A unified approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. The compatibility with the still to be found solutions of the three (and higher) dimensional Ising model allows one to write down an explicit analytic ansatz for the free energy in terms of few q-dependent Regge trajectories. The duality symmetry of the 2D Potts model together with the known resul...

9 Abstract 10 We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for 11 arbitrary cones. By using the concept of efficiency and second order invexity, we establish the weak, strong, converse 12 and self-duality theorems for our dual models. Several known results are obtained as special cases. 17 Following the earlier works of Dorn [5], D...

A closed 4-manifold (or, more generally, a finite PD4space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a PD3-complex. A Poincaré duality space is a space X of the homotopy type of a cell complex which satisfies Poincaré duality w...

In the context of gauge/gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of (Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+ 1 dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we ...

Let Hn,r be the Ariki-Koike algebra associated to the complex reflection group Sn (Z/rZ)n, and let S(Λ) be the cyclotomic q-Schur algebra associated to Hn,r, introduced by Dipper, James and Mathas. For each p = (r1, . . . , rg) ∈ Zg>0 such that r1 + · · · + rg = r, we define a subalgebra Sp of S(Λ) and its quotient algebra S. It is shown that Sp is a standardly based algebra and S is a cellular...

This paper presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we show that the coefficients in the expansion of these toric Schur polynomials, in terms of the regular Schur polynomials, are exactly the 3-point Gromov-Witten inv...

A formula is given for the dimension of the Selmer group of the rational three-isogeny of elliptic curves of the form y2 = x3+a(x−b)2. The formula is in terms of the three-ranks of the quadratic number fields Q( √ a) and Q( √ −3a) and various aspects of the arithmetic of these number fields. In addition a duality theorem is used to relate the dimension of the Selmer group of the three-isogeny w...