Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

Current distribution on a three-dimensional,bond-diluted,random-resistor network at the percolation threshold

Current and logarithm-current distributions on a three-dimensional random-bond percolation cubic network were studied at the percolation threshold by computer simulations. Predictions of a hierarchical model that combine fractal structure and randomness agree with our numerical simulations. In the thermodynamic limit the logarithm-current distribution exhibits ann(ln(i))i ^1/3 dependence below some characteristic currenti _c. This distribution may scale with lni/lnL, but the data are insufficient to make this a definite conclusion. Due to the small range of lnL considered, a study of the moments does not reveal this behavior and a study of the distribution itself is required.     

Stabilizing an uncertain production system

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp _ki . Requests arrive for parts, one at a time. With probability _i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.     

Prophet inequalities for parallel processes

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {X_{i, j}, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then

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and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.     

The Smoluchowski limit for a simple mechanical model

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D ^1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.     

贮氢合金材料电化学与表面性能的研究进展

贮氢合金材料电化学与表面性能的研究进展①杨勇李骏林祖赓（厦门大学化学系，固体表面物理化学国家重点实验室，厦门３６１００５）八十年代后期以来，人们对地球的环境保护提出了更高的要求，而便携式电器（如移动电话，摄像机与笔记本电脑等）对电池的需求也大量增加...     

Improvement of basic performances of a nickel-metal hydride battery

To develop a sealed-type nickel-metal hydride battery for use in portable equipment or in electric vehicles, investigations were conducted on negative electrodes using AB₅-type hydrogen storage alloy and positive electrodes. For the cycle life performance of the battery, alkaline treatment of the alloy and the substitution of more than 50% to the alloy with Co were effective. For the positive electrode, zinc as a solid solution in the nickel positive electrode obviously prevented γ-NiOOH from being formed in the charging process of β-Ni(OH)₂ and suppressed the migration of the electrolyte solution in the separator to the active material of the positive electrode. Also, hydrophobic treatment of the surface of the alloy was effective to prevent the elevation of the battery internal pressure of the battery in high rate charge.     

Hydrogen cycling induced diffraction peak broadening in C14 and C15 Laves phases

The diffraction peak broadening induced by hydrogen absorption-desorption cycling has been analyzed in four different Laves phase compounds with the C14 and C15 structures. The broadening is due to strain most probably originating from dislocations generated at the interface between the α and β hydride phases in connection with the cell volume difference between the two phases. It has been shown that it is strongly compound dependent. In the case of the C14 structure, the broadening is large and isotropic, and the latter can be related to the isotropy of the elastic constants of the metallic phase. The broadening is less for the compounds with the C15 structure, which can be related to a possibly softer lattice. Better ageing properties after long-term cycling are predicted for this crystal structure.     

Development of a new analytical method for the evaluation of hazards from slow decomposition of waste streams and process solutions

A wide variety of liquid streams are generated as part of the process research and development effort. Frequently these streams are drummed off, either as intermediates that must be held for processing or as wastes that must be sent off-site for disposal. Because of the long times and low concentrations often involved, current thermoanalytical techniques were inadequate to detect the potential of streams to generate gas. A custom-made apparatus, the gas evolution test cell (GETC), was developed in the Merck Research Laboratories to measure the gas generation potential of various streams under precisely defined conditions, is the key innovation for the development of a quantitative gas-generation test method.