On an inverse problem in mixture failure rates modelling

Mixtures of decreasing failure rate (DFR) distributions are always DFR. It turns out that very often mixtures of increasing failure rate distributions can decrease or show even more complicated patterns of dependence on time. For studying this and other relevant effects two simple models of mixing with additive and multiplicative failure rates are considered. It is shown that for these models an inverse problem can be solved, which means that given an arbitrary shape of the mixture failure rate and a mixing distribution, the failure rate for a governing distribution can be uniquely obtained. Some examples are considered where this operation can be performed explicitly. Possible generalizations are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Graph-like compacta: Characterizations and Eulerian loops

A compact graph-like space is a triple $\left(X,V,E\right)$, where $X$ is a compact, metrizable space, $V\subseteq X$ is a closed zero-dimensional subset, and $E$ is an index set such that $X⧹V\cong \text{◂+▸}E\times \left(0,1\right)$. New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

A point process approach to inventory models

The aim of the present paper is to make use of the modern theory of point processes to study optimal solutions for single‐item inventory. Demand for goods is assumed to occur according to a compound Poisson process and production occurs continuously and deterministically between times of demand, such that the inventory evolves according to a Markov process in continuous time. The aim is to propose a way of finding optimal production schemes by minimizing a certain expected loss over some finite period. There are holding/production costs depending on the stock level, and random penalty amounts will occur due to excess demand which is assumed backlogged. For simplicity we will not incorporate fixed costs. We give some numerical illustrations. Copyright © 2000 John Wiley & Sons, Ltd.     

Polymerization and polymers of silicic acid

Linear relationships among molecular weight, polymerization time, and gelation for the condensation of any monomer, including those of unknown size and functionality, are developed and applied to data on soluble silicic acids generated from tetraethyl silicate and from sodium silicate. The results suggest the formation of monomers containing ca. 12–15 ? OSi units with functionality of ca. 2.05 that condense with a rate constant of ca. 10^?4 liter/mole sec and an activation energy of 40–70 kJ/mole. One model compatible with these characteristics and the stoichiometry involved is a ladder polymer ca. 3 ? SiO units wide. Polymer isolation was achieved by replacing residual ? OH with (CH₃)₃Sio? , as well as by freezing of of aqueous solutions, which yielded fibers under special conditions. Solutions of the uncapped and capped polymers and melts of the latter had low viscosity even for fractions with M?_n ～100,000. This implies a coiled or globular nature for the polymers, which is supported by their limited propensity for film and fiber formation. Attemps to improve this situation by copolymerization, the use of other capping agents, and by the polymerization of precapped monomers were unsuccessful.     

Elektronische effekte in cyclopentadienyl-chrom-komplexen,die mehrere akzeptorliganden enthalten

The coordinative properties of the acceptor ligand CS are discussed on the basis of the new thiocarbonyl complexes CpCr(CO)(CS)(NO) (I), [CpCr(CS)(NO)₂]PF₆ (II), CpCr(CS)(L)(NO) (L = pyridine (III) or trimethylphosphane (IV) and related carbonyl complexes. The IR and NMR spectra (¹H, ¹³C, ³¹P) of the complexes indicate ligand—ligand interactions between CS and both the nitrosyl group and the cyclopentadienyl ring. An attempt is made to compare CS with other sulphur-containing acceptor ligands such as NS (in CpCr(CO)₂(NS)) and CS₂ (in CpCr(CS₂)(PMe₃)(NO)).     

Analysis and discretization of an optimal control problem for the time-periodic MHD equations

We consider the mathematical formulation and analysis of an optimal control problem associated with the tracking of the velocity and the magnetic field of a viscous, incompressible, electrically conducting fluid in a bounded two-dimensional domain through the adjustment of distributed controls. Existence of optimal solutions is proved and first-order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls. Semidiscrete-in-time approximations are defined and their convergence to the exact optimal solutions is shown.     

Planning and approximation models for delivery route based services with price-sensitive demands

Classical vehicle routing problems typically do not consider the impact of delivery price on the demand for delivery services. Existing models seek the minimum sum of tour lengths in order to serve the demands of a given set of customers. This paper proposes approximation models to estimate the impacts of price on delivery services when demand for delivery service is price dependent. Such models can serve as useful tools in the planning phase for delivery service providers and can assist in understanding the economics of delivery services. These models seek to maximize profit from delivery service, where price determines demand for deliveries as well as the total revenue generated by satisfying demand. We consider a variant of the model in which each customer’s delivery volume is price sensitive, as well as the case in which customer delivery volumes are fixed, but the total number of customers who select the delivery service provider is price sensitive. A third model variant allows the delivery service provider to select a subset of delivery requests at the offered price in order to maximize profit.