We investigate the existence of extremal points and the KreinMIlman representation A = co ExtA of bounded convex subsets of L(μ) which are only closed with respect to the topology of μ -a.e. convergence.

Let G = (V,E,w) be a graph with vertex and edge sets V and E, respectively, and w : E → IR a function which assigns a positive weigth or length to each edge of G. G is called a realization of a finite metric space (M,d), with M = {1, ..., n} if and only if {1, ..., n} ⊆ V and d(i, j) is equal to the length of the shortest chain linking i and j in G ∀i, j = 1, ..., n. A realization G of (M,d), i...

We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L′ ⊆ L which has the same Parikh (commutative) image as L. Bounded languages, introduced by Ginsburg and Spanier, are subsets of regular languages of the form w∗ 1w ∗ 2 · · ·w∗ k for some w1, . . . , wk ∈ Σ∗. In particular bounded subsets o...

— We study subsets of Grassmann varieties G(l, m) over a field F , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study such sets in detail, and give applications to coding theory, in particular for Grassmann codes. For l = 2 much is known about such Schubert unions with a maximal number of Fq-rational points for a given spanning dimension. We study the ...

Let G = (V,E,w) be a graph with vertex and edge sets V and E, respectively, and w : E → IR a function which assigns a positive weigth or length to each edge of G. G is called a realization of a finite metric space (M,d), with M = {1, ..., n} if and only if {1, ..., n} ⊆ V and d(i, j) is equal to the length of the shortest chain linking i and j in G ∀i, j = 1, ..., n. A realization G of (M,d), i...

Abstract Let R be a discrete valuation domain with field of fractions Q and maximal ideal generated by $\pi $ . $\Lambda an -order such that $Q\Lambda is separable -algebra. Maranda showed there exists $k\in \mathbb {N}$ for all -lattices L M , if $L/L\pi ^k\simeq M/M\pi ^k$ then $L\simeq M$ Moreover, complete indecomposable -lattice, also indecomposable. We extend Maranda’s theorem to the clas...

A computable presentation of the linearly ordered set (ω,≤), where ω is the set of natural numbers and ≤ is the natural order on ω, is any linearly ordered set L = (ω,≤L) isomorphic to (ω,≤) such that ≤L is a computable relation. Let X be subset of ω and XL be the image of X in the linear order L under the isomorphism between (ω,≤) and L. The degree spectrum of X is the set of all Turing degree...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...