Extreme points, support points and the Loewner variation in several complex variables

In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class S0(Bn) of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f (·, 0) of a Loewner chain f (z, t) = etz + ··· such that {e-tf (·, t)}t 0 is a normal family on Bn. We show that if f (·, 0) is an extreme point (respectively a support point) of S0(Bn), then e-tf (·, t) is an extreme point of S0(Bn) for t 0 (respectively a support point of S0(Bn) for t ∈[0, t0] and some t0 > 0). This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to S0(Bn) and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.     

Monte Carlo Simulation of Controlled/Living Radical Polymerization in Emulsified Systems

A new MC simulation method is proposed for the controlled/living radical polymerization in a dispersed medium, assuming an ideal miniemulsion system. This tool is used to consider the effects of particle size on the polymerization rates and the molecular weight distributions. For NMP, the polymerization kinetics are basically governed by two conflicting factors, (i) the confined space effect that promotes the coupling reaction between a radical and a trapping agent and (ii) the isolation effect of radicals into different particles that suppresses the overall frequency of bimolecular termination. For RAFT polymerization, a significant rate enhancement by reducing the particle size could be observed only for the systems with fast fragmentation of adduct radicals.

     

Measurements of analyzing powers Ay, Axx, Ayy and Axz in dp elastic scattering at Ed = 56 MeV

The differential cross section and all components of the analyzing powers A_y, A_xx, A_yy and A_xz have been measured in dp elastic scattering at 56 MeV. This is the first measurement of A_xz in the cyclotron energy region. A_xz has been measured with the beam polarized in the horizontal plane using the polarization tagging method. Faddeev calculations have been performed for four cases of the NN interaction. The Coulomb correction gave smaller effects at the present energy than at lower energies. Three of them reproduce the experimental data well. The agreement between the calculations and data for A_xz was better than that reported at lower energy. The deuteron asymptotic D- to S-state ratio has been obtained and is consistent within the limits of uncertainty with previously obtained values.     

X-Ray Tube Voltage Dependence of Wiener Spectra of Screen Structure Mottle Recorded on Front and Back Emulsions

A low-speed screen/film system was used to investigate structure mottle, i.e., the density fluctuation of an x-ray film due to inhomogeneous screen structure. The tube voltage dependence of the Wiener spectra of the structure mottle was separately determined for front and back film emulsions. The Wiener spectral values of the structure mottle of the front emulsion were greater than those of the back emulsion at lower tube voltages. The spectral values of the structure mottle of the front emulsion decreased with tube voltage, while those of the back emulsion increased. We explain these phenomena by the behavior of the Wiener spectra of the relative spatial fluctuation of fluorescence intensity due to following reasons: (1) spatial thickness fluctuation of the screen produces a relative spatial fluctuation of x-ray energy absorbed in the screen, and (2) as the distance between the emulsion of the film and the average position of the x-ray absorption in the screen lengthens, the number of random scattering and absorption of light photons increase.Presented at the International Commission for Optics Topical Meeting, Kyoto, 1994.     

Novel negatively charged cyanocuprate(I) host [Cu4(CN)7]3− built of tetrahedral Cu(I) coordination centers: Crystal structure of [{NH2(CH2CH2)2NCH2CH2NH2}2H][Cu4(CN)7]

The title inclusion compound [{NH₂(CH₂CH₂)₂NCH₂CH₂NH₂}₂H][Cu₄(CN)₇] was obtained as single crystals from an aqueous solution containing CuCN, KCN, andN-(2-aminoethyl)piperazine. It crystallizes in the monoclinic space groupP2/n,a = 12.3829(9),b = 8.5970(9),c = 12.6633(7) Å, = 109.984(5)°,z = 2,R = 0.035 for 2921 independent reflections. The inclusion structure is composed of the hydrogen-bonded dimeric onium guest [{NH₂(CH₂CH₂)₂NCH₂CH₂NH₂}₂H]³⁺ and the negatively-charged three-dimensional host [CU₄(CN)₇]^3– in which the CN-bridged framework Cu(I) atoms are all tetrahedral. A polyacene-like one-dimensional array of hexagons cornered by Cu(I) atoms and edged by -CN- linkages is arrayed in parallel to theb axis and stacked approximately along the c axis. The Cu(I) corner shared in the one-dimensional array extends an N-coordinate CN group along the c axis to a pair of unshared Cu(I) corners for which the C end behaves as a bifurcated ligand to build up the three-dimensional host structure. The cavity is composed of two networks of the hexagons at the top and bottom and pillared by six >CN- groups and accommodates a dimeric guest ofN-(2-aminoethyl)piperazinium cations protonated at each 4-N with the cations being hydrogen-bonded to each other through the 2-NH₂ groups sharing another H⁺.Presented at the Sixth International Seminar on Inclusion Compounds, Istanbul, Turkey, 27–31 August, 1995.     

Hydrothermal routes to prepare nanocrystalline mesoporous SnO2 having high thermal stability

We report simple hydrothermal routes to prepare thermally stable SnO2 particles having high specific surface areas and mesoporosity. The preparation method includes a new combination of synthetic processes: hydrolysis of tin(IV) chloride at 95 degrees C in the absence of alkaline solutions (aqueous NH3 or NaOH), formation of nanocrystalline SnO2, and subsequent hydrothermal treatments at temperatures between 100 and 200 degrees C. After annealing treatments of the hydrothermally treated SnO2 particles at 400 or 500 degrees C, their crystallite sizes remained smaller than 7.7 nm and their specific surface areas were still higher than 110 m2/g, indicative of the high thermal stability against particle growth and sintering. Furthermore, mesoporosity evolved with a relatively narrow pore size distribution typically in the range of 3.0-4.3 nm. The effects of the hydrothermal treatment were explained by uniformization of the particle size that was beneficial to the suppression of particle growth.