Rapidly Rotating Fermi Gases

We show that the density profile of a Fermi gas in rapidly rotating potential will develop prominent features reflecting the underlying Landau level like energy spectrum. Depending on the aspect ratio of the trap, these features can be a sequence of ellipsoidal volumes or a sequence of quantized steps.Comment: 4 pages, 1 postscript fil

Permutations of context-free, ET0L and indexed languages

© 2016 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France. For a language L, we consider its cyclic closure, and more generally the language Ck(L), which consists of all words obtained by partitioning words from L into k factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators Ck. This both sharpens and generalises Brandstädt's result that if L is context-free then Ck(L) is context-sensitive and not context-free in general for k ≥ 3. We also show that the cyclic closure of an indexed language is indexed

The Moldovan Confederation Conundrum

The Gagauz leadership has advanced several basic demands. The first category of demands relates to economic concerns and these appear to be the most fundamental. The situation that they insist be addressed in that there is an economic disparity between Gagauzia and the rest of the Moldovan Republic. If one looks beyond the rhetoric of Comrat, Gagauz political demands are secondary to the economic ones. They demand political parties that would operate in local elections. They want more seats in the Moldovan Parliament and believe that all laws should be published in the Gagauz language as well as in Russian and Romanian. While much has been said about Turkish involvement with Gagauzia, this has not served to generate any feeling among the Gaguz that their cultural roots are in Turkey. Those who emigrate are most likely to go, first, to the United States and, second, to Russia. Ties between Gagauzia and Transdniestria reached their closest during the early part of the 1990s. Since that time Gagauzia has found a more effective relationship working within the Moldovan Republic. The confrontations of recent months are a product of the Moldovan political crisis, not intervention from Tiraspol. They have led to a renewal of ties between these two regions. Transdniestria’s fundamental demand is to assume equal status with the Moldovan Republic within a confederation. There appear to be limited prospects for a renewal of violence such as that seen in 1992. Direct foreign intervention by any one of the three nations with the greatest interests in this situation – Russia, the Ukraine, and Romania – appears unlikely barring a renewal of violence

Prediction of large-for-gestational-age neonate by routine third-trimester ultrasound

Objectives: First, to evaluate and compare the performance of routine ultrasonographic estimated fetal weight (EFW) and fetal abdominal circumference (AC) at 31+0 - 33+6 and 35+0 - 36+6 weeks’ gestation in the prediction of large for gestational age (LGA) neonates born at ≥37 weeks’ gestation. Second, to assess the additive value of fetal growth velocity between 32 and 36 weeks’ gestation on the performance of EFW at 35+0 - 36+6 weeks’ gestation for prediction of LGA neonates. Third, to define the predictive performance for LGA neonates of different EFW cut-offs at routine ultrasound examination at 35+0 - 36+6 weeks’ gestation. Fourth, to propose a two-stage strategy for identifying pregnancies with LGA fetuses that may benefit from iatrogenic delivery during the 38th gestational week. Methods: First, data from 21,989 singleton pregnancies that had undergone routine ultrasound examination at 31+0 - 33+6 weeks’ gestation and 45,847 that had undergone routine ultrasound examination at 35+0 - 36+6 weeks were used to compare the predictive performance of EFW and AC for LGA neonates with birthweight >90th and >97th percentiles born at ≥37 weeks’ gestation. Second, data from 14,497 singleton pregnancies that had undergone routine ultrasound examination at 35+0 - 36+6 weeks’ gestation and had a previous scan at 30+0 – 34+6 weeks were used to determine, through multivariable logistic regression analysis, whether addition of growth velocity, defined by a difference in EFW and AC Z-scores between the early and late third trimester scans divided by the time interval between them, improved the performance of EFW at 35+0 - 36+6 weeks in the prediction of delivery of LGA neonates born at ≥37 weeks’ gestation. Third, in the database of the 45,847 pregnancies that had undergone routine ultrasound examination at 35+0 - 36+6 weeks’ gestation the screen positive and detection rate of LGA neonates born at ≥37 weeks’ gestation and at ≤10 days from the initial scan were calculated for different EFW percentile cut-offs between the 50th and 90th percentile. Results: First, the areas under the receiver operating characteristic curves (AUROC) of screening for LGA neonates were significantly higher with EFW Z-score than AC Z-score and at 35+0 - 36+6 than at 31+0 - 33+6 weeks’ gestation (p90th percentile at 35+0 - 36+6 weeks’ gestation the predictive performance for LGA neonates born at ≥37 weeks’ gestation was modest (65% and 46% for neonates with birthweight >97th and >90th percentiles, respectively, at screen positive rate of 10%), but the performance was better for prediction of LGA neonates born at ≤10 days from the scan (84% and 71% for neonates with birthweight >97th and >90th percentiles, respectively, at screen positive rate of 11%). Fourth, screening by EFW >70th percentile at 35+0 - 36+6 weeks’ gestation predicted 91% and 82% of LGA neonates with birthweight >97th and >90th percentiles born at ≥37 weeks’ gestation, at screen positive rate of 32%, and the respective values of screening by EFW >85th percentile for prediction of LGA neonates born at ≤10 days from the scan were 88%, 81% and 15%. On the basis of these results it was proposed that routine fetal biometry at 36 weeks’ gestation is a screening rather than diagnostic test for fetal macrosomia and that EFW >70th percentile should be used to identify pregnancies in need for another scan at 38 weeks and in the latter those with EFW >85th percentile should be considered for iatrogenic delivery during the 38th week. Conclusions: First, the predictive performance for LGA neonates by routine ultrasonographic examination during the third trimester is higher if the scan is carried out at 36 than at 32 weeks, the method of screening is EFW than fetal AC, the outcome measure is birthweight >97th than >90th percentile and if delivery occurs within 10 days than at any stage after assessment. Second, prediction of LGA neonates by EFW >90th percentile is modest and the study presents a two-stage strategy for maximizing the prenatal prediction of LGA neonates

Theory of spin-2 Bose-Einstein condensates: spin-correlations, magnetic response, and excitation spectra

The ground states of Bose-Einstein condensates of spin-2 bosons are classified into three distinct (ferromagnetic, ^^ ^^ antiferromagnetic", and cyclic) phases depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the hermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied agnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ^^ ^^ pairs" undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ^^ ^^ trios" condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.Comment: 28 pages, 4 figure

The Stability of the Dniester Moldovan Republic: A Post-Election Analysis

The communists\u27 electoral victory and the elevation of Voronin to the Presidency drew Moldova closer to the Russian Federation and raised new questions about the stability of the Dniester Moldovan Republic. The existence of the DMR no longer serves Russian interests as it did in the past. The prospects for confrontation between the DMR and Moldova are greater today as a result of the Communist Party victory. While President Voronin has privately expressed his disdain for the DMR leadership, he seems willing to accept the existence of the DMR. By the latter part of the past decade, the DMR existed primarily as a vehicle for criminal activities rather than as a bastion of Stalinism and Russian nationalism. Weapons left behind by Soviet forces have made the DMR a major factor in illegal arms trafficking

First-principles calculations of step formation energies and step interactions on TiN(001)

We study the formation energies and repulsive interactions of monatomic steps on the TiN(001) surface, using density functional total-energy calculations. The calculated formation energy of [100] oriented steps agree well with recently reported experimental values; these steps are shown to have a rumpled structure, with the Ti atoms undergoing larger displacements than the N atoms. For steps that are parallel to [110], our calculations predict a nitrogen (N) termination, as the corresponding formation energy is several hundred meV/\AA \ smaller than that of Ti-terminated steps

Religious Brotherhoods in Chechnya

In 1997, Professors Stephen R. Bowers and Marion T. Doss, Jr., began an effort to promote the systematic study of the problems of political violence and eventually opened an office in the Former Soviet Union to develop research on this topic. Their operating philosophy governing was that such a base would enable them to involve local scholars in research, thus producing internationally based studies that would reflect both the U.S. and the non-U.S. perspectives. This document is the first produced by this method and is a study of the Chechen Sufi brotherhoods in Chechnya and their role in that conflict

Quantum Phase Transition of Spin-2 Cold Bosons in an Optical Lattice

The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction in an optical lattice is proposed. After neglecting the hopping term, the site-independent Hamiltonian and its energy eigenvalues and eigenstates are obtained. We consider the hopping term as a perturbation to do the calculations in second order and draw the phase diagrams for different cases. The phase diagrams show that there is a phase transition from Mott insulator with integer number bosons to superfluid when the ratio $c_0/t$ ($c_0$ is the spin-independent on-site interaction and $t$ the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is different phase boundary between superfluid and Mott insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.Comment: 16 pages, 6 figure