This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic curve. We also compute winding numbers of loop solitons.

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links between these constructions and for the case of SL2 perform explicit computations, describing the bracket and its leaves in detail.

We have developed a new technique of using a torque rnagnetomet.er to obtain M·H hysteresis loop of a uniaxial magnetic materiaL The hysteresis curve was obtained from the loop of the torque r measured as a function of an applied field H, when the direction of the applied field q, was 9" from the uniaxial orientation. This technique was applied to obtain the hysteresis curves of several Co/Pd m...

We outline a strategy for showing convergence of loop-erased random walk on the Z square lattice to SLE(2), in the supremum norm topology that takes the time parametrization of the curves into account. The discrete curves are parametrized so that the walker moves at a constant speed determined by the lattice spacing, and the SLE(2) curve has the recently introduced natural time parametrization....

We rewrite the loop equations of the hermitian matrix model, in a way which involves no derivative with respect to the potential, we compute all the correlation functions, to all orders in the topological 1/N expansion, as residues on an hyperelliptical curve. Those residues, can be represented as Feynmann graphs of a cubic field theory on the curve.

The paper is a review of improved ca�culating and design techniques, performance rating of incinerators, and a description of the new open"pit incinerator. Of particular interest is a curve of nitrogen oxide formation with varying exe ess air and temperature developed from thermodynamic equilibrium data that has been verified by fie ld tes Is.

Pairing is carried out by two steps, Miller loop and final exponentiation. In this manuscript, the authors propose an efficient for a pairing on FK12 curve. A Hamming weight bit-length of parameter have great effect computational cost loop. Optimal-ate used as most curve currently. The optimal-ate 6z + 2 where z integer to make parameter. Our method uses which has shorter than previous Usually,...

We rewrite the loop equations of the hermitian 2-matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological 1/N expansion, as residues on an algebraic curve. Those residues, can be represented diagrammatically as Feynman graphs of a cubic interaction field theory on the curve.

The motive associated to the second Symanzik polynomial of double-box two-loop Feynman graph with generic masses and momenta is shown be an elliptic curve.