Designing delivery districts for the vehicle routing problem with stochastic demands

This paper considers the problem of designing districts for vehicle routing problems with stochastic demands. In particular, demands are assumed to be uncertain at the time when the districts are made, and these are revealed only after the districting decisions are determined. Tabu search and multistart heuristics for this stochastic districting problem are developed and compared. Computational results show that tabu search is superior over multistart.     

Representation theorems for transfinite computability and definability

 We show how Kreisel's representation theorem for sets in the analytical hierarchy can be generalized to sets defined by positive induction and use this to estimate the complexity of constructions in the theory of domains with totality. Received: 21 January 1998 / Published online: 2 September 2002     

Hereditarily effective typestreams

We prove that the hierarchy of hereditarily effective typestreams, that are effective models of inductivly defined types, has the length of the first recursivly inaccessible ordinal. Received March 27, 1995     

Light charged particle emission and fission in238U+238U collisions at 1,740 MeV

Inclusive⁴He and⁴H energy spectra and heavy fragment coincidence correlations have been measured for reactions of 7.31 MeV/u²³⁸U with²³⁸U and^?197Au targets. The H/He production cross sections are in the range 15–26 mb, and their emission spectra are very similar for the two systems. The observed strong kinematic shifts with angle are reproduced in shape and magnitude by Monte Carlo simulations of particle evaporation from projectile-like and target-like fragments, indicating competition between charged particle emission and sequential fission. No evidence is found for high energy charged particle emission associated with ultra-highZ composite systems. Heavy fragment measurements indicate an abundance of quasielastic and deeply inelastic reaction fragments, as well as sequential fission of target and projectile nuclei. For²³⁸U nuclei, the fission occurs predominantly in an asymmetric mode, reminiscent of fission at low excitation energy. For²³⁸+²³⁸U reactions in the vicinity of the grazing angle, the frequency of single sequential fission (with survival of the partner fragment) is twice as large as double sequential fission in which both the target and projectile undergo fission. In²³⁸U+¹⁹⁷Au reactions, the survival probability of the heavy fragments is even greater. The surprisingly high survival probabilities of high-Z fragments imply a preponderance of very soft collisions in these very-heavy-ion reactions, at least at energies not very far over the Coulomb barrier.     

Spectral representations and density operators for infinite-dimensional homogeneous random fields

A theory of spectral representations and spectral density operators of infinite-dimensional homogeneous random fields is established. Some results concerning the form of the spectral representation are given in the general infinite-dimensional case, while the results pertaining to the density operator are confined to Hilbert space valued fields. The concept of a purely non-deterministic (p.n.d.) field is defined, and necessary and sufficient conditions for the property of p.n.d. are obtained in terms of the spectral density operator. The theory is developed using some isomorphisms induced by families of self-adjoint operators in the linear second order space associated with the field. The method seems to lead to more direct results also in the random process case, and it sheds new light on concepts such as multiplicity of the field and rank of the spectral density operator.     

Factorizing multivariate time series operators

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a₁B + … + a_pB^p) X(t) = [Π_i=1^p (I ? α_iB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a₁, a₂,…, a_p. In fact the number of possibilities is limited upwards by $\text{(np)!}\text{(n!)}{}^{\mathrm{p}}$, there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned.     

A multi-commodity flow formulation for the generalized pooling problem

The pooling problem is an extension of the minimum cost network flow problem where the composition of the flow depends on the sources from which it originates. At each source, the composition is known. In all other nodes, the proportion of any component is given as a weighted average of its proportions in entering flow streams. The weights in this average are simply the arc flow. At the terminals of the network, there are bounds on the relative content of the various components. Such problems have strong relevance in e.g. planning models for oil refining, and in gas transportation models with quality constraints at the reception side. Although the pooling problem has bilinear constraints, much progress in solving a class of instances to global optimality has recently been made. Most of the approaches are however restricted to networks where all directed paths have length at most three, which means that there is no connection between pools. In this work, we generalize one of the most successful formulations of the pooling problem, and propose a multi-commodity flow formulation that makes no assumptions on the network topology. We prove that our formulation has stronger linear relaxation than previously suggested formulations, and demonstrate experimentally that it enables faster computation of the global optimum.     

First Synthesis of Continuous Mesoporous Copper Films with Uniformly Sized Pores by Electrochemical Soft Templating

Although mesoporous metals have been synthesized by electrochemical methods, the possible compositions have been limited to noble metals (e.g., palladium, platinum, gold) and their alloys. Herein we describe the first fabrication of continuously mesoporous Cu films using polymeric micelles as soft templates to control the growth of Cu under sophisticated electrochemical conditions. Uniformly sized mesopores are evenly distributed over the entire film, and the pore walls are composed of highly crystalized Cu.     

The Koszul dual of a weakly Koszul module

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.     

Ion-neutral reactions in the ion source of a mixture of CO2/CH3OH, CO2/C2H5OH, and CO2/2-C3H7OH by packed capillary supercritical fluid chromatography-mass spectrometry (SFC-MS)

Ion neutral reactions in the gas phase in mixtures of ROH/CO(2), R = CH(3), C(2)H(5), and 2-C(3)H(7) were studied by supercritical fluid chromatography-mass spectrometry (SFC-MS). Three main reaction series were found for this system; ionization followed by alpha-cleavage, formation of clusters, and formation of protonated dialkyl ethers from the corresponding alcohol. The ion chemistries were similar for the three alcohols, but that of 2-propanol was somewhat more complex.