Heterotic free fermionic and symmetric toroidal orbifold models

Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z2xZ2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: We give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z2xZ2 orbifold geometries in six dimensions.Comment: 1+49 pages latex, minor revisions and references adde

A rapid, two step construction of novel C<SUB>48</SUB>H<SUB>24</SUB> and C<SUB>54</SUB>H<SUB>24</SUB> polycyclic aromatic hydrocarbons represented on the C<SUB>60</SUB>-fullerene surface via a threefold intramolecular heck coupling reaction

In a new approach towards deeper, higher order 'bucky bowls', two step syntheses of novel polycyclic aromatic hydrocarbons, C48H24 and C54H24, having 13 and 16 rings, respectively, from readily available precursors and involving threefold palladium mediated intramolecular Heck coupling as the pivotal step is described

Bucky-bowls: a general approach to benzocorannulenes: synthesis of mono-, di- and tri-benzocorannulenes

We outline a conceptually simple and general route to bowl-shaped benzocorannulenes based on readily assembled PAHs which on flash vacuum pyrolysis result in the sequential formation of a five- and six-membered ring; following this approach, syntheses of mono-, di- and tri-benzocorannulenes have been achieved

Magnetic susceptibility of ultra-small superconductor grains

For assemblies of superconductor nanograins, the magnetic response is analyzed as a function of both temperature and magnetic field. In order to describe the interaction energy of electron pairs for a huge number of many-particle states, involved in calculations, we develop a simple approximation, based on the Richardson solution for the reduced BCS Hamiltonian and applicable over a wide range of the grain sizes and interaction strengths at arbitrary distributions of single-electron energy levels in a grain. Our study is focused upon ultra-small grains, where both the mean value of the nearest-neighbor spacing of single-electron energy levels in a grain and variations of this spacing from grain to grain significantly exceed the superconducting gap in bulk samples of the same material. For these ultra-small superconductor grains, the overall profiles of the magnetic susceptibility as a function of magnetic field and temperature are demonstrated to be qualitatively different from those for normal grains. We show that the analyzed signatures of pairing correlations are sufficiently stable with respect to variations of the average value of the grain size and its dispersion over an assembly of nanograins. The presence of these signatures does not depend on a particular choice of statistics, obeyed by single-electron energy levels in grains.Comment: 40 pages, 12 figures, submitted to Phys. Rev. B, E-mail addresses: [email protected], [email protected], [email protected]

Solitons in the Calogero model for distinguishable particles

We consider a large $- N,$ two-family Calogero model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the corresponding solutions are given by the static-soliton configurations. Solitons from different families are localized at the same place. They behave like a paired hole and lump on the top of the uniform vacuum condensates, depending on the values of the coupling strengths. When the number of particles in the first family is much larger than that of the second family, the hole solution goes to the vortex profile already found in the one-family Calogero model.Comment: 14 pages, no figures, late

Large Deviations of Extreme Eigenvalues of Random Matrices

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (N\times N) random matrix are positive (negative) decreases for large N as \exp[-\beta \theta(0) N^2] where the parameter \beta characterizes the ensemble and the exponent \theta(0)=(\ln 3)/4=0.274653... is universal. We also calculate exactly the average density of states in matrices whose eigenvalues are restricted to be larger than a fixed number \zeta, thus generalizing the celebrated Wigner semi-circle law. The density of states generically exhibits an inverse square-root singularity at \zeta.Comment: 4 pages Revtex, 4 .eps figures included, typos corrected, published versio

Study of metformin in polycystic ovary syndrome

Background: Objective of the study was to measure the efficacy and safety of insulin sensitizing drug metformin in reversing the metabolic and endocrine disturbances in fifty women with polycystic ovarian disease.Methods: The study was performed on 57 women with polycystic ovarian syndrome (PCOS) in the outpatient department of obstetrics and gynaecology, V. S. General Hospital, Ahmedabad. Metformin 500 mg thrice daily was given until the cysts disappeared which was taken as the end point of the study. Follicular studies were done to check the effect of metformin on ovulation. Significance was tested by paired t test and p value calculated.Results: Metformin was found effective in regressing polycystic changes in ovary, regularization of menstrual cycles and improving ovulation.Conclusions: The present study shows that metformin has a beneficial role in effective management of PCOS.

Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations

We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as $N \to \infty$. The results agree nontrivially with a recent conjecture of Berry & Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivial predictions obtained using these techniques have been proved.Comment: 13 page

Baker-Akhiezer functions and generalised Macdonald-Mehta integrals

For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a generalisation of the self-duality property of the usual Gaussian function with respect to the Fourier transformation. We show that the value of properly normalised Baker-Akhiezer function at the origin can be given by an integral of Macdonald-Mehta type and explicitly compute these integrals for all known Baker-Akhiezer arrangements. We use the Dotsenko-Fateev integrals to extend this calculation to all deformed root systems, related to the non-exceptional basic classical Lie superalgebras.Comment: 26 pages; slightly revised version with minor correction