A generalization of the katona theorem for crosst-intersecting families

LetX be ann-element set and letA and? be families of subsets ofX. We say thatA and? are crosst-intersecting if |A ∩ B| ≥ t holds for all A ∈A and for allB ∈ ?. Suppose thatA and ? are crosst-intersecting. This paper first proves a crosst-intersecting version of Harper's Theorem:

1. There are two crosst-intersecting Hamming spheresA ₀,? ₀ with centerX such that |A| ≤ |A ₀| and|?| ≤ |? ₀| hold.
2. Suppose thatt ≥ 2 and that the pair of integers (|A) is maximal with respect to direct product ordering among pairs of crosst-intersecting families. Then,A and? are Hamming spheres with centerX.

Using these claims, the following conjecture of Frankl is proven:

1. Ifn + t = 2k ? 1 then |A| |?| ≤ max \(\left\{ {\left( {K_k^n + \left( {_{k - 1}^{n - 1} } \right)} \right)^2 ,K_k^n K_{k - 1}^n } \right\}\) holds, whereK _l ⁿ is defined as \(\left( {_n^n } \right)\left( {_{n - 1}^n } \right) + \cdots + \left( {_l^n } \right).\)
2. Ifn + t = 2k then |A| |? ≤ (K _k ⁿ )² holds.

The extremal configurations are also determined.     

Enhanced rectal absorption of insulin in rabbits from hollow-type suppositories containing insulin and glyceryl-1-monooctanoate.

The absorption of two kinds of insulin (from porcine or bovine pancreas) from the rectum of rabbits after the administration of hollow-type suppositories containing insulin and glyceryl-1-monooctanoate (GMO) as an absorption-enhancing agent was investigated. Two types of suppositories were employed: type I containing insulin in an aqueous solution (approx. 25 IU/mg/100 microliters citric buffer solution at pH 3.0) in the cavity of the suppository and GMO mixed with a base material (Witepsol H-15), and type II containing insulin in a crystalline form in the same amount as in type I. Without GMO, the insulin and glucose levels in plasma were unchanged, whereas a marked increase in the plasma levels of insulin and a decrease of glucose concentrations were found following coadministration of insulin and GMO by the type I suppository. Similar enhancement of rectal absorption of insulin was obtained from porcine and bovine sources. In the case of the crystalline insulin, despite the use of the same amount of GMO, porcine insulin was more efficiently absorbed than bovine insulin by the type II suppository. GMO enhances the absorption of insulin in an aqueous solution or a crystalline form, and the dissolution rate of insulin may be an important factor in the rectal absorption of insulin.     

Tris(1‐ethyl‐3‐methyl­imidazolium) hexa­chloro­lanthanate

In the title complex, (C₆H₁₁N₂)₃[LaCl₆], centrosymmetric octahedral hexa­chloro­lanthanate anions are located at the corners and face‐centers of the monoclinic unit cell. The ring H atoms of the cations interact with the Cl atoms of the anions via hydrogen bonding, and bifurcation of the hydrogen bonding is observed. Cation–cation interactions via hydrogen bonding between the ring H atoms and π‐electrons of aromatic rings are also observed as in other imidazolium salts.     

Borderline of hydrogen bonding of silanols

Two new silanols bearing very bulky silyl groups, (i-Pr₃ Si)₃SiOH and (t − BuMe₂Si)₃SiOH were prepared by peracidoxidation of their respective silanes. The X − ray crystallographic analysis revealed that (t − BuMe₂Si)₃ SiOH forms a dimeric structure with hydrogen bonding, while (i − Pr₃ Si)₃ SiOH exists as a monomer in the crystal. The effects of the size of the substituents as well as the reactivity of these silanols are discussed.     

Total synthesis of (+)-pederine. A simple synthetic method for N-(1-methoxyalkyl)amides

A mild one-pot method for the synthesis of acyclic N-(1-methoxyalkyl)amides starting from carboxylic acids and methyl imidates had been developed and applied to the total synthesis of the insect poison pederine $\text{1}$.     

Electronic effect on the regioselectivity in the ring opening of para-substituted phenyloxiranes by acetylides

The electronic effect on the regioselectivity in the alkynylation of phenyloxiranes was investigated using three kinds of metal acetylides. BF₃ mediated lithium acetylide provided either the α- or β-alkynylated products by controlling the effect of the para-substituents of the phenyloxiranes. LiClO₄ mediated lithium acetylide and titanium acetylide, on the other hand, afforded predominantly the β- and α-products, respectively.