The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi-finite thick generalized polygons. We show here that no semi-finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its ...

The giant cholinergic neuron R2 of Aplysia was cultured in combination with identified neurons L11 and R15 and members of a group of left upper quadrant (LUQ) cells L2 to L6 from the abdominal ganglion. All of these neurons receive cholinergic input from other cells in vivo, but not from R2. In vitro, R2 reliably formed unidirectional chemical connections with these cells. Single action potenti...

We consider linear codes over some fixed finite field extension Fqm/Fq, where Fq is an arbitrary finite field. In [1], Gabidulin introduced rank metric codes, by endowing linear codes over Fqm with a rank weight over Fq and studied their basic properties in analogy with linear codes and the classical Hamming distance. Inspired by the characterization of the security in wiretap II codes in terms...

Convexity assumptions for fractional programming of variational type are relaxed to generalized invexity. The sufficient optimality conditions are employed to construct a mixed dual programming problem. It will involve the Wolfe type dual and Mond-Weir type dual as its special situations. Several duality theorems concerning weak, strong, and strict converse duality under the framework in mixed ...

We suggest new dual algorithms and iterative methods for solving monotone generalized variational inequalities. Instead of working on the primal space, this method performs a dual step on the dual space by using the dual gap function. Under the suitable conditions, we prove the convergence of the proposed algorithms and estimate their complexity to reach an ε-solution. Some preliminary computat...

In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.

A class of generalized state realizations of codes is introduced. In the graph of such a realization, leaf edges represent symbols, ordinary edges represent states, and vertices represent local constraints on incident edges. Such a graph can be decoded by any version of the sum-product algorithm. Any factor graph representation of a code can be put into this form, and any generalized state real...

The moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows are studied. It is actually shown that they are homeomorphic to those on dual modules associated with dual noncommutative flows. Moreover the method is also applicable to the case of noncommutative multi-flows.

We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.