Invariants of Lie Algebras with Fixed Structure of Nilradicals

An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n<\infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.Comment: LaTeX2e, 19 page

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Computation of Invariants of Lie Algebras by Means of Moving Frames

A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. The algorithm is applied, in particular, to computation of invariants of real low-dimensional Lie algebras. A number of examples are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. Bases of invariants of the real solvable Lie algebras up to dimension five, the real six-dimensional nilpotent Lie algebras and the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in tables.Comment: 17 pages, extended versio

Strong interconversion of non-polar phonons and Josephson plasma oscillations induced by equilibrium Josephson currents in high T_c superconductors

We analyze consequences of dynamical modulations of Josephson current by non-polar lattice mode in the Josephson junction barrier. In the high $T_c$ junctions, the effect of such modulations can be anomalously strong due to the proximity of the insulating barrier to the superconducting state. Accordingly, the interconversion of sound (as well as other non-polar phonons) and the Josephson plasma oscillations mediated by stationary Josephson currents, which may be present in the junction due to various reasons, becomes possible. We suggest that this effect can be employed for imaging of the stationary Josephson currents. Estimates of the effect are given.Comment: 11 RevTeX pages, no figure

Two-Fermion Production in Electron-Positron Collisions

This report summarizes the results of the two-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the theoretical calculations of the two fermion production process in the electron-positron collision at LEP2 center of the mass energies are reported. The Bhabha process and the production of muon, tau, neutrino and quark pairs is covered. On the basis of comparison of various calculations, theoretical uncertainties are estimated and compared with those needed for the final LEP2 data analysis. The subjects for the further studies are identified.Comment: 2-fermion working group report of the LEP2 Monte Carlo Workshop 1999/2000, 113 pages, 24 figures, 35 table

Genetic structure and domestication history of the grape

The grape is one of the earliest domesticated fruit crops and, since antiquity, it has been widely cultivated and prized for its fruit and wine. Here, we characterize genome-wide patterns of genetic variation in over 1,000 samples of the domesticated grape, Vitis vinifera subsp. vinifera, and its wild relative, V. vinifera subsp. sylvestris from the US Department of Agriculture grape germ-plasm collection. We find support for a Near East origin of vinifera and present evidence of introgression from local sylvestris as the grape moved into Europe. High levels of genetic diversity and rapid linkage disequilibrium (LD) decay have been maintained in vinifera, which is consistent with a weak domestication bottleneck followed by thousands of years of widespread vegetative propagation. The considerable genetic diversity within vinifera, however, is contained within a complex network of close pedigree relationships that has been generated by crosses among elite cultivars. We show that first-degree relationships are rare between wine and table grapes and among grapes from geographically distant regions. Our results suggest that although substantial genetic diversity has been maintained in the grape subsequent to domestication, there has been a limited exploration of this diversity. We propose that the adoption of vegetative propagation was a double-edged sword: Although it provided a benefit by ensuring true breeding cultivars, it also discouraged the generation of unique cultivars through crosses. The grape currently faces severe pathogen pressures, and the long-term sustainability of the grape and wine industries will rely on the exploitation of the grape's tremendous natural genetic diversity

Socioeconomic profile of diabetic patients with and without foot problems

Introduction: To identify the differences in a socioeconomic profile between two cohorts of diabetic patients &#x2013; one with diabetic foot problems and another without diabetic foot problems. Materials and methods: The cohort with diabetic foot problems (including cellulitis, abscess, osteomyelitis, septic arthritis, gangrene, ulcers, or Charcot joint disease) consisted of 122 diabetic patients, while the other cohort without foot problems consisted of 112 diabetic patients. Both were seen at the National University Hospital from January to April 2007. A detailed protocol was designed and the factors studied included patient profile, average monthly household income, education, compliance to diabetic medication, attendance at clinics for diabetic treatment, exercise, smoking, alcohol consumption, gender, and glycosylated haemoglobin (HbA1C) level. These were studied for significant differences using univariate and stepwise multivariate logistic regression analysis. Results: With multivariate analysis, Malay ethnicity (p&#60;0.001), education of up to secondary school only (p=0.021), low average monthly household income of less than SGD &#x0024;2,000 (p=0.030), lack of exercise (at least once a week, p=0.04), and elevated HbA1C level (&#x003E;7.0%; p=0.015) were found to be significantly higher in the cohort with diabetic foot problems than the cohort without. Conclusions: There are significant differences in the socioeconomic factors between diabetic patients with diabetic foot problems and those without

Foot Muscle Energy Reserves in Diabetic Patients Without and With Clinical Peripheral Neuropathy

Objective: To investigate changes in the foot muscle energy reserves in diabetic non-neuropathic and neuropathic patients. Research Design and Methods: We measured the phosphocreatinine (PCr)/inorganic phosphate (Pi) ratio, total $^{31}$P concentration, and the lipid/water ratio in the muscles in the metatarsal head region using MRI spectroscopy in healthy control subjects and non-neuropathic and neuropathic diabetic patients. Results: The PCr/Pi ratio was higher in the control subjects (3.23 $\pm$ 0.43) followed by the non-neuropathic group (2.61 $\pm$ 0.36), whereas it was lowest in the neuropathic group (0.60 $\pm$ 1.02) (P < 0.0001). There were no differences in total $^{31}$P concentration and lipid/water ratio between the control and non-neuropathic groups, but both measurements were different in the neuropathic group (P < 0.0001). Conclusions: Resting foot muscle energy reserves are affected before the development of peripheral diabetic neuropathy and are associated with the endothelial dysfunction and inflammation

Precision measurement of the branching fractions of J/psi -> pi+pi-pi0 and psi' -> pi+pi-pi0

We study the decays of the J/psi and psi' mesons to pi+pi-pi0 using data samples at both resonances collected with the BES III detector in 2009. We measure the corresponding branching fractions with unprecedented precision and provide mass spectra and Dalitz plots. The branching fraction for J/psi -> pi+pi-pi0 is determined to be (2.137 +- 0.004 (stat.) +0.058-0.056 (syst.) +0.027-0.026 (norm.))*10-2, and the branching fraction for psi' -> pi+pi-pi0 is measured as (2.14 +- 0.03 (stat.) +0.08-0.07 (syst.) +0.09-0.08 (norm.))*10-4. The J/psi decay is found to be dominated by an intermediate rho(770) state, whereas the psi' decay is dominated by di-pion masses around 2.2 GeV/c2, leading to strikingly different Dalitz distributions.Comment: 15 pages, 2 figure