This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop the formalism of infinite sequences of braid moves, called a braid limit. We relate this to a partial order, called the limit weak order, on ...

The loop space LP1 of the Riemann sphere consisting of all C k or Sobolev W k,p maps S → P1 is an infinite dimensional complex manifold. We compute the Picard group Pic(LP1) of holomorphic line bundles on LP1 as an infinite dimensional complex Lie group with Lie algebra the Dolbeault group H(LP1). The group of Möbius transformations G and its loop group LG act on LP1. We prove that an element o...

A minor-closed class of matroids is (strongly) fractal if the number n-element in dominated by excluded minors. We conjecture that when K an infinite field, K-representable strongly fractal. prove sparse paving with at most k circuit-hyperplanes a least three. The minor-closure spikes (with k≥5) satisfies strictly weaker condition: 2t-element However, there are only finitely many minors ground ...

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.

The motivation for computing in a suitably chosen homomorphic image of the original problem domain is that the computation there is either easier or is possible, whereas in the original domain it was either harder or impossible. For example, any homomorphic image of the infinite ring of integers is a finite ring, and computation in a finite set is usually easier than in an infinite set; as we h...

Thorough understanding of steel rail response to wheel load is a key step towards design and evaluation of the railway track structure. In current practice, maximum vertical deflection and bending moment are calculated using the theory of infinite beam on continuous elastic foundation (Winkler model), in which the foundation stiffness is assumed as constant. However, variation of track modulus ...

Partition properties are perhaps the most fruitful of the various methods for defining and discussing large cardinals in set theory. In this paper we weaken in a natural way the most well known of these partition properties and examine the extent to which the cardinals defined remain "large." 1. 1.1. An area of set theory which has come under a great deal of study recently is that concerned wit...

We associate with each convex optimization problem, posed on some locally space, infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets suitable Lagrangian-Haar dual problem. obtain necessary sufficient conditions for H-reducibility, that is, equivalence to subproblem obtained replacing whole index T element H. Special attention is addressed linear op...