Codes with given distances

One of the main results says that ifC is a binary linear code of length 4t and of dimension greater than 2t, thenC contains a word of weight 2t and this bound is best possible. Several results of similar flavor are established both for linear and non-linear codes. For the proof a lemma introducing the binormal forms of binary matrices is needed. The results are applied to determine the coset chromatic number of Hadamard graphs, to solve a problem of Galvin and to give a short proof of a theorem of Gleason on self-dual doubly-even codes.     

Limit Theorem for Controlled Backward SDEs and Homogenization of Hamilton–Jacobi–Bellman Equations

We prove a convergence theorem for a family of value functions associated with stochastic control problems whose cost functions are defined by backward stochastic differential equations. The limit function is characterized as a viscosity solution to a fully nonlinear partial differential equation of second order. The key assumption we use in our approach is shown to be a necessary and sufficient assumption for the homogenizability of the control problem. The results generalize partially homogenization problems for Hamilton–Jacobi–Bellman equations treated recently by Alvarez and Bardi by viscosity solution methods. In contrast to their approach, we use mainly probabilistic arguments, and discuss a stochastic control interpretation for the limit equation.     

Morphology of polytetrafluoroethylene prepared by radiation-induced emulsion polymerization

The original morphology of polytetrafluoroethylene prepared by radiation-induced emulsion polymerization was studied by electron microscopy. The morphology depends on molecular weight, which in turn depends on polymerization conditions, especially the emulsifier concentration. The molecular weight decreases with increasing emulsifier concentration. The morphology changes with molecular weight roughly as follows: fibrils below 10⁵, rods between 10⁵ and 5 × 10⁵, and granular particle above 10⁶. The crystallinity is high for all morphologies.     

Electron spin resonance studies on radiation graft copolymerization. I. Grafting initiated by alkyl radicals trapped in irradiated polyethylene

The behavior of trapped radicals in polyethylene which is irradiated in air at room temperature, under grafting of methylmechacrylate or butadiene has been studied by electron spin resonance. Part of the alkyl radicals are converted to allyl radicals by reaction with double bonds and the others disappear by recombination under vacuum. The active species of grafting are alkyl radicals when the vapor pressure of monomers is relatively high, while at low pressure allyl radicals also play a role as well as alkyl radicals. In the grafting at 20°C, the grafting yields depend mainly on the decay rate of alkyl radicals which come out of the crystalline regions of polyethylene. The decay rate of alkyl radicals and the rate of grafting at the initial stage increase with decreasing crystallite size of polyethylene.     

Synthesis of CD-ring structure of cortistatin A, an anti-angiogenic steroidal alkaloid from marine sponge

Stereoselective synthesis of the CD-ring structure of cortistatin A (1), a novel anti-angiogenic steroidal alkaloid from Indonesian marine sponge, was achieved. The stereogenic tertiary carbon center bearing the isoquinoline moiety was constructed by 1,3-chiral transfer method using Johnson-Claisen rearrangement of the chiral allylic alcohol 5. Subsequent intramolecular Michael-aldol reaction afforded the targeted trans-hydrindane skeleton with moderate stereoselectivity.     

A nanocarbon film electrode as a platform for exploring DNA methylation

We describe the quantitative nonlabel electrochemical detection of both cytosine (C) and methylcytosine (mC) in oligonucleotides using newly developed nanocarbon film electrodes. The film consists of nanocrystalline sp2 and sp3 mixed bonds formed by employing the electron cyclotron resonance (ECR) sputtering method. We successfully used this film to develop a simple electrochemical DNA methylation analysis technique based on the measurement of the differences between the oxidation currents of C and mC since our ECR nanocarbon film electrode can directly measure all DNA bases more quantitatively than conventional glassy carbon or boron-doped diamond electrodes. The excellent properties of ECR nanocarbon film electrodes result from the fact that they have a wide potential window while maintaining the high electrode activity needed to oxidize oligonucleotides electrochemically. Proof-of-concept experiments were performed with synthetic oligonucleotides including different numbers of C and mC. This film allowed us to perform both C- and mC-positive assays solely by using the electrochemical oxidation of oligonucleotides without bisulfite or labeling processes.     

Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton–Jacobi equations

This paper is concerned with the ergodic problem for superquadratic viscous Hamilton–Jacobi equations with exponent \(m>2\). We prove that the generalized principal eigenvalue of the equation converges to a constant as \(m\rightarrow \infty \), and that the limit coincides with the generalized principal eigenvalue of an ergodic problem with gradient constraint. We also investigate some qualitative properties of the generalized principal eigenvalue with respect to a perturbation of the potential function. It turns out that different situations take place according to \(m=2\), \(2<m<\infty \), and the limiting case \(m=\infty \).