(c) Columns of A are independent. (d) A is tall (i.e., n ≤ m) and full-rank (i.e., rank(A) = min(m,n) = n). Solution: We will show the chain of equivalences (a) =⇒ (b) =⇒ (c) =⇒ (d) =⇒ (a). (a) =⇒ (b): By the rank–nullity theorem, we have dim(N (A)) + rank(A) = n, which implies rank(A) = n (since dim(N (A)) = 0). Since rank(A) = rank(A ), we then have rank(A ) = n. Since rank is equivalent to t...

Modulation of the immune system by cancer protective food bioactives has preventive and therapeutic importance in prostate cancer, but the mechanisms remain largely unclear. The current study tests the hypothesis that the diet-derived cancer protective compounds, indole-3-carbinol (I3C) and 3,3'-diindolylmethane (DIM), affect the tumor microenvironment by regulation of inflammatory responses in...

1,1-Bis(3'-indolyl)-1-(p-t-butylphenyl)methane (DIM-C-pPhtBu) is a peroxisome proliferator-activated receptor gamma (PPARgamma) agonist, and treatment of SKOV3 ovarian cancer cells with this compound (5 micromol/L) inhibits cell proliferation, whereas up to 15 micromol/L rosiglitazone had no effect on cell growth. DIM-C-pPhtBu also inhibits G0-G1 to S phase cell cycle progression and this is li...

BACKGROUND The development of 3, 3'-diindolyl methane (DIM) resistant parasite Leishmania donovani (LdDR50) by adaptation with increasing concentrations of the drug generates random mutations in the large and small subunits of heterodimeric DNA topoisomerase I of Leishmania (LdTOP1LS). Mutation of large subunit of LdTOP1LS at F270L is responsible for resistance to DIM up to 50 µM concentration....

The research on distributed system’s dim target detection and tracking is very important to improve the performance of infrared guard system. When the image background is very intricate, and there are few pels of targets, it is very hard to check the target. An local texture analysis method which is very fit for dim target detection in low signal to noise rate was adopted to realize the detecti...

Exogenous glucocorticoids are known to inhibit wound repair, but the roles and mechanisms of action of endogenous glucocorticoids during the healing process are as yet unknown. Therefore, we wounded mice expressing a DNA-binding-defective mutant version of the glucocorticoid receptor (GR(dim) mice) and also analysed fibroblasts from these animals in vitro. We found a remarkably enlarged granula...