Selmer groups and anticyclotomic Zp\mathbb{Z}_p-extensions

Let $E/\mathbb{Q}$ be an elliptic curve, $p$ a prime and $K_{\infty}/K$ the anticyclotomic $\mathbb{Z}_p$-extension of a quadratic imaginary field $K$ satisfying the Heegner hypothesis. In this paper we give a new proof to a theorem of Bertolini which determines the value of the $\Lambda$-corank of $\text{Sel}(E/K_{\infty})$ in the case where $E$ has ordinary reduction at $p$. In the case where $E$ has supersingular reduction at $p$ we make a conjecture about the structure of the module of Heegner points mod $p$. Assuming this conjecture we give a new proof to a theorem of Ciperiani which determines the value of the $\Lambda$-corank of $\text{Sel}(E/K_{\infty})$ in the case where $E$ has supersingular reduction at $p$.Comment: Made a slight change to the conjectur

THE GENETICS OF INSULIN RESISTANCE IN FAMILIES WITH POLYCYSTIC OVARY SYNDROME

Polycystic ovary syndrome (PCOS) is a familial disorder characterized by major metabolic consequences related to insulin resistance (IR), including T2DM and metabolic syndrome (MS). There is mounting evidence, which supports association of each of G-174C variant in IL-6 and Pro12Ala variant in PPARλ genes with PCOS-associated biochemical or metabolic features in hyperandrogenic and PCOS adults/adolescents. The major aim of this study was to demonstrate the ability to enroll PCOS probands, who have one or more clinically PCOS-diagnosed woman, and their multigenerational family members for a total sample size of 100-125 to study IR and inflammation markers in such families. Additional important aims were to test for linkage between the IL6 and PPARλ genes' loci and for associations between the IL6G-174C SNP and the Pro12Ala PPARλ SNP with IR, MS and its components, serum inflammation levels (IL-6 and CRP) and testosterone in this special population of PCOS families. IR was defined by a HOMA-IR value > 3.9 in adults and HOMA-IR values which are age-gender specific in adolescents. MS was defined according to the ATP III diagnostic criteria in adults and the same criteria, modified for age in adolescents. In total, 101 individuals were recruited from 9 multigenerational extended families; eight of the families were Caucasian and the remaining was African American. No evidence for linkage of each of the IL6 and the PPARγ markers to any of the examined phenotypes was found. However, interesting significant SNP-phenotype associations were found in this population of PCOS families. The Ala12 allele was found to be negatively associated with diastolic blood pressure (DBP) and with fasting glucose. Moreover, the G allele of the IL6 SNP was found to be positively associated with DBP, serum IL6 and testosterone levels. These associations are particularly important because they were adjusted for covariates which are known or were found to be significantly associated with the outcome in our population and were the results of the variance components association test, a test which accounts for family relationships. The findings are of major public health significance, mainly because they are the first to be reported in PCOS extended families

First principles investigation of the electronic structure of La2MnNiO6: A room-temperature insulating ferromagnet

Using first principles calculations within DFT based on the full potential APW+lo method, we calculated the electronic and magnetic structures for the ferromagnetic and antiferromagnetic states of La2MnNiO6 and analyzed the site projected density of states and electronic band structures. Our calculations show that the ground state of La2MnNiO6 is ferromagnetic insulating with the magnetization in agreement with Hund's first rule and experimental findings.Comment: 10 pages, 3 figure

Coherent view of crystal chemistry and ab initio analyses of Pb(II) and Bi(III) Lone Pair in square planar coordination

The stereochemistry of 6s2 (E) lone pair of divalent Pb and trivalent Bi (PbII and BiIII designated by M*) in structurally related PbO, PbFX (X= Cl, Br, I), BiOX (X= F, Cl, Br, I) and Bi2NbO5F is rationalized. The lone pair LP presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M*-E directions and distances. Detailed description of structural features of both elements in the title compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the evolution of M*-E distance versus the changes with the square pyramidal SP coordination polyhedra. All are different, in red PbO one finds {PbEO4E4} square antiprism, a {[Bi.E]O4X4Xapical} monocapped square antiprism in PbFX and BiOX and {BiEO4F4}square antiprism in Bi2NbO5F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on PbII within {PbEO4E4} in PbOE, {PbEF4X4} in PbFXE and Bi(III) within {BiEO4X4} square antiprisms, contrary to Bi(III) within {[Bi.E]O4F4Fapical} monocapped square antiprism. Larger hardness (larger bulk modules B0) and band gap characterize BiOF versus PbO due to the presence of F which brings antibonding Bi-F interactions oppositely to mainly bonding Bi-O. In PbFX and BiOX series there is a systematic decrease of B0 with the increasing volume following the nature and size of X which is decreasingly electronegative and increasingly large. The electronic densities of states mirror these effects through the relative energy position and relative electronegativities of F/X and O/X leading to decrease the band gap.Comment: 20 text pages/ 10 multifigures/large review article, J. Progress Solid State Chemistry, under production MAY 201

High-order WENO scheme for Polymerization-type equations

Polymerization of proteins is a biochimical process involved in different diseases. Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In this paper we consider a general polymerization model and propose a high-order numerical scheme to investigate the behavior of the solution. An important property of the equation is the mass conservation. The fifth-order WENO scheme is built to preserve the total mass of proteins along time