Network flows and non-guillotine cutting patterns

Up till now there has been no exact and effective algorithm for the problem of finding optimal cutting patterns of rectangles which are not restricted to those with the ‘guillotine’ property. This problem can be interpreted in a resource constrained scheduling context. The contribution of this paper to this topic is a good characterization of the flow functions and graphs corresponding to cutting patterns.     

Zero-sum games with incompletely defined payoff

It is shown that a saddle-point solution exists in a two-person, zero-sum game whose payoff is given by a matrix which is not completely defined. On the other hand, we show that such games do not always have a value, so that a saddle-point solution is not necessarily an optimal solution.This work was supported by the Centre d'Etudes Atomiques, Saclay, France.     

Mixed halide complexes of lead. A comparison with theoretical predictions

Experimentally and theoretically derived formation constants of mixed lead halide complexes are compared at 25.0°C and one molar ionic strength. The formation constant of PbBrCl, ₁₁=79±10, is somewhat larger than the theoretical results, ₁₁=55, predicted using the formation constants of PbBr₂ and PbCl₂. The molar absorptivity of PbBrCl was observed to be intermediate in character between the molar absorptivities of PbBr₂ and PbCl₂. Determinations of the formation constants of PbBr₂Cl^– and PbBrCl₂ ^– are in reasonable agreement with the predictions based on the formation constants of PbBr₃ ^– and PbCl₃ ^–. Mixed ligand species dominated the complexation scheme of Pb(II) in our test media.     

Kinetic and NMR spectroscopic studies of chiral mixed sodium/lithium amides used for the deprotonation of cyclohexene oxide

The mixed-metal complex formed from n-butylsodium, n-butyllithium, and a chiral amino ether has been studied by NMR spectroscopy. Three different mixed-metal amides were used as chiral bases for the deprotonation of cyclohexene oxide. The selectivity and initial rate of reaction were compared for sodium-amido ethers, lithium-amido ethers, and mixtures of sodium and lithiumamido ethers in diethyl ether and tetrahydrofuran, respectively. The mixed sodium/lithium amides are more reactive than the single sodium and lithium amides, whereas the stereoselectivities are higher when lithium amides are used. The alkali-metal/gamma-amido ethers exhibit both higher initial reaction rates and stereoselectivities than their beta-amido ether analogues. NMR spectroscopic studies of mixtures of n-butylsodium (nBuNa), n-butyllithium (nBuLi), and the gamma-amino ethers in diethyl ether show the exclusive formation of dimeric mixed-metal amides. In diethyl ether, the lithium atom of the mixed-metal amide is internally coordinated and the sodium atom is exposed to solvent; however, in tetrahydrofuran, both metals are internally coordinated.     

多孔介质中两相不可压缩可混溶驱动问题的动态混合元方法及其特征修正格式

许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、边界层等, 其位置随时间而变动.多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性 的"局部化现象"问题,其数学模型为耦合非线性偏微分方程组的初边值问题.为减轻数 值解在局部前沿位置的数值振荡,提高解的精确性,本文给出了该问题的动态混合元格 式和沿特征线修正的动态混合元格式,证明了其收敛性,并给出了误差估计.