高阶奇性常微分方程的边值问题（Ⅰ）──—非退化情形

本文对高阶奇性常微分方程的非退化边值问题建立了非共轭性存在定理和上、下解型存在定理．     

Air-exposure effect on the resistivity of thin bismuth films

A survey of previous studies on vacuum deposited metal films shows that in high frequency measurements, explicit reference to the effect of air-exposure is not made. The present work on bismuth films (in-situ and air-exposed) at dc and rf frequencies, carried out mainly to study the air-exposure effect, shows that in-situ dc and rf and exposed rf all show nearly the same resistivity for thick continuous films. But air-exposed dc film resistances, when compared to in-situ dc resistances, show that the grain boundary reflection coefficient, R _gin Mayadas-Shatzkes model changes from 0·2 to 0·6. This is shown to be due to the grain boundary oxidation. The result is substantiated by rf measurements.     

A geometric method in nonlinear programming

A differential geometric approach to the constrained function maximization problem is presented. The continuous analogue of the Newton-Raphson method due to Branin for solving a system of nonlinear equations is extended to the case where the system is under-determined. The method is combined with the continuous analogue of the gradient-projection method to obtain a constrained maximization method with enforced constraint restoration. Detailed analysis of the global behavior of both methods is provided. It is shown that the conjugate-gradient algorithm can take advantage of the sparse structure of the problem in the computation of a vector field, which constitutes the main computational task in the methods.This is part of a paper issued as Stanford University, Computer Science Department Report No. STAN-CS-77-643 (Ref. 45), which was presented at the Gatlinburg VII Conference, Asilomar, California, 1977. This work was supported in part by NSF Grant No. NAT BUR OF ECON RES/PO No. 4369 and by Department of Energy Contract No. EY-76-C-02-0016.The main part of this work was presented at the Japan-France Seminar on Functional Analysis and Numerical Analysis, Tokyo, Japan, 1976. The paper was prepared in part while the author was a visitor at the Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 1976–77, and was completed while he was a visitor at the Computer Science Department, Stanford University, Stanford, California, 1977. He acknowledges the hospitality and stimulating environment provided by Professor G. H. Golub, Stanford University, and Professors N. J. Rose and C. D. Meyer, North Carolina State University.     

Preconcentration of samples in sandwich tanks for continuous thin-layer chromatography

It is demonstrated that horizontai sandwich tank with two cover plates can be used to preconcentrate sample solutions. Narrow sharply-defined starting zones are obtained just outside the smaller cover plate when the series of spots of the sample solution are applied on the thin layer and predeveloped with a volatile solvent. After evaporation of the solvent, the whole area of the TLC-plate is covered with two plates and developed with a suitable solvent.     

Limit distributions and one-parameter groups of linear operators on Banach spaces

Let = {U_t: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set (X) of all probability measures on X. By (Q; ) we denote the class of all limit measures of {U_tn(μ₁ * μ₂*…*μ_n)*δ_xn}, where {μ_n}Q, {x_n}X and measures U_tnμ_j (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes L_m( ) as follows: L₀( )= ( (X); ), L_m( )= (L_m−1( ); ) for m=1, 2,… and L_∞( )=_m=0^∞L_m( ). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from L_m( ), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators.     

Photodynamic Therapy for Cancer Cells Using a Flash Wave Light Xenon Lamp

We determined photodynamic therapy (PDT) efficacy using a flash wave (FW) and a continuous wave (CW) light, of which the fluence rate was 70 W/cm², for murine thymic lymphoma cells (EL-4) cultivated in vitro. The irradiation frequency and the pulse width of the FW light were in the range of 1–32 Hz and less than one millisecond, respectively. 5-Aminolevulinic acid-induced protoporphyrin IX (ALA-PpIX) was used as a photosensitizer. When EL-4 with ALA administration was irradiated by the light for 4 h (irradiation fluence: 1.0J/cm²), the survival rate of EL-4 by the FW light was lower than that by the CW light, except for the FW light with irradiation frequency of 32 Hz, and decreased gradually with decreasing irradiation frequency. Moreover, the FW light, especially at lower irradiation frequency, was superior to the CW light for the generation of singlet oxygen in an aqueous PpIX solution. Therefore, thehigher PDT efficacy for EL-4 of the FW light would be caused by the greater generation of singlet oxygen in the cells.     

Formation of Si-nanoparticles in a microwave reactor: Comparison between experiments and modelling

The formation and growth of silicon-nanoparticles from silane in a microwave reactor was investigated. Experiments were performed for the following conditions: precursor concentration 380–2530 ppm, pressures of 20–30 mbar, microwave powers 120–300 W. The formed particles were examined in-situ with a particle mass spectrometer. Additionally, particles were collected on grids and analyzed by transmission electron microscopy, X-ray diffraction, and by determining the specific surface area by BET. The particle size was found to be in the range of 5–8 nm in diameter. A simple model was used to simulate the particle formation processes taking place inside the reactor. The microwave energy coupled into the reactor flow was treated as a spatially distributed energy source resulting in a local temperature increase. The particles were assumed to have a monodisperse size distribution. To allow an approximation of their shape they were characterized by their volume and surface area. The model takes nucleation, convection, coagulation, and coalescence into account. The fluid flow inside the microwave reactor was simulated with the commercial CFD-code Fluent.     

An Example of Embedded Singular Continuous Spectrum for One-Dimensional Schrödinger Operators

We present a new example of a potential such that the corresponding Schrödinger operator in the halfaxis has singular continuous spectrum embedded in the absolutely continuous spectrum. The singular part is supported in an essentialy dense set. This generalizes a result of C. Remling [3].Mathematics Subject Classification: 34L40, 81Q10.     

The reactions of perfluorinated α- and β-alkoxyradicals with hydrogen chloride, chlorine and fluorine

The kinetics of the reactions of the macroradicals R_f′OCF₂ (I) and R_f′OCF₂CF₂ (II) with HCl, Cl₂ and F₂ have been studied in the liquid phase, being R_f′ a poly(oxydifluoromethylene-oxytetrafluoroethylene) chain with average molecular weight of about 10⁴ Da. Radical (I) showed a higher reactivity compared to radical (II) with all the three radical transfer agents.In case of HCl the activation energy for the reaction:

     

On lineability of sets of continuous functions

We study the existence of vector spaces of dimension at least two of continuous functions on (subsets of) , every non-zero element of which admits one and only one absolute maximum.