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.     

Tetrakis-acridinyl peptide: a novel fluorometric reagent for nucleic acid analysis based on the fluorescence dequenching upon DNA binding

Tetrakis-acridinyl peptide 1 assuming a right-handed helical stacked conformation of the acridinyl units can bind to DNA duplex with a very high affinity of 10(8) (M-bp)(-1) even at a high salt concentration of 0.2 M NaCl, irrespective of the base composition. Peptide 1 gave rise to 1600-times enhancement of its fluorescence upon binding to an AT polymer due to the collapse of this stacked structure, but the fluorescence is not enhanced with a GC polymer, though the binding constants of 1 for both polymers were the same.     

HPLC determination of (+)-pseudoephedrine and (-)-ephedrine in Japanese herbal medicines containing Ephedra herb using solid-phase extraction

We developed a rapid and simple HPLC method combined with solid-phase extraction (SPE) for quantitative analysis of (+)-pseudoephedrine (PEP) and (-)-ephedrine (EP) in Japanese herbal (Kampo) medicines such as Kakkon-to, Sho-seiryu-to, Goshaku-san and Bofu-tsusho-san. SPE was performed on TOYOPAK IC-SP M containing propylsulfonic groups. Determination of PEP and EP was carried out using ion-pair reversed-phase HPLC with sodium dodecyl sulfate. N-Benzyldiethylamine was used as an internal standard. The analytical procedure was validated with regard to specificity, linearity, accuracy, and precision. These data suggest that the analytical method developed in this study is useful for quantitative analysis of PEP and EP in various formulations of Kampo medicine containing Ephedra herb.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

Reactions of hydropolysilanes with alcohols catalysed by tris(triphenylphosphine)chlororhodium

[RhCl(PPh₃)₃] is a very effective catalyst for the cleavage of Si-Si bonds by alcohols.     

Chiral molecular glass: synthesis and characterization of enantiomerically pure thiophene-based [7]helicene

Synthesis of thiophene-based [7]helicenes, which are functionalized for both design of organic chiral glasses with strong chiroptical properties and for further homologation to higher [n]helicenes, is reported. The key synthetic transformations are kinetic resolution of the intermediate diketone and the annelation step forming the center benzene ring by means of an intramolecular McMurry reaction. Based upon X-ray crystallographic determinations of the absolute configurations for (+)-enantiomers of the diketone and the [7]helicene, stereochemical correlation between the (R) axial chirality of the diketone and the (M) helical chirality of the [7]helicene is established. One such enantiopure trimethylsilyl-substituted [7]helicene possesses enchanced chiroptical properties and forms a chiral molecular glass.     

Improved preparation of racemic 2-amino-3-(heteroaryl)propanoic acids and related compounds containing a furan or thiophene nucleus

Racemic 2-amino-3-(heteroaryl)propanoic acids (1), mostly with a furan or thiophene nucleus as a heteroaryl group, were synthesized in 48-94% yield by the reduction of 3-(heteroaryl)-2-(hydroxyimino)propanoic acids (5) with zinc dust and formic acid in the presence of a catalytic amount of iron dust at 60 degrees C for 2 h. Under these conditions, unfavorable hydrogenolysis of bromine on the thiophene nucleus does not occur. Traditional N-formylation of the prepared 3-(heteroaryl)alanine (1) with a mixture of formic acid and acetic anhydride afforded 2-(formylamino)-3-(heteroaryl)propanoic acids (6) in 51-95% yield.