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.     

Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories

For square contingency tables with ordered categories, Tomizawa (Calcutta Stat Assoc Bull 43:123–125, 1993a; Sankhyā Ser B 60:293–300, 1998) gave theorems that the marginal homogeneity (MH) model is equivalent to certain two or three models holding simultaneously. This paper proposes a generalized MH model, which describes a structure of the odds that an observation will fall in row category i or below and column category i + 1 or above, instead of in column category i or below and row category i + 1 or above. In addition, this paper gives the theorems that the MH model is equivalent to the generalized MH model and some models holding simultaneously whose each indicates: (1) the equality of m-order moment of row and column variables, (2) the equality of skewness of them and (3) the equality of kurtosis of them. When the MH model fits the data poorly, these may be useful for seeing the reason for the poor fit; for instance, the poor fit of the MH model is caused by the poor fit of the equality of row and column means rather than the generalized MH model. Examples are given.     

Platinum Nanoflowers on Scratched Silicon by Galvanic Displacement for an Effective SALDI Substrate

We report a new and facile method for synthesizing 3D platinum nanoflowers (Pt Nfs) on a scratched silicon substrate by electroless galvanic displacement and discuss the applications of the Pt Nfs in surface‐assisted laser desorption/ionization‐mass spectrometry (SALDI‐MS). Surface scratching of n‐type silicon is essential to induce Pt Nf growth on a silicon substrate (to obtain a Pt Nf silicon hybrid plate) by the galvanic displacement reaction. The Pt Nf silicon hybrid plate showed excellent SALDI activity in terms of the efficient generation of protonated molecular ions in the absence of a citrate buffer. We propose that the acidity of the Si? OH moieties on silicon increases because of the electron‐withdrawing nature of the Pt Nfs; hence, proton transfer from the Si? OH groups to the analyte molecules is enhanced, and finally, thermal desorption of the analyte ions from the surface occurs. Signal enhancement was observed for protonated molecular ions produced from a titania nanotube array (TNA) substrate on which Pt nanoparticles had been photochemically deposited. Moreover, surface modification of the Pt Nf silicon hybrid plate by perfluorodecyltrichlorosilane (FDTS) (to obtain an FDTS‐Pt Nf silicon hybrid plate) was found to facilitate soft SALDI of labile compounds. More interestingly, the FDTS‐Pt Nf silicon hybrid plate acts 1) as a high‐affinity substrate for phosphopeptides and 2) as a SALDI substrate. The feasibility of using the FDTS‐Pt Nf silicon hybrid plate for SALDI‐MS has been demonstrated by using a β‐casein digest and various analytes, including small molecules, peptides, phosphopeptides, phospholipids, carbohydrates, and synthetic polymers. The hybridization of Pt Nfs with a scratched silicon substrate has been found to be important for achieving excellent SALDI activity.     

Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ～3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ～20 K and coexists with the topological superconducting state.     

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.     

Acyldesilylation of 5-Trimethylsilyl-2-furancarboxaldehyde

5－Acyl－2－furancarboxaldehydes2arelmpol－tantIntermedlateslforsynthesizingnaturallyoccuTTingfuranoldfattyacidswhichhaveantloxldanteffectsandantlneoplastlcactlvltlesInbiologicalsystems－．Nakayamaela尸reportedsuccessfulhalodesllylatlonofethyls－trlm...     

Solvent‐dependent formation of inclusion complexes between methylated cyclodextrins and biodegradable polymers

The inclusion complexes (ICs) of unmodified natural and methylated α‐cyclodextrins (CDs) with biodegradable polymers, polyethylene glycol and poly(ε‐caprolactone), were prepared by two methods, that is, the one using water and the other using chloroform as the solvent for the respective CDs. The ICs obtained were characterized by IR, WAXD, DSC, and ¹³C CP/MAS NMR. It was found that the possibility and the phenomena of IC formation could be varied with the degree of methyl substitution of CD as well as the type of solvents used. Methylated α‐CDs showed the prominent characteristics of IC formation with polymers in the case where chloroform was used than in the case where water was used as the solvent for CDs, while vice versa in the case of native α‐CD. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 879–891, 2008     

Crosstalk Suppression in Header Recognition Unit Using Time-Space Conversion

We demonstrate a suppression effect of a crosstalk among a target and similar header signals using the header recognition filter designed by a design technique of the multiple-object discriminant filter.     

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases is described. We have achieved a total synthesis and revised the structure of plakevulin A. Several analogues including untenone A, manzamenone A, and optically active plakevulin A, were prepared and tested with an enzyme inhibition assay for mammalian DNA polymerases. The effect of the methyl ester moiety, and the substituents at the 1- and 4-positions of plakevulin A on DNA polymerase activities are discussed.     

Two Non-closure Properties on the Class of Subexponential Densities

Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.