Entropy of random chaotic interval map with noise which causes coarse-graining

A random chaotic interval map with noise which causes coarse-graining induces a finite-state Markov chain. For a map topologically conjugate to a piecewise-linear map with the Lebesgue measure being ergodic, we prove that the Shannon entropy for the induced Markov chain possesses a finite limit as the noise level tends to zero. In most cases, the limit turns out to be strictly greater than the Lyapunov exponent of the original map without noise.     

Equiaffine immersions of general codimension and its transversal volume element map

With an equiaffine immersion of codimension 1 into the affine space with the natural equiaffine structure, the conormal map is associated. In this paper, for an equiaffine immersion of general codimension into the space, we shall define the map corresponding to the conormal map, which is called the transversal volume element map. And we shall investigate if, an equiaffine immersion of general codimension into the space is determined by its affine fundamental form and its transversal volume element map.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Local Subexponentiality and Self-decomposability

The class of exponential tilts of convolution equivalent distributions is determined. As a corollary, the local subexponentiality of one-sided infinitely divisible distributions is characterized. It is applied to the subexponentiality of the densities of a self-decomposable distribution and its Lévy measure. Bondesson’s conjecture on the density of the Lévy measure of a lognormal distribution is solved as an example. Results of Denisov et al. on the distributions of random sums are extended to the two-sided case. Finally, the local subexponentiality of the distribution of the supremum of a random walk is characterized.     

Enantiomer separation of hydrophobic amino compounds by high-performance liquid chromatography using crown ether dynamically coated chiral stationary phase

CROWNPAK CR(+) column, which is powerful for the separation of amino acid enantiomers, must be used at a column temperature below 50°C and a mobile phase containing less than 15% methanol, because the chiral crown ether moiety of the stationary phase is dynamically coated on an ODS matrix. The second peak of the enantiomers of alanine-β-naphthylamide (Ala-β-NA) appeared at 204 min (k₂=148) by using ordinary mobile phase, that is, a mixture of 10 mM perchloric acid and 15% methanol. In this study, enantiomer separations of Ala-β-NA and 1-(1-naphthyl)ethylamine (1-NEA), both of which are hydrophobic amino compounds, were investigated through the modification of the mobile phase. Addition of crown ether, cyclodextrins (CDs), cations, etc., affected the stability of the complex between an analyte and the chiral moiety, leading to fast separation. The second peak of the enantiomers of Ala-β-NA appeared at 68 min (k₂=49) through the addition of 10 mM β-CD, or at 61 min (k₂=44) using potassium dihydrophosphate as a buffer component. This method was applied for the optical purity testing of -Ala-β-NA, which is used as one of the chiral derivatization reagents for carboxylic compounds. Validations such as reproducibility and linearity were also demonstrated and this method was found to be sufficient as a quality control method for the optical purity testing of -Ala-β-NA. As little as 0.05% -form in -Ala-β-NA could be determined.     

Synthesis of the proposed structure of plakevulin A: revised structure of plakevulin A

A total synthesis of the proposed structure of plakevulin A was accomplished. However, the NMR spectral data of the synthetic plakevulin A were not identical of those of the reported compound. We next converted the synthetic plakevulin A into 1-dihydrountenone A. The ¹H and ¹³C NMR spectral data of 1-dihydrountenone A were identical with those of reported plakevulin A except for the peaks derived from levulinic acid. Thus, we repurified sample of the natural product and confirmed that the natural sample contained 1-dihydrountenone A and levulinic acid in the ratio of one to one. We also found that not plakevulin A but 1-dihydountenone A possessed the inhibitory activity against mammalian DNA polymerases α and β.     

Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions

For any stable distribution on the line, recurrence-transience of the selfsimilar additive process {X _t ,t0} with (X ₁)= is determined. Comparison with the stable Lévy process {Y _t ,t0} with (Y ₁)= is made: if is not strictly stable, then {Y _t } is transient but {X _t } is recurrent except the obviously transient case of monotone sample functions.     

Mediated amperometric biosensor for hypoxanthine based on a hydroxymethylferrocene-modified carbon paste electrode

An amperometric enzyme electrode for the determination of hypoxanthine in fish meat is described. The hypoxanthine sensor was prepared from xanthine oxidase immobilized by covalent binding to cellulose triacetate and a carbon paste electrode containing hydroxymethylferrocene. The xanthine oxidase membrane was retained behind a dialysis membrane at a carbon paste electrode. The sensor showed a current response to hypoxanthine due to the bioelectrocatalytic oxidation of hypoxanthine, in which hydroxymethyiferrocene served as an electron-transfer mediator. The limit of detection is 6 × 10^?7 M, the relative standard deviation is 2.8% (n=28) and the response is linear up to 7 × 10^?4 M. The sensor responded rapidly to a low hypoxanthine concentration (7 × 10^?4 M), the steady-state current response being achieved in less than 1 min, and was stable for more than 30 days at 5 ° C. Results for tuna samples showed good agreement with the value determined by the conventional method.     

Preparation of alpha-elastin nanoparticles by gamma irradiation

Nanoparticles were prepared by utilizing the thermosensitive aggregation of alpha-elastin and gamma ray crosslinking. Three different heating process, “Slow heating”, “Fast heating”, and “Heat shock”, were applied for the aggregation of the alpha-elastin and examined to yield nanoparticles by gamma rays crosslinking. As a result, only “Slow heating” process yielded nanoparticles with diameters of about ca. 300 nm above cloud point (CP) and about ca. 100 nm below CP, and a narrow size distribution above 1.0 mg/ml concentration (exclude 1.0 mg/ml).