Distances between oriented curves in geometric modeling

We consider the choice of a functional to measure the distance between two parametric curves. We identify properties of such a distance functional that are important for geometric design. Several popular definitions of distance are examined, and new functionals are presented which satisfy the desired properties. This revised version was published online in August 2006 with corrections to the Cover Date.     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

Orthonormal polynomial bases in function spaces

We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of polynomials. We show that this order is optimal.     

Identification of a light-regulated protein kinase activity from seedlings of Arabidopsis thaliana

Protein kinase transduction pathways are thought to be involved in light signaling in plants, but other than the photoreceptors, no protein kinase activity has been shown to be light-regulated in vivo. Using an in-gel protein kinase assay technique with histone H III SS as an exogenous substrate, we identified a light-regulated protein kinase activity with an apparent molecular weight ca 50 kDa. The kinase activity increased transiently after irradiation of dark-grown seedlings with continuous far red light (FR) and blue light (B) and decreased after irradiation with red light (R). The maximal activation was achieved after 30 min to 1 h with FR or B. After irradiation times longer than 2 h, the kinase activity decreased to below the sensitivity level of the assay. In Arabidopsis mutants lacking either the photoreceptors phytochrome A, phytochrome B or the blue-light receptor cryptochrome 1, kinase activity was undetectable, whereas in the photomorphogenic mutants cop1 and det1 the kinase activity was also observed in the absence of light signals, though still stimulated by B and FR. Interestingly, the R inhibition of the kinase activity was lost in the mutant hy5. Pretreatment with cycloheximide blocked the kinase activity.     

The Impact of C2 Insertion into a Carbazole Donor on the Physicochemical Properties of Dibenzo[a,j]phenazine-Cored Donor–Acceptor–Donor Triads

Novel electron donor–acceptor–donor (D-A-D) compounds comprising dibenzo[a,j]phenazine as the central acceptor core and two 7-membered diarylamines (iminodibenzyl and iminostilbene) as the donors have been designed and synthesized. Investigation of their physicochemical properties revealed the impact of C₂ insertion into well-known carbazole electron donors on the properties of previously reported twisted dibenzo[a,j]phenazine-core D-A-D triads. Slight structural modification caused a drastic change in conformational preference, allowing unique photophysical behavior of dual emission derived from room-temperature phosphorescence and triplet–triplet annihilation. Furthermore, electrochemical analysis suggested sigma-dimer formation and electrochemical polymerization on the electrode. Quantum chemical calculations also rationalized the experimental results.     

Polyphosphate chains by addition of oxiranes to phosphoric acid

Addition of diepoxides to the acids of phosphorus provides a new, attractive route to polyphosphates. In order to understand better the mechanism of this reaction and the structure of the products, the model reactions, namely additions of simple oxiranes to the acids of phosphorus, have been studied. It was shown that this reaction is catalysed by the P-OH groups of the acids. Activation of the oxirane molecule occurs predominantly by formation of the hydrogen bonded species while ionized form of acid plays only a minor role at the studied conditions (1,4-dioxane solution, 25°C). Reactivity of subsequent P-OH groups in phosphoric acid increases with increasing degree of substitution by -OCH₂CH₂OH groups. The ratio of the rate constants of formation of mono-, di-, and triesters of phosphoric acid is equal to 1/2/4. This has been attributed to the formation of internal hydrogen bonds, involving substituents and the P-OH groups. The observed order of the rate constants shows that reaction can not be stopped at the diester stage (linear units) and triester species (branched units) are formed fast. However, due to the large difference in the rate of hydrolysis, especially pronounced at basic conditions, triesters of phosphoric acid can easily be converted into the corresponding diesters by simple hydrolysis. Thus, the addition of diepoxides to phosphoric acid, followed by hydrolysis, leads to essentially linear polyphosphate chains.     

Surface tension modelling of liquid Cd–Sn–Zn alloys

The thermodynamic model in conjunction with Butler equation and the geometric models were used for the surface tension calculation of Cd–Sn–Zn liquid alloys. Good agreement was found between the experimental data for limiting binaries and model calculations performed with Butler model. In the case of ternary alloys, the surface tension variation with Cd content is better reproduced in the case of alloys lying on vertical sections defined by high Sn to Zn molar fraction ratio. The calculated surface tension is in relatively good agreement with the available experimental data. In addition, the surface segregation of liquid ternary Cd–Sn–Zn and constituent binaries has also been calculated.     

An application of the Fokker-Planck equation in stochastic reservoir theory

The distribution of the storage and of the outflow of a reservoir with a piecewise linear constant operating rule and Gaussian white-noise input is derived by analytically solving the Fokker-Planck equation. The proposed operating rule may approximate the well-known standard policy or, by increasing the number of intervals with constant outflow, may approximate the operating rule of existing reservoirs. The form of the solution renders possible the probabilistic analysis of the behavior of a water reservoir without numerical calculations.     

Imaging of nanostructures with sub-100?nm spatial resolution using a desktop EUV microscope

Laser-produced plasma sources of short-wavelength radiation offer an interesting alternative to synchrotron and free-electron laser installations. Recently, we reported on a newly developed desktop EUV microscope based on plasma generated from a gas-puff target and diffractive optics. The half-pitch resolution of the microscope approached 50?nm. Compared to analogous microscopes based on synchrotron sources, our system is compact and cost-effective. In this paper, we present the results of imaging experiments on a thin polycrystalline object that was carried out in order to further examine the applicability of the microscope. We have demonstrated here that EUV microscopy can provide structural information that cannot be accessed by conventional optical microscopy or SEM.