A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

Reaction of 1,3-dimethyl-5-acetyl-barbituric acid (DAB) with primary amines. Access to intermediates for selectively protected spermidines

The ability of 1,3-dimethyl-5-acetyl-barbituric acid (DAB) to react with primary amines in a chemoselective fashion was applied to the synthesis of a selectively protected spermidine.     

Preparation of a new hydrophilic copolymer from a polylactone and the structure analyses

A new hydrophilic copolymer having three kinds of hydroxyl groups, i.e. primary OH on -hydroxy allyl alcohol component, secondary OH on cyclic hemiacetal component and tertiary OH on -hydroxy acrylate component, was prepared by reducing a ‘polylactone’, poly(1-oxa-2-oxobutane-1,4:3,3-tetrayl), with NaBH₄ in mixed solvents containing an alcohol. The structural analyses were performed by the solution ¹H NMR and the solid state ¹³C NMR spectroscopies of the reduced samples. The composition of the three components turned out to be variable to the alcohol species used for the mixed solvent.     

An embedding domain approach for a class of 2-d shape optimization problems: mathematical analysis

This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains.     

Growth process of TiC clusters from Ti nanoparticles with evaporated carbon layer

Titanium carbide formation by the solid–solid reaction on the surface of Ti nanoparticles was studied in situ using a high-resolution transmission electron microscope with a heating stage. The cross-sectional image of the Ti surface was clearly observed. Vacuum-deposited carbon covered the whole the surface of Ti nanoparticles in spite of the partly evaporation on the nanoparticle surface. The diffusion of the carbon atoms inside the Ti nanoparticles depended on the size of the nanoparticles. When the Ti nanoparticle diameter was less than 30 nm, carbon atoms diffused into the Ti nanoparticle and formed TiC. The superstructure of the Ti nanoparticles was observed, which revealed the growth process of TiC to be the diffusion of carbon atoms. For Ti nanoparticles with diameter larger than 30 nm it was observed that diffusion of Ti atoms into the carbon layer was dominant, which resulted in formation of TiC in the carbon layer at the surface of Ti nanoparticles.     

Identifying phylogenetic trees

A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when identifies an X-tree, and the second describes when a compatible subset of is of maximum size.     

The Linear Rational Pseudospectral Method with Preassigned Poles

We present a linear rational pseudospectral (collocation) method with preassigned poles for solving boundary value problems. It consists in attaching poles to the trial polynomial so as to make it a rational interpolant. Its convergence is proved by transforming the problem into an associated boundary value problem. Numerical examples demonstrate that the rational pseudospectral method is often more efficient than the polynomial method.     

Polarization-Insensitive All-Optical Time-Division Demultiplexer Constructed with a Nonlinear Loop Interferometer

A polarization-insensitive 40-Gb/s time-division demultiplexer was demonstrated in a polarization-diversity loop configuration. The power penalty was measured to be 2.3 dB at a bit error rates of 10-9 for 10 Gb/s output signals.     

Local effect of electric and magnetic fields on the position of an attached shock in a supersonic diffuser

Effective ways for controlling shock wave configurations by means of external actions are sought. One such way is a local effect of electric and magnetic fields. In this paper, the local effect of external fields is implemented by current localization in a limited region of a diffuser. The experiment is carried out in a diffuser providing the complete internal compression of the gas with a Mach number at the inlet M=4.3. As a working medium, a xenon plasma is used. The plasma flow is formed in a shock tube equipped with an accelerating nozzle. Two ways of current localization are tested. In the first one, the diffuser inlet is a short channel of Faraday generator type. In this case, the ponderomotive force basically decelerates or accelerates the flow depending on the direction of the electric field. In the second way, the current flows through a narrow near-wall region between adjacent electrodes. In this case, the ponderomotive force compresses or expands the gas. In both cases, it is shown that the angle of an attached shock due to MHD interaction can be both decreased and increased. The central problem with the MHD control of shock waves is near-electrode and near-wall phenomena.