Advances in rapid and effective break-in/conditioning/recovery of automotive PEMFC stacks

Automotive proton exchange membrane fuel cell stacks need to meet manufacturer specified rated beginning-of-life (BOL) performance before being assembled into vehicles and shipped off to customers. The process of “breaking-in” of a freshly assembled stack is often referred to as “conditioning.” It has become an intensely researched area especially in automotive companies, where imminent commercialization of fuel cell electric vehicles (FCEVs) demands a short, energy- and cost-efficient, and practical conditioning protocol. Significant advances in reducing the conditioning time from 1 to 2 days to as low as 4h or less, in some cases without the use of additional inert gases such as nitrogen, and with minimal use of hydrogen, and specialized test stations will be discussed.     

Oxidation behaviour of uranium and neptunium in stabilised zirconia

Yttria stabilised zirconia (YSZ) based (Zr,Y,U)O_2−x and (Zr,Y,Np)O_2−x solid solutions with 6 and 20 mol% actinide were prepared with Y/Zr ratios ranging from 0.2 to 2.0 to investigate uranium and neptunium oxidation behaviour depending on the oxygen vacancies in the defect fluorite lattice. Sintering at 1600 °C in Ar/H₂ yields a cubic, fluorite-type structure with U(IV) and Np(IV). Annealing (Zr,Y,U)O_2−x with Y/Zr=0.2 at 800 °C in air results in a tetragonal phase, whereas (Zr,Y,U)O_2−x with higher Y/Zr ratios and (Zr,Y,Np)O_2−x retain the cubic structure. XANES and O/M measurements indicate mixed U(V)-U(VI) and Np(IV)-Np(V) oxidation states after oxidation. Based on X-ray diffraction, O/M and EXAFS measurements, different oxidation mechanisms are identified for U- and Np-doped stabilised zirconia. In contrast to U, excess oxygen vacancies are needed to oxidise Np in (Zr,Y,Np)O_2−x as the oxidation process competes with Zr for oxygen vacancies. As a consequence, U(VI) and Np(V) can only be obtained in stabilised zirconia with Y/Zr=1 but not in YSZ with Y/Zr=0.2.     

Comments on “Statistical reasoning with set-valued information: Ontic vs. epistemic view” by Inés Couso and Didier Dubois

I discuss some aspects of the distinction between ontic and epistemic views of sets as representation of imprecise or incomplete information. In particular, I consider its implications on imprecise probability representations: credal sets and sets of desirable gambles. It is emphasized that the interpretation of the same mathematical object can be different depending on the point of view from which this element is considered. In the case of a fuzzy information on a random variable, it is possible to define a possibility distribution on the simplex of probability distributions. I add some comments about the properties of this possibility distribution.     

Nd:YAG激光器光栅式扫描预处理的计算模拟与优化分析

 采用计算模拟的方法,研究了光栅式扫描预处理的扫描方式以及脉冲能量波动、定位误差对预处理效率的影响。研究发现,脉冲能量波动及其定位误差使预处理效率降低,同时其影响与扫描方式之间存在相互调制作用,因此可以通过选择合适的扫描方式以及扫描间隔来优化预处理流程,提高预处理效率。此外发现,光斑呈等边三角形排列时的预处理效率优于正方形。     

On the complexity of linear programming under finite precision arithmetic

In this paper we study the complexity of solving linear programs in finite precision arithmetic. This is the normal setup in scientific computation, as digital computers work in finite precision. We analyze two aspects of the complexity: one is the number of arithmetic operations required to solve the problem approximately, and the other is the working precision required to carry out some critical computations safely. We show how the conditioning of the problem instance affects the working precision required and the computational requirements of a classical logarithmic barrier algorithm to approximate the optimal value of the problem within a given tolerance. Our results show that these complexity measures depend linearly on the logarithm of a certain condition measure. We carry out the analysis by looking at how well Newton's Method can follow the central trajectory of the feasible set, and computing error bounds in terms of the condition measure. These results can be interpreted as a theoretical indication of good numerical behavior of the logarithmic barrier method, in the sense that a problem instance twice as hard as the other from the numerical point of view, requires only at most twice as much precision to be solved. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This research has been supported through grants from Fundación Andes, under agreement C12021/7, and FONDECYT (project number 1930948).     

On Finite and Strong Convergence of a Proximal Method for Equilibrium Problems

We introduce the notions of conditioning and well-posedness for equilibrium problems. Using these concepts, we obtain finite and strong convergence results for the proximal method that improve, develop, and unify several theorems in optimization and nonlinear analysis.     

Randomized Preprocessing of Homogeneous Linear Systems of Equations

Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the estimated solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our approach and extend it to solving nonsingular linear systems, inversion and generalized (Moore-Penrose) inversion of general and structured matrices by means of Newton’s iteration, approximation of a matrix by a nearby matrix that has a smaller rank or a smaller displacement rank, matrix eigen-solving, and root-finding for polynomial and secular equations and for polynomial systems of equations. Some by-products and extensions of our study can be of independent technical intersest, e.g., our extensions of the Sherman-Morrison-Woodbury formula for matrix inversion, our estimates for the condition number of randomized matrix products, and preprocessing via augmentation.     

Optimal conditioning in the convex class of rank two updates

Davidon's new quasi-Newton optimization algorithm selects the new inverse Hessian approximation at each step to be the optimally conditioned member of a certain one-parameter class of rank two updates to the last inverse Hessian approximationH. In this paper we show that virtually the same goals of conditioning can be achieved while restricting to the convex class of updates, which are bounded by the popular DFP and BFGS updates. This suggests the computational testing of alternatives to the optimal conditioning strategy.This research supported by NSF grant 73-03413, contract P04361 of the National Bureau of Economic Research, Cambridge, Massachusetts, and a National Science Foundation Graduate Fellowship, forms a portion of the author's doctoral thesis at Cornell University directed by Professor J.E. Dennis.     

Dempster's rule of combination

The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.