Following neurulation, the frog segments c.40 somites and concurrently undergoes a striking elongation along the anteroposterior axis. This elongation (excluding the head) is largely the result of a presegmental extension of posterior tissue with a lesser contribution from the extension of segmented tissue. Presegmental extension is entirely the result of activity within a narrow zone of extens...

Arbarello, de Concini, and Kac have constructed a central extension of the ideles group on a smooth projective algebraic curve C. We show that this central extension induces the theta-bundle on the class group of degree g−1 divisors on C, where g is the genus of the curve C. The other result of the paper is the relation between the product of the norms of the tame symbols over all points of the...

A technique for reconstructing a class of quadric surfaces from 3D data is presented. The technique is driven by a linear least-squaresbased fitting mechanism. Previously, such fitting was restricted to recovery of central quadrics; here, extension of that basic mechanism to allow recovery of one commonly-occurring class of non-central quadric, the elliptic paraboloids, is described. The extens...

The five simple exceptional complex Lie superalgbras of vector fields are described. One of them is new; the other four are explicitely described for the first time. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation. The description of several of the exceptional Lie superalgebras is associated with the Lie superalgebra a...

We construct an $L_\infty$-algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to universal central extension Lie algebra Hamiltonian vector fields.

We use a fermionic extension of the bosonic module to obtain a class of B(0, N)-graded Lie superalgebras with nontrivial central extensions. 0 Introduction B(M − 1, N)-graded Lie superalgebras were first investigated and classified up to central extension by Benkart-Elduque (see also Garcia-Neher’s work in [GN]). Those root graded Lie superalgebras are a super-analog of root graded Lie algebras...