Comparative theoretical study of formaldehyde decomposition on PdZn, Cu, and Pd surfaces

Methanol steam reforming, catalyzed by Pd/ZnO (PdZn alloy), is a potential source of hydrogen for on-board fuel cells. CO has been reported to be a minor side product of methanol decomposition that occurs in parallel to methanol steam reforming on PdZn catalysts. However, fuel cells currently used in vehicles are very sensitive to CO poisoning. To contribute to the understanding of pertinent reaction mechanisms, we employed density functional slab model calculations to study the decomposition of formaldehyde, a key intermediate in methanol decomposition and steam reforming reactions, on planar surfaces of Pd, Cu, and PdZn as well as on a stepped surface of PdZn. The calculated activation energies indicate that dehydrogenation of formaldehyde is favorable on Pd(111), but unfavorable on Cu(111) and PdZn(111). On the stepped PdZn(221) surface, the dehydrogenation process was calculated to be more competitive to formaldehyde desorption than on PdZn(111). Thus, we ascribe the experimentally observed small amount of CO, formed during steam reforming of methanol on the Pd/ZnO catalyst, to occur at metallic Pd species of the catalyst or at defect sites of PdZn alloy.     

Razumikhin-type theorems on exponential stability of impulsive delay systems

^** Corresponding author. Email: xzliu{at}math.uwaterloo.ca This paper studies the exponential stability of impulsive delaysystems. By employing the Razumikhin technique and Lyapunovfunctions, several exponential stability criteria are establishedfor both linear and non-linear impulsive delay systems. Someexamples are also worked through to illustrate our results.     

Substructure mining using elaborate chemical representation

Substructure mining algorithms are important drug discovery tools since they can find substructures that affect physicochemical and biological properties. Current methods, however, only consider a part of all chemical information that is present within a data set of compounds. Therefore, the overall aim of our study was to enable more exhaustive data mining by designing methods that detect all substructures of any size, shape, and level of chemical detail. A means of chemical representation was developed that uses atomic hierarchies, thus enabling substructure mining to consider general and/or highly specific features. As a proof-of-concept, the efficient, multipurpose graph mining system Gaston learned substructures of any size and shape from a mutagenicity data set that was represented in this manner. From these substructures, we extracted a set of only six nonredundant, discriminative substructures that represent relevant biochemical knowledge. Our results demonstrate the individual and synergistic importance of elaborate chemical representation and mining for nonlinear substructures. We conclude that the combination of elaborate chemical representation and Gaston provides an excellent method for 2D substructure mining as this recipe systematically explores all substructures in different levels of chemical detail.     

Numerical performance of parallel group explicit solvers for the solution of fourth order elliptic equations

Many applications in applied mathematics and engineering involve numerical solutions of partial differential equations (PDEs). Various discretisation procedures such as the finite difference method result in a problem of solving large, sparse systems of linear equations. In this paper, a group iterative numerical scheme based on the rotated (skewed) five-point finite difference discretisation is proposed for the solution of a fourth order elliptic PDE which represents physical situations in fluid mechanics and elasticity. The rotated approximation formulas lead to schemes with lower computational complexities compared to the centred approximation formulas since the iterative procedure need only involve nodes on half of the total grid points in the solution domain. We describe the development of the parallel group iterative scheme on a cluster of distributed memory parallel computer using Message-Passing Interface (MPI) programming environment. A comparative study with another group iterative scheme derived from the centred difference formula is also presented. A detailed performance analysis of the parallel implementations of both group methods will be reported and discussed.     

General framework for testing Poisson‐Voronoi assumption for real microstructures

Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson‐Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single‐phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson‐Voronoi assumption based on images of two‐dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.     

Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.     

The impact of data collection on fill rate performance in the (R,s, Q) inventory model

In this paper we consider the determination of the reorder point s in an (R, s, Q) inventory model subject to a fill rate service level constraint. We assume that the underlying demand process is a compound renewal process. We then derive an approximation method to compute the reorder level such that a target service level is achieved. Restrictions on the input parameters are given, within which this method is applicable. Moreover, we will investigate the effects on the fill rate performance in case the underlying demand process is indeed a compound renewal process, while the demand process is modelled as a discrete-time demand process. That is, the time axis is divided in time units (for example, days) and demands per time unit are independent and identically distributed random variables. It will be shown that smooth and erratic behaviour of the inter-arrival times have different impacts on the performance of the fill rate when demand is modelled as a discrete-time process and in case the underlying demand process is a compound renewal process.     

Explicit congruences for the partition function modulo every prime

Let p(n) denote the number of unrestricted partitions of the positive integer n, and let m be a prime $\geq 13$. We prove, for k = 1, explicit congruences of the form where $r_{m,k}, \delta_{m,k}$ are integers depending on m and k and $\phi_{m,k}(z)$ are explicitly computable level one holomorphic modular forms of small weight. We also give theoretical and numerical support that the congruences also hold for k > 1. Our main idea is a level reduction result for the modular forms which originated from Atkin-Lehner. From our result, we deduce periodicity properties for the partition function with short periods which improve upon recent results of K. Ono. Received: 24 January 2002