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.     

Simple and rapid spectrophotometric determination of iron after preconcentration as its 1,10-phenanthroline complex on the natural polymer "chitin"

Preconcentration by collection of metal complexes on chitin has been applied to the spectrophotometric determination of iron in water. The iron is collected as its 1,10-phenanthroline (phen) complex on a column of chitin in the presence of tetraphenylborate as counter-ion. The iron(II)-phen complex retained on the chitin is eluted with an acetone-1M acetic acid mixture (8:2 v/v), and the absorbance of the eluate is measured at 512 nm. Beer's law is obeyed over the concentration range 1.1-11.2 mug of iron in 10 ml of eluate. In the presence of EDTA as masking agent, Ca, Mg, Al, Mn, Zn, Cd and Pb do not interfere in concentrations up to 100 times that of iron(II) and Co, Ni and Cu do not interfere in concentrations up to 20 times that of iron(II). Common inorganic anions do not interfere in concentrations up to 10,000 times that of iron(II). The proposed method has been applied to determination of iron in tap water.     

Regulation of lithospermic acid B and shikonin production in Lithospermum erythrorhizon cell suspension cultures

Cell suspension cultures of Lithospermum erythrorhizon produced a large amount of lithospermic acid B, a caffeic acid tetramer, as well as shikonin derivatives (each ca. 10% of dry wt.) when cultured in shikonin production medium M-9. Various culture factors for increasing the production of lithospermic acid B were investigated. Lithospermic acid B production was inhibited by 2, 4-D or NH4+, whereas it was stimulated by Cu2+. These regulatory patterns were similar to those for the production of shikonin derivatives in these cell cultures, suggestive of close relations and similar metabolic regulation between the production of these compounds. Cultivation under light illumination, however, showed that these metabolisms were independently regulated. In particular, blue light showed a stimulatory effect on lithospermic acid B production, while shikonin production was strongly inhibited, indicative of an effective condition for lithospermic acid B production.