Context Pseudohypoparathyroidism type I (PHP-I) is divided into PHP-Ia with Albright hereditary osteodystrophy and PHP-Ib, which usually shows no Albright hereditary osteodystrophy features. Although PHP-Ia and PHP-Ib are typically caused by genetic defects involving α subunit of the stimulatory G protein (Gsα)-coding GNAS exons and methylation defects of the GNAS differentially methylated regi...

There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves and, moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of Jac(X0(D)) such that the abelian variety Jac(X0(D))/c(D) is the jacobian of the curve XD.

We present a subgroup analysis of the first double-blind, placebo-controlled, randomised trial with vitamin D3 in MS. In the overall study population, there were 34 patients in the vitamin D arm and 32 patients in the placebo arm. All the patients were using interferon-β-1b (IFNB) therapy. The subgroup consisted of 15 patients in the vitamin D arm and 15 patients in the placebo arm, who had eit...

A formal “small tension” expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10), where K(E10) is the maximal compact subgroup of the hyperbolic KacMoody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible represent...

Sequence analysis was performed of all or part of the genes encoding the fusion (F), polymerase (L) and attachment (G) proteins of two French non-A/non-B avian pneumovirus (APV) isolates (Fr/85/1 and Fr/85/2). The two isolates shared at least 99.7% nt and 99.0% aa sequence identity. Comparison with the F genes from subgroup A, subgroup B or Colorado APVs revealed nt and aa identities of 70.0-80...

Let $\mathfrak{g}$ be a complex simple Lie algebra and let $\mathfrak{g}_0$ the sub-algebra fixed by diagram automorphism of $\mathfrak{g}$. $G$ complex, simply-connected, algebraic group with $\mathfrak{g}$, $G_0$ connected subgroup $\mathfrak{g}_0$. $\rho$ half sum positive roots In this article, we give necessary sufficient condition for highest weight $\mathfrak{g}_0$-representation $V_0(d\...

We attach copies of the circle to points a subset D separable metric space X and construct an earring E ( , ) . show that fundamental group is isomorphic subgroup Hawaiian group, if simply-connected locally simply-connected. In addition path-connected, can be recovered from

For a topological manifold M let H(M) be the group of homeomorphisms of M endowed with the Whitney topology and Hc(M) the subgroup of H(M) consisting of homeomorphisms with compact support. The identity component H0(M) of H(M) is an open normal subgroup in Hc(M) and it induces the factorization Hc(M) ≈ H0(M)×Mc(M) for the mapping class group Mc(M) = Hc(M)/H0(M). For each connected non-compact s...

These notes are based on two lectures which were given by the author at the Workshop on Arithmetic Algebraic Geometry, I.I.T. Guwhati, India, fall 2008. They were intended to give a quick survey on classical complex modular forms and their l-adic Galois representations. Accordingly, the focus is rather on results and examples whereas proofs are mainly sketched or omitted. Nothing in these notes...