in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

background: in this study, the effects of three structural analogues of adenosine upon proliferation of human tumor cells were investigated. previous research showed a cytotoxic effect of adenosine via a3 receptor and a1 receptor and sometimes this effect was receptor independent. the researches showed a differential cytotoxic effect of adenosine and its a3 agonists on cancerous cells, while ot...

6,798,120 B1 9/2004 Fearing et al. 7,267,150 B2 * 9/2007 Shimizu et a1. ............. .. 156/378 7,446,423 B2 * 11/2008 Sakai et a1. ...... .. 257/783 7,678,211 B2 * 3/2010 Takasaki et a1. 156/64 7,896,047 B2 * 3/2011 Yamamoto ....... .. 156/378 7,988,803 B2 * 8/2011 Takasaki et a1. ....... .. 156/64 8,091,764 B2 * 1/2012 Suga et a1. ............. .. 228/18021 2006/0264086 A1 11/2006 Nolan 2008...

Let θ(a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ(a1, a2, · · · , ak) is chromatically unique if ak < a1 + a2, and find examples showing that θ(a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.

6,876,998 B2 * 4/2005 Evans ................................. .. 1/1 7,761,480 B2 * 7/2010 Toledano et a1. .. 707/804 7,818,313 B1* 10/2010 TsimelZon et a1. 707/718 8,131,540 B2 * 3/2012 Marchisio et a1. 704/9 2004/0034632 A1* 2/2004 Carmel et a1. 707/5 2005/0033711 A1* 2/2005 Horvitz et a1. . 706/5

Urea has a critical role in urinary concentration. Mice lacking the inner medullary collecting duct (IMCD) urea transporter A1 (UT-A1) and urea transporter A3 (UT-A3) have very low levels of urea permeability and are unable to concentrate urine. To investigate the role of UT-A1 in the concentration of urine, we transgenically expressed UT-A1 in knockout mice lacking UT-A1 and UT-A3 using a cons...

Let A1,…,Am be families of k-subsets an n-set. Suppose that one cannot choose pairwise disjoint edges from s+1 distinct families. Subject to this condition we investigate the maximum |A1|+…+|Am|. Note subcase m=s+1, A1=…=Am is Erdős Matching Conjecture, most important open problems in extremal set theory. We provide some upper bounds, a general conjecture and its solution for range n≥4k2s.