We examine n×nmatrices over Zm, with 0’s in the diagonal and nonzeros elsewhere. If m is a prime, then such matrices have large rank (i.e., n1/(p−1) − O(1) ). If m is a non-prime-power integer, then we show that their rank can be much smaller. For m = 6 we construct a matrix of rank exp(c √ log n log log n). We also show, that explicit constructions of such low rank matrices imply explicit cons...

In graphs of bounded arboricity, the total complexity of all maximal complete bipartite subgraphs is O(n). We describe a linear time algorithm to list such subgraphs. The arboricity bound is necessary: for any constant k and any n there exists an n-vertex graph with O(n) edges and (n/ log n) maximal complete bipartite subgraphs Kk,`. ∗Work supported in part by NSF grant CCR-9258355.

Hierarchical terrain models describe a topographic surface at di erent levels of detail, providing a multiresolution representation as well as a data compression mechanism. In this paper, we consider the problem of computing the visibility map, with respect to a xed viewpoint, on a hierarchical triangle-based terrain model. This problem presents two aspects: the extraction of a visibility map a...

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

Let O denote the ring of integers of an algebraic number field of degree m which is totally and tamely ramified at the prime p. Write ζq = exp(2πi/q), where q = pr. We evaluate the twisted Kloosterman sum ∑ α∈(O/qO)∗ χ(N(α))ζ T (α)+z/N(α) q , where T and N denote trace and norm, and where χ is a Dirichlet character (mod q). This extends results of Salié for m = 1 and of Yangbo Ye for prime m di...

background: the aim of this study is to verify the effects of the combined and classic training of different isometric rates of force development (rfd) parameters of legs. materials and methods: three groups of female athletes was tested: experimental group (n = 12), classically trained group (n = 11), and control group (n = 20) of athletes. the isometric “standing leg extension” and “ris...

Let G=Cn×Cn, where Cn denotes a cyclic group of order n, and let k∈[0,n−1]. We study the structure sequences terms from G with maximal length |S|=2n−2+k that fail to contain nontrivial zero-sum subsequence at most 2n−1−k. For k≤1, this is inverse question for Davenport Constant. k=n−1, η(G) invariant concerning short subsequences. The in both these cases (known respectively as Property B C) was...

We show that the expected number of maximal empty axis-parallel boxes amidst n random points in the unit hypercube [0, 1] in R is (1±o(1)) (2d−2)! (d−1)! n ln d−1 n, if d is fixed. This estimate is relevant for analyzing the performance of exact algorithms for computing the largest empty axis-parallel box amidst n given points in an axis-parallel box R, especially the algorithms that proceed by...