We study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by q ∈ (0, 1) and where at most 2 j ∈ N particles per site are allowed. The process is constructed from a (2 j + 1)-dimensional representation of a quantum Hamiltonian with Uq(sl2) invariance by applying a suitable ground-state transformation. After s...

In [E6] a relation is proved between the Poincaré series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. We study this relation for Fuchsian singularities and show that it is connected with the mirror symmetry of K3 surfaces and with automorphisms of the Leech lattice. We also indicate...

Traditionally in natural duality theory the algebras carry no topology and the objects on the dual side are structured Boolean spaces. Given a duality, one may ask when the topology can be swapped to the other side to yield a partner duality (or, better, a dual equivalence) between a category of topological algebras and a category of structures. A prototype for this procedure is provided by the...

In this paper two types of duals are considered for a class of variational problems involving higher order derivatives. The duality results are derived without any use of optimality conditions. One set of results is based on MondWeir type dual that has the same objective functional as the primal problem but different constraints. The second set of results is based on a dual of an auxiliary prim...

Multidimensional convolutional codes arise as a generalization of “classical” onedimensional codes. We will introduce m-dimensional convolutional codes of length n as submodules of Dn where D is the polynomial ring in m variables over a finite field. Besides their coding theoretic significance, they can also be regarded as the annihilating modules of systems of partial difference equations, the...

of the Dissertation Self-dual Hall Modules by Matthew Bruce Young Doctor of Philosophy in Mathematics Stony Brook University 2013 In the past twenty years Hall algebras have played an important role in many areas of mathematics and physics, including the theory of quantum groups and string theory. In its original setting the Hall algebra is constructed from a finitary exact category, the multip...

A classical flow is a nonnegative linear combination of unit flows along simple paths. A multiroute flow, first considered by Kishimoto and Takeuchi, generalizes this concept. The basic building blocks are not single paths with unit flows but rather tuples consisting of k edge disjoint paths, each path with a unit flow. A multiroute flow is a nonnegative linear combination of such tuples. We pr...

We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in a sort of duality, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of c...

in this paper, we try to determine the status of the relation between dahr world and matrial world. the conclusion shows the subjective duality and objective unity of dahr and material entities. two interpretations of this duality can be suggested. in the first interpretation, this unity, and the duality supposed, are explained on the basis of different intellectual cognition of immaterial and ...

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.