A sphere as a surface which contains many circles II

A sphereM inE ³ is characterized as a simply connected complete smooth surface which contains a circle through each pointp M contained in a normal plane ofM atp.The author would like to thank Professor K. Ogiue for his valuable suggestions.     

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.     

Temperature-induced crystallization and compactibility of spray dried composite particles composed of amorphous lactose and various types of water-soluble polymer

The purpose of this study was to investigate the temperature-induced crystallization and the compactibility of the composite particles containing amorphous lactose and various types of polymers. The composite particles were prepared by spray-drying an aqueous solution of lactose and various types of gel forming water-soluble polymers at various formulating ratios. The stabilizing effect of hydroxypropylcellulose (HPC) and polyvinyl pyrrolidone (PVP) on amorphous lactose in the composite particles was smaller than that of sodium alginate in comparing at the same formulating ratios. The difference in the stability of amorphous lactose in the composite particles was attributed to the difference in the glass transition temperature (Tg) of the composite particles caused by the polymers formulated. The tensile strength of compacted spray-dried composite particles containing the polymers was higher than commercial lactose for direct tabletting (DCL21). The tensile strength of the composite particles was increased with an increase in water content in the particles. The difference in compactibility of the composite particles containing the different amount of polymer and water could be explained by the difference in Tg of the particles.     

Comparisons of elemental concentrations in hair of the inhabitants of heavy metal polluted areas with those of normal Japanese

Human hair collected from the mercury, arsenic and cadmium polluted areas has been analysed by instrumental neutron activation method. The concentrations of 27 elements were compared with those of normal Japanese. Correlation coefficients of logarithmic concentrations between the elements were calculated and their significance levels were determined. Factor contribution and factor loadings of the elements were calculated for each factor by making use of principal component analysis. The factor score of each sample was also calculated for each factor to examine the effects of the contamination by heavy metals on individuals.