In this paper, we determine the dimension of the rectangular product of certain nite lattices. In fact, if L1 and L2 be nite lattices which satisfy the some conditions, then we have dim(L1 L2) = dim(L1) + dim(L2) 1:

It is shown that if $\gamma: [a,b] \to S^2$ $C^3$ with $\det(\gamma, \gamma', \gamma'') \neq 0$, and $A \subseteq \mathbb{R}^3$ a Borel set, then $\dim \pi_{\theta} (A) \geq \min\left\{ 2,\dim A, \frac{ \dim A}{2} + \frac{3}{4} \right\}$ for a.e. $\theta \in [a,b]$, where $\pi_{\theta}$ denotes projection onto the orthogonal complement of $\gamma(\theta)$ ``$\dim$'' refers to Hausdorff dimensio...

Algebraically closed fields, real closed fields, and pseudofinite fields have, for every natural number n, have a finite number of extensions of degree n; we show they share this property with all fields which, like them, satisfy a very basic property of preservation of a type of model-theoretic dimension. This result is attained by showing that a certain action of the group GLn on such a field...

Comparability graphs are graphs which have transitive orientations. The dimension of a poset is the least number of linear orders whose intersection gives this poset. The dimension dim(X) of a comparability graph X is the dimension of any transitive orientation of X, and by k-DIM we denote the class of comparability graphs X with dim(X) ≤ k. It is known that the complements of comparability gra...

Although 3,3'-diindolylmethane (DIM) has been suggested to reduce the risk of colorectal cancer, the underlying biological mechanism is not clearly understood. In the present study, we investigated the effect of DIM on the migratory and invasive activities of the human colorectal cancer cell lines DLD-1 and HCT116. DIM significantly inhibited the migration and invasion of colorectal cancer cell...

An endogenous circadian pacemaker uses photic input to synchronize mammalian physiological and behavioral rhythms to the 24 h day. Sunlight during dusk and dawn is thought to entrain the pacemaker of nocturnal rodents, whereas moonlight and starlight are presumed to exert little influence. We show that, to the contrary, dim illumination (<0.005 lux), similar in intensity to starlight and dim mo...

There is a large body of scientific evidence suggesting that 3,3'-Diindolylmethane (DIM), a compound derived from the digestion of indole-3-carbinol, which is abundant in cruciferous vegetables, harbors anti-tumor activity in vitro and in vivo. Accumulating evidence suggests that AMP-activated protein kinase (AMPK) plays an essential role in cellular energy homeostasis and tumor development and...

Objective- Evaluation of leg scoring as a method for hoof trimming neccesity. Design- Prospective randomised trial. Animals-  Hundred and sixty holstein dairy cows. Procedure- One hundred and fifty cows selected in a dairy farm in dry period 2-3 weeks before calving (stage one), all cows were photographed, right, left and overall scores (A three point scoring system, in which score one is fo...

The outer multiset dimension $$\textrm{dim}_\textrm{ms}(G)$$ of a graph G is the cardinality smallest set vertices that uniquely recognize all outside this by using multisets distances to set. It proved $$\textrm{dim}_\textrm{ms}(G) = n(G) - 1$$ if and only regular with diameter at most 2. Graphs $$\textrm{dim}_\textrm{ms}(G)=2$$ are described recognized in polynomial time. A lower bound on lex...

For a poset X, Dim(X) is the smallest positive integer t for which X is isomorphic to a subposet of the Cartesian product of t chains. Hiraguchi proved that if 1 X I > 4, then Dim(X) < [ X l/2]. For each k Q 2, we define Dim,(X) as the smallest positive integer t for which Xis isomorphic to a subposet of the Cartesian product oft chains, each of length k. We then prove that if 1 X I > 5, Dim,(X...