(6) Let G be a column Y-constant line Y-increasing matrix over E2 T and i1, i2, j1, j2 be natural numbers. Suppose 〈i1, j1〉 ∈ the indices of G and 〈i2, j2〉 ∈ the indices of G. If (G◦ (i1, j1))2 = (G◦ (i2, j2))2, then j1 = j2. (7) Let G be a line X-constant column X-increasing matrix over E2 T and i1, i2, j1, j2 be natural numbers. Suppose 〈i1, j1〉 ∈ the indices of G and 〈i2, j2〉 ∈ the indices o...

and Applied Analysis 3 As a special case, if n 2 in 1.3 , then we have the functional equation 1.2 . Also, if n 3 in 1.3 , we obtain 2 ∑ i1 2 3 ∑ i2 i1 1 f ⎛ ⎝ 3 ∑ i 1, i / i1,i2 xi − 2 ∑ r 1 xir ⎞ ⎠ 3 ∑ i1 2 f ⎛ ⎝ 3 ∑ i 1, i / i1 xi − xi1 ⎞ ⎠ f ( 3 ∑

The title compound {systematic name: 12-[(2E)-3,7-dimethyl-2,6-octa-dien-yl]-5,8-dihydr-oxy-2,2-dimethyl-2H,6H-pyrano[3,2-b]xanthen-6-one}, C(30)H(32)O(6), has four fused rings (A/B/C/D) and the xanthone ring system (A/B/C) is essentially planar, with dihedral angles of 1.85 (13) and 2.47 (13)°, respectively, between rings A and B, and between rings B and C. The chromene ring D is in a sofa for...

Let n be a positive odd integer and let p > n + 1 be a prime. We mainly derive the following congruence: ∑ 0<i1<···<in<p ( i1 3 ) (−1)i1 i1 · · · in ≡ 0 (mod p).

We explore the supergravity solution of D5-branes intersecting as an I1-brane. In a suitable near-horizon limit the geometry is in qualitative agreement with that found in the microscopic open-string analysis as well as the NS5-brane analysis of Itzhaki, Kutasov and Seiberg. In particular, the ISO(1, 1) Lorentz symmetry of the intersection domain is enhanced to ISO(1, 2). The discussion is gene...

The oligomerization of UGTs [UDP (uridine diphosphate)-glucuronosyltransferases] modulates their enzyme activities. Recent findings also indicate that glucuronidation is negatively regulated by the formation of inactive oligomeric complexes between UGT1A enzymes [i1 (isoform 1)] and an enzymatically inactive alternatively spliced i2 (isoform 2). In the present paper, we assessed whether deletio...

The induction and synthesis of metallothionein was studied in the isolated perfused rat liver, using Cd(I1) as the inducing metal. Perfusing the liver with 25 to 100 pg of Cd(I1) for 180 min revealed that the amount of Cd(I1) in metallothionein increased with the dosage of Cd(II), saturation being achieved at 75 pg. Zn(I1) in metallothionein decreased to about 60% of the level found in control ...

The induction and synthesis of metallothionein was studied in the isolated perfused rat liver, using Cd(I1) as the inducing metal. Perfusing the liver with 25 to 100 pg of Cd(I1) for 180 min revealed that the amount of Cd(I1) in metallothionein increased with the dosage of Cd(II), saturation being achieved at 75 pg. Zn(I1) in metallothionein decreased to about 60% of the level found in control ...