We give a very simple new proof of the celebrated intersection theorem of D. K. Ray-Chaudhuri and R. M. Wilson. The new proof yields a generalization to nonuniform set systems. Let N(n, s, r) = ( n s ) + ( n s− 1 ) + · · ·+ ( n s− r + 1 ) . Generalized Ray-Chaudhuri – Wilson Theorem. Let K = {k1, . . . , kr}, L = {l1, . . . , ls}, and assume ki > s − r for all i. Let F be a family of subsets of...

Phagocytes such as dendritic cells and macrophages, which are distributed in the small intestinal mucosa, play a crucial role in maintaining mucosal homeostasis by sampling the luminal gut microbiota. However, there is limited information regarding microbial uptake in a steady state. We investigated the composition of murine gut microbiota that is engulfed by phagocytes of specific subsets in t...

A kind of new fuzzy compactness, called near SR-compactness, is de4ned for an arbitrary L-subset and for L a complete DeMorgan algebra. This kind of fuzzy compactness is between Lowen’s strong fuzzy compactness and the second author’s SR-compactness. Characterizations and examples of near SR-compact L-subsets are given, and its topological properties are systematically investigated. c © 2003 El...

Booreana mice carrying the c-Myb308G point mutation were analyzed to determine changes in early hematopoiesis in the bone marrow and among mature cells in the periphery. This point mutation led to increased numbers of early hematopoietic stem and progenitor cells (HSPCs), with a subsequent reduction in the development of B cells, erythroid cells, and neutrophils, and increased numbers of myeloi...

Theorem 1.1. Let G, X, p0, and r be as above. Suppose T is translation invariant, maps L log L to L, and is bounded on L0 . Then T is bounded on L, 1 < p < p0 with an operator norm of O((p − 1) ). This theorem is false without the assumption of translation invariance, since L is not an interpolation space between L log L and L0 . For a concrete counterexample, take E and F be subsets of X of me...

Thermokarst is the process of ground subsidence caused by either the thawing of ice-rich permafrost or the melting of massive ground ice. The consequences of permafrost degradation associated with thermokarst for surface ecology, landscape evolution, and hydrological processes have been of great scientific interest and social concern. Part of a tundra patch affected by wildfire in northern Alas...

X iv :m at h/ 00 12 20 2v 1 [ m at h. A G ] 2 0 D ec 2 00 0 The Moduli Space of Bilevel-6 Abelian Surfaces G.K. Sankaran & J. Spandaw The moduli space Abil t of (1, t)-polarised abelian surfaces with a weak bilevel structure was introduced by S. Mukai in [11]. Mukai showed that Abil t is rational for t = 2, 3, 4, 5. More generally, we may ask for birational invariants, such as Kodaira dimension...

{ the most stringent form of a bounded language { and still separate 2 Space(S) from 2 Space(S). Thus a separation of the rst level would require a syntatically more complex languages than the second level. For k > 2 the languages L k and L k used in this paper to establish the separation are no longer bounded. But by Proposition 4.1 the third level can also be separated using simple bounded la...

In this paper, we consider a general covering problem in which k subsets are to be selected such that their union covers as large a weight of objects from a universal set of elements as possible. Each subset selected must satisfy some structural constraints. We analyze the quality of a k-stage covering algorithm that relies, at each stage, on greedily selecting a subset that gives maximum impro...