Zeta functions of<Emphasis Type="Italic">q</Emphasis>-perfect numbers

We introduce a notion ofq-analogue of the perfect numbers. We also define a new zeta function which we call a zeta function ofq-perfect numbers. In this paper, the properties of theq-perfect numbers and the zeta functions are studied. Especially, we determine theq-perfect numbers whenq is a root of unity.     

Radical deoxygenation of hydroxyl groups via phosphites

A highly efficient, two-step sequence method for the deoxygenation of hydroxyl groups has been developed. The method involves the preparation of the 2-(2-iodophenyl)ethyl methyl phosphite derivative of an alcohol using methyl dichlorophosphite and 2-(2-iodophenyl)ethanol. Treatment of the phosphite intermediate with (n-Bu)3SnH/AIBN in refluxing benzene cleanly produces the deoxygenation product of the original alcohol.     

On a p-Local Geometry Associated with a Complex of Non-Trivial p-Subgroups

Let D be a complex of non-trivial p-subgroups of a finite groupG, closed under G-conjugation. In this paper, a p-local geometry^p(G; D) is introduced for G associated with the complex D. Thehomotopy equivalence between ^p(G; D) and D is also studied.2000 Mathematics Subject Classification 20E15, 51E24.     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Luminescent Polymer Consisting of 9,12‐Linked o‐Carborane

The synthesis of novel luminescent polymer containing p‐phenylene‐ethynylene and 9,12‐linked o‐carborane units alternately in the main chain is reported. The obtained polymer exhibits intense blue photoluminescence, providing the first insights into the optical properties of a 9,12‐disubstituted o‐carborane dye.  π‐Conjugated substituent at 9 and/or 12‐positions in o‐carborane is electrically independent, and both the HOMO and the LUMO levels slightly increase, whereas LUMO of the π‐conjugated substituent at 1 and/or 2‐positions in o‐carborane decrease.  Thus, it is deduced that polymers consisting of the 9,12‐linked o‐carborane unit are able to be applied as light‐emitting materials.

     

1,2,4-triazines. III. A convenient and general synthesis of 4H-[1,3,4]thiadiazolo[2,3-c][1,2,4]triazin-4-ones

4H-[1,3,4]Thiadiazolo[2,3-c][1,2,4]triazin-4-ones were prepared by cyclization of 3-thio-4-amino-1,2,4-tri-azine-3,5(2H,4H)-diones with a variety of acids in the presence of concentrated sulfuric acid. The synthesis appears to be general.     

Algorithm for in vitro Sun Protection Factor based on transmission spectrum measurement with concomitant evaluation of photostability

In the in vitro evaluation of Sun Protection Factor (SPF), the photostability of the ultraviolet (UV) filters can have a major impact, especially for high-SPF formulations, but is generally not taken into consideration. In this study, we present a UV transmission spectrum measurement system utilizing a high-sensitivity UV photomultiplier tube with concomitant evaluation of photostability. We have developed an algorithm to estimate SPF in vitro by converting the amount of UV light transmission through the sunscreen layer into cumulative relative erythema effectiveness to obtain one minimal erythema dose. Thus, the algorithm uses the same endpoint as in vivo SPF methods, but with a photomultiplier tube as the detector instead of skin. The values obtained showed an excellent correlation with in vivo SPF values, even for high-SPF sunscreens exceeding SPF 50. This method should be suitable as an in vitro SPF testing method for regulatory purposes.     

Quantitative Detection for Porphyromonas gingivalis in Tooth Pocket and Saliva by Portable Electrochemical DNA Sensor Linked with PCR

Here, a quantitative electrochemical analysis of periodontal bacteria in gingival crevicular fluid (GCF) and saliva by direct polymerase chain reaction (PCR) is presented. The electrochemical measurement was performed by mixing with PCR products and electrochemical indicator (bisbenzimidazole trihydrochloride). The peak current of indicator is reduced due to slower diffusion when the dye intercalates into the amplified DNA, and the degree of reduction in the peak current is correlates with the quantity of amplified DNA. Therefore, a quantitative analysis is possible by using our electrochemical method at the end point of PCR. In the GCF testing, The number of Porphyromonas gingivalis (Pg) detected by our electrochemical method at the end point of PCR were almost same compared with that were calculated by the conventional method of quantitative real? time PCR. In the saliva testing, the relationship between number of Pg in saliva and average pocket depth, and age‐dependence were also clearly observed. Since the saliva sample is obtained in a non‐invasive manner, this method is useful for the primary screening of periodontal disease. Moreover, our detection method is simple and uses a hand‐held potentiostat making it suitable for development of an on‐site periodontal diagnosis system.