SOME BLENDING INTERPOLATION METHODS IN CAGD

Some of the blending interpolation methods (which) stated by a convex combination technique are presented. This includes C1 ,C2 blending triangular interpolanls and C1 -blending quadrilateral inter polanls for surfaces. The mentioned methods can be generalized to the construction of C" blending interpolants.     

Quantitative stability of variational systems: III.ε-approximate solutions

We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.     

Chemical diffusion of oxygen in tin dioxide: Effects of dopants and oxygen partial pressure

Tin dioxide SnO_2−δ is a pronounced n-type electron conductor due to its oxygen deficiency. This study investigates the rate of chemical diffusion of oxygen in SnO_2−δ single crystals, which is a crucial step in the overall stoichiometry change of the material. The chemical diffusion coefficient D^δ was determined from conductivity- and EPR-relaxation methods. The temperature dependence was found to be . The dependence on crystal orientation, dopant content and oxygen partial pressure was below experimental error. The latter observation leads to the conclusion that the chemical diffusion coefficient is close to the diffusion coefficient of oxygen vacancies. Along with the relaxation process resulting from the chemical diffusion of oxygen, additional processes were observed. One of these was attributed to complications in the defect chemistry of the material. The relevance of the results for the kinetics of drift processes of Taguchi sensors is discussed.     

Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service σ(θ_tω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes $\text{(T}{}_{\mathrm{n}}\text{, n ∈}\text{Z}\text{)[T}{}_{\mathrm{n}}\text{< T}{}_{\mathrm{n}}\text{+1, lim}{}_{\mathrm{\pm \infty }}\text{T}{}_{\mathrm{n}}\text{= ±∞]}$ such that

for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [T_n, T_n+1[ the demand of service accumulated during the proceding intervals [T_n?1, T_n[ and take a rest of fixed duration D.     

Photophysical processes and photochemical reactions involved in poly(N-vinylcarbazole) and in copolymers with carbazole units

This paper is devoted to the analysis of the photochemical behaviour of copolymers with carbazole units exposed to long-wavelength radiation. These copolymers are constituted of two types of carbazolylethyl methacrylate units (CEM) with octyl methacrylate moieties (OMA). The exposure of copolymers and PVK to UV light results in dramatic modifications of the physical and photophysical properties of the polymer. These modifications can be correlated with modifications of the chemical structure of the matrix. The photoageing of copolymers and PVK has been analysed by fluorescence, ESR, UV-vis and infrared spectroscopies. The effects of crosslinking and chain scissions were determined by gel fraction measurements and size exclusion chromatography.     

Shortcut method for evaluation and design of a hybrid process for enantioseparations

Hybrid processes for enantioseparations have a considerable potential for reducing investment and operational costs. An example is the combination of simulated moving bed (SMB) chromatography and selective crystallisation. However, the design of integrated processes is a difficult task. A shortcut method is presented that can serve as a tool for design and estimation of the potential of such processes. The approach requires only limited experimental data and thus allows for systematic parameter studies. The method is based on the determination of the purity-performance characteristic of the SMB process and rigorous application of mass balances. The use of relative mass fluxes allows derivation of simple algebraic expressions for essential process parameters. The significant potential of combining SMB and crystallisation is demonstrated for the example of the separation of mandelic acid enantiomers.     

The application of the concept of reaction layer to the study of electrode processes coupled with the second-order chemical reactions at microelectrodes under steady-state conditions

Under steady-state conditions, the current equations of the second-order EC, ECE and DISPI reactions at microdisk, microspherical and microring electrodes are derived with the aid of the concept of the reaction layer. The conditions under which these equations would be valid are also discussed. Using these equations, methods to determine the kinetic parameters for the second-order EC, ECE and DISPI reactions are presented. The reduction of 2,6-diphenyl-pyrylium cation and oxidation of triphenylamine were investigated as examples of the second-order EC and ECE reactions.     

Characterization of Autocatalytic Reactions in Modified Cellulose/NMMO Solutions by Thermal Analysis and UV/VIS Spectroscopy

The thermal stability of cellulose/N-methylmorpholine-N-oxide (NMMO) solutions were investigated using UV/VIS spectrometry with a temperature programming cuvette and caloric measurements by means of the Systag calorimeter RADEX (mini-autoclave). Both analytical methods allow to characterize the influences of stabilizers and additives. With the temporal course of the optical density, temperature and pressure thermal runaway reactions with gas evolution and accumulation of chromophoric degradation products were recognized. Kinetic model calculations compared with UV/VIS measurements demonstrate the existence of autocatalytic reactions in cellulose/NMMO solutions. Varying the heating rate autocatalysis can be proved by dynamic caloric measurements as well.     

Optimal dynamic advertising policies for hereditary processes

In this paper, the Nerlove-Arrow model of optimal dynamic advertising policies is generalized by assuming a general probability distribution of the forgetting time, rather than the exponential one. A control problem with integrodifferential equations of motion is defined for which the transitory and steady-state properties of the optimal advertising policy are examined. The effects of assumptions like IHR-distributions and DHR-distributions, the existence of an upper bound for the forgetting time, etc., are explained. It is shown that there are two (in the case of an exponential distribution even three) different current-value adjoint functions associated with the problem, and relations between the two (three) are established. Also provided is a sensitivity analysis.Thanks are due to G. Feichtinger and S. Jorgensen for useful discussions.     

Mechanism of silicon film deposition in the RF plasma reduction of silicon tetrachloride

Plasma-chemical reduction of SiCl₄ in mixtures with H₂ and Ar has been studied by optical emission spectroscopy (OES) and laser interferometry techniques. It has been found that the Ar:H₂ ratio strongly affects the plasma composition as well as the deposition (r _D) and etch (r _E) rates of Si: H, Cl films and that the electron impact dissociation is the most important channel for the production of SiCl_x species, which are the precursors of the film growth. Chemisorption of SiCl_x and the reactive surface reaction SiCl_x+H–SiCl_(x–1)0+HCl are important steps in the deposition process. The suggested deposition model givesr _D [SiCl_x][H], in agreement with the experimental data. Etching of Si: H, Cl films occurs at high Ar: H₂ ratio when Cl atoms in the gas phase become appreciable and increases with increasing Cl concentration. The etch rate is controlled by the Cl atom chemisorption step.