A little theorem of the bigℳ in interior point algorithms

When we apply interior point algorithms to various problems including linear programs, convex quadratic programs, convex programs and complementarity problems, we often embed an original problem to be solved in an artificial problem having a known interior feasible solution from which we start the algorithm. The artificial problem involves a constant (or constants) which we need to choose large enough to ensure the equivalence between the artificial problem and the original problem. Theoretically, we can always assign a positive number of the order O(2 ^L ) to in linear cases, whereL denotes the input size of the problem. Practically, however, such a large number is impossible to implement on computers. If we choose too large, we may have numerical instability and/or computational inefficiency, while the artificial problem with not large enough will never lead to any solution of the original problem. To solve this difficulty, this paper presents a little theorem of the big, which will enable us to find whether is not large enough, and to update during the iterations of the algorithm even if we start with a smaller. Applications of the theorem are given to a polynomial-time potential reduction algorithm for positive semi-definite linear complementarity problems, and to an artificial self-dual linear program which has a close relation with the primal—dual interior point algorithm using Lustig's limiting feasible direction vector.     

Quantum cascade multi-electron injection into Si-quantum-dot floating gates embedded in SiO2 matrices

The use of silicon-quantum-dots (Si-QDs) as floating gates in metal-oxide-semiconductor-field-effect-transistors (MOSFETs) has been attracting great attention. It has been reported that large decreases in drain current are observed within a very short time in Si-QDs memories, indicating that the collective motion of electrons occurs during electron injection into Si-QDs. In this study, we present a theoretical report which indicates that the interaction length between QDs is about 5-10 nm. From these results, we propose a mechanism for “quantum cascade multi-electron injection”.     

An analogue of the Nielsen-Schreier formula for pro-<Emphasis Type="Italic">p</Emphasis>-groups

We introduce a condition analogous to the Nielsen-Schreier formula, and investigate basic properties of pro-p-groups satisfying the condition. Partly supported by the Grant-in Aid for Scientific Research (C), Japan Society for the Promotion of Science. Received: 23 January 2006     

Molecular crystalline capsules that release their contents by light

Here, we present single crystalline capsules of a photoresponsive molecule produced by simple recrystallization from organic solutions without direct human processing. During the crystal growth process, a movie was taken of the capsule taking in the organic solution. The capsules responded rapidly (<1 s) to the UV light stimuli and released the captured solution or solute. In principle, they can take in any substance dissolved in organic solvents, and their size can be controlled. Moreover, the capsule can be broken by multi-photon excitation using a near-infrared laser within the biological window. Furthermore, because the molecular packing in the crystal is unidirectional, the response can be controlled by the polarization of the light. This study shows the new potential of photoresponsive molecules.

A novel diarylethene formed “crystalline capsules” containing liquid inclusions, and chemicals trapped in the capsules were released by photoinduced breaking. Operations by multiphoton and linear polarized light were demonstrated.     

Preparation and characterization of unique inorganic-organic hybrid mesoporous materials incorporating arenetricarbonyl complexes [-C6H4M(CO)3-] (M = Cr, Mo)

Unique inorganic-organic hybrid mesoporous materials incorporating arenetricarbonyl complexes [-C6H4M(CO)3-] (M = Cr, Mo) within their mesoporous frameworks have been successfully prepared by a simple CVD treatment of the phenylene-bridged organosilica mesoporous materials with metal hexacarbonyls [M(CO)6] (M = Cr, Mo). FT-IR and UV-vis investigations revealed that the arenetricarbonyl complexes exist stably even at temperatures above 473 K under vacuum.     

New synthetic route to granulatimide and its structural analogues

The Stille coupling reaction of stannylindole 12 with 4-iodoimidazole 13 (or 24) in the presence of PdCl(2)(PPh(3))(2) gave the corresponding indole-imidazole coupling product 14 (or 25), thereby affording a new synthetic approach to the alkaloid granulatimide (7), isolated from the Brazilian ascidian Didemnum granulatum, as well as its structural analogues, 10-methylgranulatimide (23), 17-methylgranulatimide (30), 10,17-dimethylgranulatimide (31).