We prove the long-standing Eckmann{Ruelle conjecture in dimension theory of smooth dynamical systems. We show that the pointwise dimension exists almost everywhere with respect to a compactly supported Borel probability measure with non-zero Lyapunov exponents, invariant under a C 1+ diieomorphism of a smooth Riemannian manifold. Let M be a smooth Riemannian manifold without boundary, and f : M...

Human CD56(bright) natural killer (NK) cells possess little or no killer immunoglobulin-like receptors (KIRs), high interferon-gamma (IFN-gamma) production, but little cytotoxicity. CD56(dim) NK cells have high KIR expression, produce little IFN-gamma, yet display high cytotoxicity. We hypothesized that, if human NK maturation progresses from a CD56(bright) to a CD56(dim) phenotype, an intermed...

The inductive dimension dim(G) of a finite undirected graph G is a rational number defined inductively as 1 plus the arithmetic mean of the dimensions of the unit spheres dim(S(x)) at vertices x primed by the requirement that the empty graph has dimension −1. We look at the distribution of the random variable dim on the Erdös-Rényi probability space G(n, p), where each of the n(n− 1)/2 edges ap...

The dimension of a poset (X, P), denoted dim (A", P), is the minimum number of linear extensions of P whose intersection is P. It follows from Dilworth's decomposition theorem that dim (X, P)& width (X, P). Hiraguchi showed that dim(X, P)s \X\/Z In this paper, A denotes an antichain of (A", P) and E the set of maximal elements. We then prove that dim {X, P) s |X A\; dim(X, P) < 1 + width (X E);...

DIM (3,3'-di-indolylmethane), an abundant dietary component of cruciferous vegetables, exhibits a wide spectrum of pharmacological properties. In the present study, we show that DIM is a potent inhibitor of Leishmania donovani topoisomerase I with an IC50 of 1.2 microM. Equilibrium dialysis shows that DIM binds strongly to the free enzyme with a binding constant of 9.73x10(-9) M. The binding af...

As a natural health supplement, 3,3'-diindolylmethane (DIM) is proposed as a preventive and chemotherapeutic agent for cancer by inhibiting cell proliferation and inducing cell apoptosis. However, we found that in contrary to high level of DIM (30 μM), low level of DIM (1 μM and 10 μM) obviously promoted gastric cancer cell growth and migration. In addition, we found that low level of DIM incre...

Let G be a graph and let S(G), M(G), T(G) the subdivision, middle, total of G, respectively. dim(G), edim(G), mdim(G) metric dimension, edge mixed dimension In this paper, for subdivision it is proved that max{dim(G), edim(G)} ≤ mdim(S(G)) mdim(G). A family graphs Gn constructed which mdim(Gn) − mdim(S(Gn)) ≥ 2 holds shows inequality can strict, while cactus = For middle dim(M(G)) holds, if tre...

3,3'-Diindolylmethane (DIM), an indole derivative produced on consumption of broccoli and other cruciferous vegetables, has been shown to have multiple anticancer effects in both in vivo and in vitro models. The present study was carried out to clarify the mechanism of DIM's antiangiogenic activity. We found that DIM can inhibit vascular endothelial growth factor (VEGF)-induced cell proliferati...

3,3'-Diindolylmethane (DIM), ring-substituted DIMs and 1,1-bis(3'-indolyl)-1-(p-substitutedphenyl)methanes (C-DIMs) inhibit growth of Panc-1 and Panc-28 pancreatic cancer cells. Although DIMs (diarylmethanes) and selected C-DIMs (triarylmethanes), such as the p-t-butyl derivative (DIM-C-pPhtBu), activate the aryl hydrocarbon receptor and peroxisome proliferator-activated receptor gamma, respect...