This paper considers completions of tope graphs complexes oriented matroids (COMs) to ample partial cubes the same Vapnik--Chervonenkis dimension (VC-dimension). We show that these exist for (OMs) and uniform (CUOMs). implies OMs CUOMs satisfy sample compression conjecture---one central open questions learning theory. conjecture graph every COM can be completed an cube without increasing VC-dim...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform whose every reductions to $k$ parties are maximally mixed. We present constructions strength 2 with levels prime power, as well some 3. As a consequence, we give infinite 2-uniform $N$ systems dimension power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform $N$-qubit 6$ and $N\neq 7,8,9,11$; ...

We provide a simple algorithm and data structures for d-dimensional unbiased maximal Poisson-disk sampling. We use an order of magnitude less memory and time than the alternatives. Our results become more favorable as the dimension increases. This allows us to produce bigger samplings. Domains may be non-convex with holes. The generated point cloud is maximal up to round-off error. The serial a...

A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

In a previous paper [20] in this series, we gave L estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimension k. In this paper we give uniform estimates when the subspace approaches a degenerate region in the case k = 1, and when all the exponents p are between 2 and ∞. In particular we recover the non-endpoint uniform estimates f...