On conservative approximation by linear polynomial operators an extension of the Bernstein's operator

In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained. This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107     

Morphologies of microporous polyethylene and polypropylene crystallized from solution in supercritical propane

The morphologies of solvent-free, microporous, mechanically self-supporting cylinders of linear polyethylene and isotactic polypropylene, crystallized from solution in supercritical propane, were examined by an SEM technique. The morphology of gels (or foams), obtained with little or no shrinkage from 2% to 35% solutions by weight of polyethylene (99% to 85% porosities), is shown in some detail. Lamellae with very little or considerable mutual organization occur, often in the form of stacks with straight or coiled axes (axialites). Further growth of these can lead to particles with a roughly spherical overall shape and a predominantly radial orientation of the lamellae at the particle surface. Subcooled isotactic polypropylene, on the other hand, crystallizes in the form of perfectly shaped birefringent microspheres of very uniform size. ©1995 John Wiley & Sons, Inc.     

On characterizing collections arising from N-gons in the plane

Consider a labeled convex n-gon in the plane and a point x in general position in the interior. We associate with this a collection (x) of 3-element sets, namely those 3-element subsets of the vertices which contain x in their interior. We investigate the problem of characterizing those collections of subsets which can be represented in this matter. We give a complete characterization of this and a related problem.School of Mathematics, University of Minnesota, Minneapolis, MN 55455. This work was supported in part by NSF grant DMS-8700995.Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England. Work done while Hill Visiting Professor at the University of Minnesota.     

Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

Radical concentration measurements in hydrocarbon diffusion flames

Absolute OH· concentrations and relative H-atom and O-atom profiles have been measured in a laminar, co-flowing methane/air diffusion flame burning at atmospheric pressure. Laser absorption and laser-induced fluorescence methods were used to probe the A ² X ²II_itransition in OH·. The maximum OH· concentration is found to be 1.8±0.2 ×10¹⁶ cm^–3 (mole fraction =5.0×10^–3) at a temperature of 2080 K, which is twice the value calculated assuming local total equilibrium but less than half that predicted from partial equilibrium (O₂+H₂ 2OH·). Multiphoton ionization (2+1 process at 243 nm) has been used to detect H atoms, while laser-induced fluorescence at 845 nm excited by two-photon absorption at 226 nm was employed to observe O atoms. In both cases it was found that low photon intensities (2×10⁸W/cm²) and a retroreflected beam, Doppler-free geometry was required in order to avoid the photolytic production of the species of interest. For all of the concentration profile data it is necessary to correct the raw signals for variations in collisional quenching. In the case of the multiphoton ionization measurements the variation in electron detection sensitivity as a function of flame position must be accounted for as well. Establishing absolute H-atom and O-atom concentrations is discussed in terms of partial equilibrium considerations and detailed flame structure calculations.Formerly the National Bureau of Standards     

Wiener-Hopf factorisation of Brownian motion

Summary We study how Brownian motion behaves under time change by a fluctuating additive functionalA _t , in particular letting be the first passage time ofA _t to zero we computeP _–x[B dy] explicitly in certain cases. The calculation is not an easy one, our method uses the Désiré André relation for the overshoot of a Lévy process and depends on some elliptic function identities. This paper only considers the one boundary case whereA _t is increasing (resp. decreasing) on the positive (resp. negative) half line.     

Some variations on Kac's formula for Brownian motion

We show that under suitable conditions $$\begin{gathered} E_x f\left\{ {a + \int_0^t \beta \left[ {b + \int_0^s {\alpha \left( {X_r } \right)dr, c + s, X_s } } \right]ds, b + \int_0^t {\alpha \left( {X_s } \right)ds, c + t, X_t } } \right\} \hfill \\ = e^{tG} f\left[ {a, b, c, x} \right] \hfill \\ \end{gathered} $$ whereX _t is a Brownian motion andG is the generator of a (C ₀) contraction semigroupe ^tG.     

Crystal and molecular structure of 1R,3S,5S,7R,10R-3,6,6,10,14-Pentamethyltricyclo[10.3.0.05,7]pentadeca-11,14-diene-1, 10-dihydroxy-2,13-dione (Japodagrol), C20H28O4

A new cytotoxic macrocyclic diterpenoid named Japodagrol, C₂₀H₂₈O₄, has been isolated from the ornamental plantJatropha podagrica, family Euphorbiaceae, grown in Nigeria. The structure of the title compound, C₂₀H₂₈O₄, was solved by X-ray analysis.M _r =332.44, monoclinic space groupC2,a=23.285(4),b=6.5105(12),c=12.505(3) Å,=98.504(17),V=1874.8 ų,Z=4,D _c =1.178 Mg/m³. CuK radiation (graphite crystal monochromator, =1.54184 A), (CuK)=6.13 cm^–1,F(000)=720,T=290 K. Final conventionalR factor=0.035,R _w =0.038 for 3349 observed reflections. The structure was solved with the programDirdif. The 5-membered ring is closed to a half-chair form. The compound contains inter- and intramolecular hydrogen bonds.     

Electrical characteristics of a small active volume (1 cm3) discharge-pumped XeCl laser

Through the use of a PFL (pulse-forming line) of conveniently changeable output impedance Z_O, the electrical characteristics of a small volume-discharge of standard XeCl laser gas mix was studied. The impedance Z_D from a 2×0.5×1(=1) cm³ discharge was found to be about 10. A PFL of very low impedance is therefore rather inefficient in driving the discharge, because of the impedance mismatch and the slower current rise time. The data presented will be useful for the design of excimer lasers of small discharge volume, which find applications in serving as master oscillator or in high repetition rate operation.