LACES DEFINITION. Let P be a finite set of properties. A mapping l that Ž . assigns to any subset S ; P another subset l S is called a lace map if, for all S, G, S , S ; P: 1 2 Ž . Ž . i l S ; S; Ž . Ž . Ž . Ž . ii l S ; G ; S « l G s l S ; Ž . Ž . Ž . Ž . Ž . iii l S s l S « l S j S s l S . 1 2 1 2 1 Ž . Ž . Ž . A set L for which l L s L is called a lace. By applying ii to G s l S , Ž Ž .. Ž ....

The Olson constant $\mathcal{O}L(\mathbb{F}_{p}^{d})$ represents the minimum positive integer $t$ with property that every subset $A\subset \mathbb{F}_{p}^{d}$ of cardinality contains a nonempty vanishing sum. problem estimating is one oldest questions in additive combinatorics, long and interesting history even for case $d=1$. In this paper, we prove any fixed $d \geq 2$ $\epsilon > 0$, $\math...

Murine splenic stroma has been found to provide an in vitro niche for hematopoiesis of dendritic-like APC. Two distinct cell types have been characterized. The novel "L-DC" subset has cross-presenting capacity, leading to activation of CD8(+) T cells, but not activating CD4(+) T cells, which is consistent with their CD11c(lo)CD11b(hi)MHC-II(-) phenotype. For L-DC, an equivalent tissue-specific ...

We consider computation trees (CTs) with operations $S \subset {+,-, *, DIV, DIV_c}$, where $DIV$ denotes integer division and $DIV_c$ integer division by constants. We characterize the families of languages $L \subset N$ that can be recognized over ${+,-, DIV_c}$ and ${+,-, *, DIV}$, resp. and show that they are identical. Furthermore, we prove lower bounds for CT's with operations ${+,-, DIV_...

A partial Steiner (k, l)-system is a k-uniform hypergraph G with the property that every l-element subset of V is contained in at most one edge of G . In this paper we show that for given k, l and t there exists a partial Steiner (k, l)-system such that whenever an l-element subset from every edge is chosen, the resulting l-uniform hypergraph contains a clique of size t. As the main result of t...

We consider the problem of packing squares with profits into a bounded square region so as to maximize their total profit. More specifically, given a set L of n squares with positive profits, it is required to pack a subset of them into a unit size square region [0;1℄ [0;1℄ so that the total profit of the squares packed is maximized. For any given positive accuracy ε > 0, we present an algorith...

The traditional method of pairwise job interchange compares the cost of sequences that differ only in the interchange of two jobs. It assumes that either there are no intermediate jobs (adjacent pairwise interchange) or that the interchange can be performed no matter what the intermediate jobs are ( nonadjacent pairwise interchange). We introduce a generalization that permits the pairwise inter...

The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph‎. ‎A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$‎, ‎one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...

Let (Q.,l,ß) be a probability space, X a Banach space, and L (fi, X) the Banach space of Bochner integrable functions f: Í2 —> X . Let W = {/ € Ll(p, X) : for a.e. w in Í2, ||/(w)|| < 1} . In this paper we characterize the rwc (relatively weakly compact) subsets of L (ß, X). The main results are as follows: Theorem A. A subset H of W is rwc iff given any sequence (/„) in H there exists a sequen...