Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

双冠醚研究(Ⅳ)——Schiff碱型和仲胺型双-(苯并15冠-5)对碱金属苦味酸盐的萃取行为

仲胺型双冠醚与四苯硼酸碱金属盐在丙酮溶液中。25℃下的电导说明它们与Na~+可能形成1∶1络合物(冠醚单元∶金属离子),而与K~+、Rb~+、Cs~+离子则形成2∶1络合物。用Schlff碱型和仲胺型双-(苯并15-冠-5)在水-氯仿体系中进行萃取,测量了分配比D和萃取平衡常数K,发现后者的K值均大于前者。双冠醚F_2对K~+的萃取能力最强,选择性最佳。     

一阶导数分光光度法测定血中一氧化碳含量的研究

本文通过理论推导及实验证明CO饱和血与正常血一阶导数的振幅高度比为一常数。将CO中毒检血氨稀释液取一半通CO至饱和,与另一半分别加入Na_2S_2O_4后在500～600nm测定一阶导数光谱在579nm处量出振幅值经计算可得CO在血中含量。     

A Kinetic Evidence for the Nitroxyl Radicals Recycling Mechanism in the Photostabilizing Process of HALS

The photoinduced bulk polymerization of a reactive-hindered amine fight stabilizers(r-HALS), 4-acryloyl-2, 2, 6, 6-tetramethylpiperidinyl (ATMP), was performed at 80℃ by using a DPC technique. An unique periodic exponential attenuation-type oscillating curve was found when the polymerization was carried out in air, but this phenomenon was not found in nitrogen.It is supposed that this unique kinetic performance may be attributed to nitroxyl radicals that are produced in situ from the oxidation of ATMP. ATMP polymer with narrow polydispersity (d =1.03) can be obtained by photoinduced solution polymerization of ATMP. The signal detected in ESR may be assigned to the nitroxyl radicals in the matrix of ATMP polymer. Since this kind of recycling of nitroxyl radicals is well documented for the photostabilizing mechanism of HALS, the present results may serve as a kinetic evidence for this mechanism.     

Syntheses of TiO2(B) nanowires and TiO2 anatase nanowires by hydrothermal and post-heat treatments

TiO₂(B) nanowires and TiO₂ anatase nanowires were synthesized by the hydrothermal processing in 10 M NaOH aq. at 150 °C followed by the post-heat treatment at 300-800 °C. As-synthesized Na-free titanate nanowires (prepared by the hydrothermal treatment and repeated ion exchanging by HCl (aq.) were transformed into TiO₂(B) structure with maintaining 1-D morphology at 300-500 °C, and further transformed into anatase structure at 600-800 °C with keeping 1-D shape. At 900 °C, they transformed into rod-shaped rutile grains. Microstructure of these 1-D TiO₂ nanomaterials is reported.     

High purity gadolinium by the electrolysis of GdF3

The anodic overvoltage on carbon and platinum electrodes in the electrochemical production of high purity gadolinium from molten 75 LiF-25 mol% GdF₃ solutions is discussed. At the cell temperature of 840°C calciumimpregnated anodes led to the reduction of inert electrode films and to a current yield of nearly 100%.The deposited gadolinium contained 75, 22, 54 and less than 100 ppm of the interstitial elements H, N, O and C respectively; the concentrations of the highest other analysed impurities were: Si (89), Fe (15), Y (5), Zr (3), Nd (3), Tb (71), Ta (49), W (23) and Re (<3 ppm).Partly performed at the Ames Laboratory—U.S. Department of Energy.