that is both analytic (as a mapping of complex manifolds) and algebraic: addition of points in E(C) corresponds to addition in C modulo the lattice L. This correspondence between lattices and elliptic curves over C is known as the Uniformization Theorem; we will spend this lecture and part of the next proving it. To make the correspondence explicit, we need to specify the map Φ from C/L and an ...

Recently we proposed a formalism, based in nuclear statistical spectroscopy, for efficient computation of nuclear level density, or densities of states, through a sum of partitioned binomial functions (SUPARB). In this Letter we extend the formalism to the calculation of locally averaged expectation values, with specific application to spin-cutoff factors and the angular momentum dependence of ...

The E6/U(1)N gauge extension of the Supersymmetric Standard Model, first proposed by Ma, is shown to have exactly the requisite ingredients to realize the important new idea that dark matter is the origin of neutrino mass. With the implementation of a discrete Z2 × Z2 symmetry, and particle content given by three 27 representations of E6, neutrino masses are naturally generated in two loops, wi...

strain, leading to the formation of a periodic array of elongated, almost closed ellipses, as shown in Fig. 2D for 3 1⁄4 "0.21. Since the specimens are made of an elastomeric material, the process is fully reversible and repeatable. Upon release of the applied vertical displacement, the deformed structures recover their original congurations. Interestingly, Figs. 2C–D clearly shows that the po...

A quantum error-correcting code is a way of encoding quantum states into qubits (two-state quantum systems) so that error or decoherence in a small number of individual qubits has little or no effect on the encoded data. The existence of quantum error-correcting codes was discovered only recently [1]. Although the subject is relatively new, a large number of papers on quantum error correction h...

There is a resurgence of interest in Fixed Field Alternating Gradient (FFAG) accelerators, both in the traditional “scaling” and in novel “non-scaling” machines. We focus on the variable-tune linear-field FFAG which offers very high momentum compaction. Muons require fast acceleration to avoid decay losses; this necessitates using superconducting magnets and cavities whose field and frequency a...

Let V be a finite-dimensional superspace over C and g a simple (or a “close” to simple) matrix Lie superalgebra, i.e., a Lie subsuperalgebra in gl(V ). Under the classical invariant theory for g we mean the description of g-invariant elements of the algebra A p,q k,l = S . (V k ⊕Π(V ) ⊕ V ∗p ⊕Π(V )). We give such description for gl(V ), sl(V ) and osp(V ) and their “odd” analogs: q(V ), sq(V );...

In this paper, we construct a combination HS-Litehorn of the Halpern-Shoham interval temporal logic HS [15] with the description logic DL-Litehorn [12, 1], which is a Horn extension of the standard language OWL 2 QL. The temporal operators of HS are of the form 〈R〉 (‘diamond’) and [R] (‘box’), where R is one of Allen’s interval relations After, Begins, Ends, During, Later, Overlaps and their in...