The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

UV luminescent organic-capped ZnO quantum dots synthesized by alkoxide hydrolysis with dilute water

A novel synthesis route to organic-capped and colloidal ZnO quantum dots (QDs) has been developed. Specifically, zinc-di-t-butoxide and zinc-di-n-butoxide are hydrolyzed by very dilute water (400-600 mass ppm) in hydrophilic benzylamine and polymerized to ZnO by dehydration and/or a butanol elimination reaction. Growth of the ZnO QDs and exchange of the surface capping ligand from the hydroxyl groups and/or benzylamine to the oleylamine occur by heating the colloidal solution after addition of the oleylamine at 100-180°C. The final ZnO QDs with diameters in the range of 3-7 nm are highly dispersible in various organic solvents. The ZnO QDs exhibit the quantum size effect upon UV emission; it was controlled between 3.39 and 3.54 eV in the present study. The defect-related Vis emission decreased and the UV emission becomes dominant when zinc-di-n-butoxide with a 99.99% zinc purity is used as the starting material. The intensity of the photoluminescence UV emission is 1.5 times higher than that of the Vis emission.     

Hamiltonian cycles in n‐extendable graphs

A graph G of order at least 2n+2 is said to be n‐extendable if G has a perfect matching and every set of n independent edges extends to a perfect matching in G. We prove that every pair of nonadjacent vertices x and y in a connected n‐extendable graph of order p satisfy deg_G x+deg_G y ≥ p ? n ? 1, then either G is hamiltonian or G is isomorphic to one of two exceptional graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 75–82, 2002     

Further studies on palytoxin. II. structure of palytoxin

The full structure of palytoxin, a potent coelenterate toxin, is reported.     

Stereoselective cross-coupling reaction of 1,1-Diboryl-1-alkenes with electrophiles: a highly stereocontrolled approach to 1,1,2-triaryl-1-alkenes

Palladium-catalyzed cross-coupling reaction of 1,1-diboryl-1-alkenes with aryl and alkenyl iodides was found to proceed stereoselectively, giving rise to the corresponding mono-coupled product as a single diastereomer with E-configuration. Second coupling of the initial product with another aryl iodide affords diverse triarylalkenes in their stereochemically pure form. This highly stereoselective approach for triarylalkenes allows one to synthesize both diastereomers in one pot from 1,1-diboryl-1-alkenes.     

Improvements in Carrier-to-Noise-Ratio (CNR) of Lightwave Amplitude Modulated Vestigial-Sideband (AM-VSB) Transmission Systems by the Use of Optical Isolators

In lightwave community antena television (CATV) systems as well as other optical fiber communication networks, a transmitted optical signal is known to be degraded by an intensity noise produced within the fiber due to the interference between the signal and doubly reflected light. We report on the improvements to the signal degradation due to the double Rayleigh backscattering by inserting optical isolators in the trunk lines of the systems. A carrier-to-noise ratio (CNR) has been calculated as a function of the number and the insertion loss of the isolators. The calculated results indicate that there is an optimum number of isolators, and if the insertion loss is less than 0.3 dB, the CNR degradation can be restored by more than 60%. To test the calculated results, we conducted experiments for the specific case of employing one isolator, and obtained good agreements between the two.