Multiple positive solutions to third-order three-point singular semipositone boundary value problem

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: \begin{cases} x'''(t)-\ld f(t,x) =0, &t\in(0,1); [.3pc] x(0)=x'(\eta)=x''(1)=0, & \end{cases} where ${1/2}<\eta<1$, the non-linear term f(t,x):(0,1)\times(0,+\i)\to (-\i,+\i) is continuous and may be singular at $t=0$, $t=1$, and $x=0$, also may be negative for some values of $t$ and $x$, \ld is a positive parameter.Comment: 14 page

Existence and uniqueness of the stationary measure in the continuous Abelian sandpile

Let \Lambda be a finite subset of Z^d. We study the following sandpile model on \Lambda. The height at any given vertex x of \Lambda is a positive real number, and additions are uniformly distributed on some interval [a,b], which is a subset of [0,1]. The threshold value is 1; when the height at a given vertex exceeds 1, it topples, that is, its height is reduced by 1, and the heights of all its neighbours in \Lambda increase by 1/2d. We first establish that the uniform measure \mu on the so called "allowed configurations" is invariant under the dynamics. When a < b, we show with coupling ideas that starting from any initial configuration of heights, the process converges in distribution to \mu, which therefore is the unique invariant measure for the process. When a = b, that is, when the addition amount is non-random, and a is rational, it is still the case that \mu is the unique invariant probability measure, but in this case we use random ergodic theory to prove this; this proof proceeds in a very different way. Indeed, the coupling approach cannot work in this case since we also show the somewhat surprising fact that when a = b is rational, the process does not converge in distribution at all starting from any initial configuration.Comment: 22 page

Isolation and characterization of the CCR4 associated factors

In yeast, Sacchoromyces cerevisiae, transcription of $\underline{ADH2}$ gene (encodes alcohol dehydrogenase II) under glucose derepression conditions requires not only the gene-specific activator, Adr1p, but also the general transcriptional factors like Ccr4p. Ccr4p belongs to the LRR-containing protein superfamily, members of which have often been found to associate with other proteins to form a functional protein complex. This dissertation reports three major conclusions from my research. 1. The CCR4 protein is associated with at least three other proteins by immunoprecipitation using the CCR4 antibody, and more importantly, the LRR in the CCR4 protein is not only essential, but also sufficient to form the CCR4 complex. 2. Using the yeast two hybrid procedure with LexA-CCR4 as a bait, seven genes were isolated. Two of them are known genes, $\underline{\rm CAF1}$ and $\underline{\rm DBF2},$ respectively. Three of them encoding novel proteins contain the known structural motifs: ATP-binding motif for $\underline{\rm CAF16},$ zinc-finger DNA-binding motif for $\underline{\rm CAF10},$ and WD40 repeats for $\underline{\rm CAF4.\ CAF6}$ and $\underline{\rm CAF17}$ showed no sequence similarity to any genes in the current Data Base. Using LexA-CAF16 as a bait to perform the yeast two hybrid procedure, four genes, encoding Caf16p, Map1p, Srb9p and Mth1p were also identified. 3. The CCR4 complex is purified by using 6His tagged $\underline{\rm CCR4}$ and $\underline{\rm CAF1}.$ The purified CCR4 complex from the CAF1-6His containing whole cell extract through three chromatographic procedures has a molecular weight of 1.0 $\times$ 10\sp6 Da, including Ccr4p, Caf1p, Caf16p, Caf17p, Dbf2p and other unidentified proteins such as 185 kDa, 145 kDa and 110 kDa proteins. These results give us an inside view into understanding how CCR4 complex is involved in diverse cellular processes, and strongly suggests that CCR4 complex affects different cellular events by interacting with other functional proteins or protein complexes