The support of the logarithmic equilibrium measure on sets of revolution in R3\R^3

For surfaces of revolution $B$ in $\R^3$, we investigate the limit distribution of minimum energy point masses on $B$ that interact according to the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance between points. We show that such limit distributions are supported only on the ``out-most'' portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvature). Our analysis proceeds by reducing the problem to the complex plane where a non-singular potential kernel arises whose level lines are ellipses

Symplectic Reduction and Symmetry Algebra in Boundary Chern-Simons theory

We derive the Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary by using the symplectic reduction method and the Noether procedures.Comment: References are adde

First-principles investigation of magnetism and electronic structures of substitutional 3d3d transition-metal impurities in bcc Fe

The magnetic and electronic structures of $3d$ impurity atoms from Sc to Zn in ferromagnetic body-centered cubic iron are investigated using the all-electron full-potential linearized augmented plane-wave method based on the generalized gradient approximation (GGA). We found that in general, the GGA results are closer to the experimental values than those of the local spin density approximation. The calculated formation enthalpy data indicate the importance of a systematic study on the ternary Fe-C-$X$ systems rather than the binary Fe-$X$ systems, in steel design. The lattice parameters are optimized and the conditions for spin polarization at the impurity sites are discussed in terms of the local Stoner model. Our calculations, which are consistent with previous work, imply that the local spin-polarizations at Sc, Ti, V, Cu, and Zn are induced by the host Fe atoms. The early transition-metal atoms couple antiferromagnetically, while the late transition-metal atoms couple ferromagnetically, to the host Fe atoms. The calculated total magnetization ($M$) of bcc Fe is reduced by impurity elements from Sc to Cr as a result of the antiferromagnetic interaction, with the opposite effect for solutes which couple ferromagnetically. The changes in $M$ are attributed to nearest neighbor interactions, mostly between the impurity and host atoms. The atom averaged magnetic moment is shown to follow generally the well-known Slater-Pauling curve, but our results do not follow the linearity of the Slater-Pauling curve. We attribute this discrepancy to the weak ferromagnetic nature of bcc Fe. The calculated Fermi contact hyperfine fields follow the trend of the local magnetic moments. The effect of spin-orbit coupling is found not to be significant although it comes into prominence at locations far from the impurity sites.Comment: 26 pages, 11 figure

The two dimensional Hubbard model:a theoretical tool for molecular electronics

When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The aim of the present paper is to introduce this model, and give some examples of the systems which it can describe. After a short mathematically oriented discussion, it will be shown how to calculate the electrical conductivity of a particular planar system: a rectangular lattice with mutually independent conductivities along the two axes,but without using the 2D Hamiltonian. This system could find applications in high Tc studies. It will finally be shown that the electrical conductivity of graphene can be determined not by using the full formalism of the $2D$ Hubbard model, but by a slight reformulation of the Hamiltonian of the 1D Hubbard modelComment: Lecture given at the 16 Int.School of Cond.Matt.Physics,August 29.,-September 3 2010.,Varna (Bulgaria

Superconducting transition of a two-dimensional Josephson junction array in weak magnetic fields

The superconducting transition of a two-dimensional (2D) Josephson junction array exposed to weak magnetic fields has been studied experimentally. Resistance measurements reveal a superconducting-resistive phase boundary in serious disagreement with the theoretical and numerical expectations. Critical scaling analyses of the $IV$ characteristics indicate contrary to the expectations that the superconducting-to-resistive transition in weak magnetic fields is associated with a melting transition of magnetic-field-induced vortices directly from a pinned-solid phase to a liquid phase. The expected depinning transition of vortices from a pinned-solid phase to an intermediate floating-solid phase was not observed. We discuss effects of the disorder-induced random pinning potential on phase transitions of vortices in a 2D Josephson junction array.Comment: 9 pages, 7 figures (EPS+JPG format), RevTeX

From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic sigma-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.Comment: LaTeX, 37 pages. Some typos fixed. Final version, to appear in Nucl. Phys.

Role of Exclusive Breastfeeding and S-iga Antibodies Antirotavirus Breast Milk Towards Risk of Acute Rotavirus Diarrhea in Infants Age of 1-6 Months: Do They Corelate to Breastfeeding "Daily Dose" and Antibody Titers?

Exclusive breastfeeding reduces the incidence of diarrhea, especially in children who live in densely populated neighborhood. This study aims to determine the relationship between exclusive breastfeeding and breast milk contains antirotavirus s-IgA antibodies towards risk of acute rotavirus diarrhea in infants aged of 1-6 months. Case-control study design is applied to determine the relationship between exclusive breastfeeding and breast milk contains s-IgA antibodies antirotavirus with risk of acute rotavirus diarrhea. Cases in this study were patients with acute rotavirus diarrhea and controls were patients without acute rotavirus diarrhea. Cases and controls were matched based on age. There were 23 cases and 69 controls. The proportion who received exclusive breastfeeding was 34.8% in cases and 34.4% in controls, with OR of 1.21 (95% CI: 0.45 to 3.28) and p = 0.28. Breast milk contains sIgA antibodies antirotavirus for case was 17.39% and controls was 23.2%, OR was 1.12 (95% CI: 0.29 to 4.29), p = 0.203. In conclusion, exclusive breastfeeding and breast milk contains sIgA antibodies antirotavirus were not associated with risk of acute rotavirus diarrhea in infants 1-6 months. This may be caused by differences in population and demographic studies as well as low of milk sIgA antibody antirotavirus titters. Further research of breastfeeding regardless of antirotavirus containing high antibody titters sIgA is needed