log(1/r)$ if $d = 2$. Individually, a localized charge distribution is either a point charge or assumed to be rotationally symmetric. The extremal measure solving the continuous external field problem for weak fields is shown to be the uniform measure on the sphere but restricted to the exterior of spherical caps surrounding the localized charge distributions. The radii are determined by the relative strengths of the generating charges. Furthermore, we show that the minimal energy points solving the related discrete external field problem are confined to this support. For $d-2\leq s<d$, we show that for point sources on the sphere, the equilibrium measure has support in the complement of the union of specified spherical caps about the sources. Numerical examples are provided to illustrate our results.Comment: 23 pages, 4 figure

Quinoidization of regioregular oligo(THIENO[3,4-b]THIOPHENE)s

Caracterización de oligotiofenosUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Metalloporphyrin-incorporated diphosphine ligands for metal ion-binding

Poster: no. P48Diphosphine ligands have been widely used in organometallic chemistry and catalysis.1 By incorporation of functional units such as metallomacrocycles, the resulting functionalized diphosphines could exhibit unusual properties or binding behavior. In this study, we prepared several examples of ruthenium porphyrin phosphine complexes [RuII(Por)(dppm)2] (1; Por = TTP, 4-MeO-TPP, F20-TPP; dppm = bis(diphenylphosphino)methane) by a similar method to that previously reported for their congeners.2 Reaction of complexes 1 with a number of metal …published_or_final_versio

Observation of contemporaneous optical radiation from a gamma-ray burst

The origin of gamma-ray bursts (GRBs) has been enigmatic since their discovery. The situation improved dramatically in 1997, when the rapid availability of precise coordinates for the bursts allowed the detection of faint optical and radio afterglows - optical spectra thus obtained have demonstrated conclusively that the bursts occur at cosmological distances. But, despite efforts by several groups, optical detection has not hitherto been achieved during the brief duration of a burst. Here we report the detection of bright optical emission from GRB990123 while the burst was still in progress. Our observations begin 22 seconds after the onset of the burst and show an increase in brightness by a factor of 14 during the first 25 seconds; the brightness then declines by a factor of 100, at which point (700 seconds after the burst onset) it falls below our detection threshold. The redshift of this burst, approximately 1.6, implies a peak optical luminosity of 5 times 10^{49} erg per second. Optical emission from gamma-ray bursts has been generally thought to take place at the shock fronts generated by interaction of the primary energy source with the surrounding medium, where the gamma-rays might also be produced. The lack of a significant change in the gamma-ray light curve when the optical emission develops suggests that the gamma-rays are not produced at the shock front, but closer to the site of the original explosion.Comment: 10 pages, 2 figures. Accepted for publication in Nature. For additional information see http://www.umich.edu/~rotse

Mechanical properties related to the relaxor-ferroelectric phase transition of titanium-doped lead magnesium niobate

2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Clades and clans: a comparison study of two evolutionary models

The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under these two models provides valuable insights into macro-evolutionary processes, and is important in hypothesis testing and Bayesian analyses in phylogenetics. Here we show that these distributions are log-convex, which implies that very large clades or very small clades are more likely to occur under these two models. Moreover, we prove that there exists a critical value $\kappa(n)$ for each $n\geqslant 4$ such that for a given clade with size $k$, the probability that this clade is contained in a random tree with $n$ leaves generated under the YHK model is higher than that under the PDA model if $1<k<\kappa(n)$, and lower if $\kappa(n)<k<n$. Finally, we extend our results to binary unrooted trees, and obtain similar results for the distributions of clan sizes.Comment: 21page

The Reform of Employee Compensation in China’s Industrial Enterprises

Although employee compensation reform in Chinese industrial sector has been discussed in the literature, the real changes in compensation system and pay practices have received insufficient attention and warrant further examination. This paper briefly reviews the pre- and post-reform compensation system, and reports the results of a survey of pay practices in the four major types of industrial enterprises in China. The research findings indicate that the type of enterprise ownership has little influence on general compensation practices, adoption of profit-sharing plans, and subsidy and allowance packages. In general, pay is linked more to individual performance and has become an important incentive to Chinese employees. However, differences are found across the enterprise types with regard to performance-related pay. Current pay practices are positively correlated to overall effectiveness of the enterprise

Testing supersymmetry at the LHC through gluon-fusion production of a slepton pair

Renormalizable quartic couplings among new particles are typical of supersymmetric models. Their detection could provide a test for supersymmetry, discriminating it from other extensions of the Standard Model. Quartic couplings among squarks and sleptons, together with the SU(3) gauge couplings for squarks, allow a new realization of the gluon-fusion mechanism for pair-production of sleptons at the one-loop level. The corresponding production cross section, however, is at most of ${\cal O}(1)$fb for slepton and squark masses of ${\cal O}(100)$GeV. We then extend our investigation to the gluon-fusion production of sleptons through the exchange of Higgs bosons. The cross section is even smaller, of ${\cal O}(0.1)$fb, if the exchanged Higgs boson is considerably below the slepton-pair threshold, but it is enhanced when it is resonant. It can reach ${\cal O}(10)$fb for the production of sleptons of same-chirality, exceeding these values for $\widetilde{\tau}$'s of opposite-chirality, even when chirality-mixing terms in the squark sector are vanishing. The cross section can be further enhanced if these mixing terms are nonnegligible, providing a potentially interesting probe of the Higgs sector, in particular of parameters such as $A$, $\mu$, and $\tan\beta$.Comment: 28 pages, 11 figure

Early and efficient detection of Mycobacterium tuberculosis in sputum by microscopic observation of broth cultures.

Early, efficient and inexpensive methods for the detection of pulmonary tuberculosis are urgently needed for effective patient management as well as to interrupt transmission. These methods to detect M. tuberculosis in a timely and affordable way are not yet widely available in resource-limited settings. In a developing-country setting, we prospectively evaluated two methods for culturing and detecting M. tuberculosis in sputum. Sputum samples were cultured in liquid assay (micro broth culture) in microplate wells and growth was detected by microscopic observation, or in Löwenstein-Jensen (LJ) solid media where growth was detected by visual inspection for colonies. Sputum samples were collected from 321 tuberculosis (TB) suspects attending Bugando Medical Centre, in Mwanza, Tanzania, and were cultured in parallel. Pulmonary tuberculosis cases were diagnosed using the American Thoracic Society diagnostic standards. There were a total of 200 (62.3%) pulmonary tuberculosis cases. Liquid assay with microscopic detection detected a significantly higher proportion of cases than LJ solid culture: 89.0% (95% confidence interval [CI], 84.7% to 93.3%) versus 77.0% (95% CI, 71.2% to 82.8%) (p = 0.0007). The median turn around time to diagnose tuberculosis was significantly shorter for micro broth culture than for the LJ solid culture, 9 days (interquartile range [IQR] 7-13), versus 21 days (IQR 14-28) (p<0.0001). The cost for micro broth culture (labor inclusive) in our study was US $4.56 per sample, versus US$11.35 per sample for the LJ solid culture. The liquid assay (micro broth culture) is an early, feasible, and inexpensive method for detection of pulmonary tuberculosis in resource limited settings