A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self‐similar solutions to nonlinear wave equations are proved on up to five space dimensions. © 2006 Wiley Periodicals, Inc.     

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.     

Applicability of headspace solid-phase microextraction to the determination of multi-class pesticides in waters

The applicability of headspace solid-phase microextraction (HS-SPME) to pesticide determination in water samples was demonstrated by evaluating the effects of temperature on the extraction of the pesticides. The evaluations were performed using an automated system with a heating module. The 174 pesticides that are detectable with gas chromatograph were selected objectively and impartially based on their physical properties: vapor pressure and partition coefficient between octanol and water. Of the 174 pesticides, 158 (90% of tested) were extracted with a polyacrylate-coated fiber between 30 and 100 degrees C and were determined with gas chromatograph-mass spectrometry. The extraction-temperature profiles of the 158 extracted pesticides were obtained to evaluate the effects of temperature on the extraction of pesticides. The pesticides were classified into four groups according to the shape of their extraction-temperature profiles. The line of demarcation between extractable pesticides and non-extractable pesticides could be drawn in the physical property diagram (a double logarithmic plot of their vapor pressure and partition coefficient between octanol and water). The plot also revealed relationships between classified extraction features and their physical properties. The new method for multi residue screening in which the analytes were categorized into sub-groups based on extraction temperature was developed. In order to evaluate the quantitivity of the developed method, the 45 pesticides were chosen among the pesticides that are typically monitored in waters. Linear response data for 40 of the 45 was obtained in the concentration range below 5 microg/l with correlation coefficients ranging between 0.979 and 0.999. The other five pesticides had poor responses. Relative standard deviations at the concentration of the lowest standard solution for each calibration curve of the pesticides ranged from 3.6 to 18%. The value of 0.01 microg/l in the limits of detection for 17 pesticides was achieved only under the approximate conditions for screening, not under the individually optimized conditions for each pesticide. Recoveries of tested pesticides in actual matrices were essentially in agreement with those obtained by solid-phase extraction.     

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.