We give combinatorial models for the homotopy type of complements elliptic arrangements (i.e., certain sets abelian subvarieties in a product curves). presentation fundamental group such spaces and, as an application, we treat case ordered configuration curves. Our are finite polyhedral CW complexes, and our tools choice acyclic categories (small without loops). As stepping stone, characterizat...

This paper, in a sense, completes a series of three papers. In the previous two [1] [2], we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic cohomology. In the present paper, we make that more concrete by defining a fully quantized free field theory based on elliptic cohomology of 10-dimensional spacetime. Moreover, we describe ...

We discuss certain preconditioning techniques for solving indefinite linear systems of equations arising from mixed finite element discretizations of elliptic equations of second order. The techniques are based on various approximations of the mass matrix, say, by simply lumping it to be diagonal or by constructing a diagonal matrix assembled of properly scaled lumped element mass matrices. We ...

the mordell-weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎in our previous paper, h‎. ‎daghigh‎, ‎and s‎. ‎didari‎, on the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎bull‎. ‎iranian math‎. ‎soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using selmer groups‎, ‎we have shown that for a prime $p$...

We consider the Euler type integral associated to the configuration space of points on an elliptic curve, which is an analogue of the hypergeometric function associated to the configuration space of points on a projective line. We calculate the twisted homology group, with coefficients in the local system associated to a power function gα of an elliptic function g, and the intersection form. Ap...

Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functi...

We introduce the quasi-Hopf superalgebras which are Z2 graded versions of Drinfeld’s quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymm...