非平稳φ-混合序列强律收敛速度的进一步探讨

本文研究非平稳φ 混合序列的强大数律：无需混合速度限制,给出了完全收敛成立的充要条件;在弱混合速度条件下,讨论了Ｍａｒｃｉｎｋｉｅｗｉｃｚ Ｚｙｇｍｕｎｄ强律成立的必要条件,进而得出混合情形的Ｍａｒｃｉｎｋｉｅｗｉｃｚ Ｚｙｇｍｕｎｄ强律,其结果与独立情形相一致．     

Threshold control by a single-server retrial queue with batch arrivals and group services

A controlled single-server retrial queueing system is investigated. Customers arrive according to batch Markovian arrival process. The system has several operation modes which are controlled by means of a threshold strategy. The stationary distribution is calculated. Optimization problem is considered and a numerical example is presented.     

Decay of Dissipative Equations and Negative Sobolev Spaces

We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.     

Molecular structure of paramagnetic <Emphasis Type="Italic">bis</Emphasis>-diisobutyl dithiophosphinate complexes of lanthanides(III) with 1,10-phenanthroline in solution by the data of NMR relaxation spectroscopy

NMR relaxation spectroscopy (RS) is used to examine the molecular structure of paramagnetic bis-diisobutyl dithiophosphinate complexes of lanthanides (by the example of europium and lutetium) with 1,10-phenanthroline in CDCl₃ solution. The results obtained are consistent with the results of studying the molecular structure of bis-diisobutyl dithiophosphinate complexes of yttrium with 1,10-phenanthroline in the crystalline phase by XRD.     

Solutions to a reduced Poisson-Nernst-Planck system and determination of reaction rates

We study a reduced Poisson-Nernst-Planck (PNP) system for a charged spherical solute immersed in a solvent with multiple ionic or molecular species that are electrostatically neutralized in the far field. Some of these species are assumed to be in equilibrium. The concentrations of such species are described by the Boltzmann distributions that are further linearized. Others are assumed to be reactive, meaning that their concentrations vanish when in contact with the charged solute. We present both semi-analytical solutions and numerical iterative solutions to the underlying reduced PNP system, and calculate the reaction rate for the reactive species. We give a rigorous analysis on the convergence of our simple iteration algorithm. Our numerical results show the strong dependence of the reaction rates of the reactive species on the magnitude of its far field concentration as well as on the ionic strength of all the chemical species. We also find non-monotonicity of electrostatic potential in certain parameter regimes. The results for the reactive system and those for the non-reactive system are compared to show the significant differences between the two cases. Our approach provides a means of solving a PNP system which in general does not have a closed-form solution even with a special geometrical symmetry. Our findings can also be used to test other numerical methods in large-scale computational modeling of electro-diffusion in biological systems.     

Influence of Cu substrate surface oxides and heating rates during reflow on melting point of Sn-3.5Ag solder

Three types of copper substrates, fresh, aged (kept for years in open atmosphere) and acid washed aged, were investigated for the reflow behaviour of a solder using different heating rates. Melting point of the Sn-3.5Ag solder was lowered on the aged Cu substrate. Reduction was found to be higher in high heating rate and declined with the decrease in the heating rate. Melting point was lowered from 221 °C to 175 °C with the heating rate of 180 °C/min, but recovered to 210 °C when aged Cu substrate was washed with sulphuric acid. XPS depth profile revealed the presence of Cu₂O up to the greater depth in the aged substrate compared to the fresh and acid washed aged substrates. Study showed the relation of reduction in melting point with the depth of Cu₂O on the surface of aged Cu substrates. It was proposed that lower dissipation of heat generated in high heating rates by the oxidation of the flux carbon during reduction of high Cu₂O amount in aged carbon was responsible for the variations in melting points.     

交叉许可还是合资研发——创新应用的边际收益率的视角

本文在考虑创新应用的边际收益率的情形下,建立了一个统一的分析框架,比较了交叉许可与合资研发两种合作创新组织模式下,企业的创新水平及收益,进而给出了两种合作创新组织模式的相对优劣。结果表明:当创新被用于开发同质产品时,合资方式效率更高;当创新被用于开发非竞争性产品时,应该选择交叉许可模式;而当创新被用于开发差异化产品时,合作创新的组织模式选择还与创新的产出弹性有关。     

Comparison of gas-phase mechanisms applied to RDX combustion model

Two detailed gas-phase chemical mechanisms for RDX – Yetter and coworkers, herein ‘Y2’ [K. Prasad, R.A. Yetter, M.D. Smooke, Combust. Sci. Technol. 124 (1997) p. 35.]; Cal. Tech. group, herein ‘CTM’ [(a) A.D. Chakraborty, R.P. Muller, S. Dasgupta, W.A. Goddard, III, J. Phys. Chem. A 104 (2000) 2261. (b) D. Chakraborty, R.P. Muller, S. Dasgupta, W.A. Goddard, III, J. Comput. Aided Mater. Des. 8 (2001) 203. (c) D. Chakraborty, R.P. Muller, S. Dasgupta, W.A. Goddard, III, Available from: http://www.wag.caltech.edu/home/rpm/projects/hedm/] – have been tested using a recently developed combustion model. The results are compared with each other and experimental data. Burning rates predicted using CTM are about 15% higher than Y2, but both compare well with experimental data across a wide pressure range. Also, majority species profiles are in reasonable agreement with data from a 0.5 atm pressure experiment. However, comparison of predicted trace species profiles to experiments indicates neither mechanism reproduces all measured trace species well; furthermore, most of these trace species occur along main reaction pathways. Detailed chemical analysis indicates the main initial RDX reaction is surprisingly very different for the two mechanisms. NO₂ scission dominates using Y2, but HONO elimination dominates using CTM, in spite of the NO₂ scission reaction having by far the largest RDX decomposition rate coefficient in each mechanism. Analysis shows the unexpected result using CTM is due to a curious global kinetics phenomenon arising in the product pathway: the ring-opening reaction, RDXR → RDXRO, where RDXR is the cyclic radical formed upon NO₂ scission, has a much smaller rate coefficient in CTM compared to Y2. This causes the reaction to be a bottleneck, and so the NO₂ scission reaction goes into partial equilibrium rather than being forwards. Tests were performed to see how the predicted burning rates would be affected by changes in some of the most sensitive rate parameters. Some of the key parameters leading to the differing predictions have been identified. These results will help guide future efforts to understand and develop an accurate representation of the actual RDX combustion chemistry.     

Analysis of reliability systems via Gini-type index

Different strategies of reliability theory for the analysis of coherent systems have been studied by various researchers. Here, the Gini-type index is utilized as an applicable tool for the study and comparison of the ageing properties of complex systems. A new stochastic order in terms of Gini-type index is introduced to compare the speed of ageing of components and systems. The parallel-series and series-parallel systems with shared components are studied by their corresponding Gini-type indexes. Also, the generalization of Gini-type index for the multidimensional case is discussed, and is used to compare components lifetimes properties in the presence of other dependent components. It is shown that the ageing properties of a component lifetime can differ when the other components are working or have already failed. Numerous illustrative examples are given for better intuition of Gini-type and generalized Gini-type indexes throughout the paper.     

Theoretical calculation of atomic spectrum for 1s23l4l′ states of beryllium-like ions

Using the saddle-point variation and saddle-point complex-rotation methods, energies, radiative, and Auger rates are calculated for the doubly-excited states 1s²3l4l′ of beryllium-like ions. The total wave function is expanded by the restricted variation method to saturate the functional space and improve the nonrelativistic energy. Relativistic corrections and mass polarization effects are taken into account by the first-order perturbation theory. The partial Auger rates for these states are studied. The calculated Auger electron energies are compared with the experimental results which are observed in high resolution electron spectroscopy. The total radiative rates and the total Auger rates for these doubly-excited states 1s²3l4l′ in the beryllium-like ions are also analyzed along with the increase of atomic number Z. Calculated results show that the total Auger rates are several orders of magnitude larger than the total radiative rates for these low-Z systems.