An adaptive large neighborhood search heuristic for the Pollution-Routing Problem

The Pollution-Routing Problem (PRP) is a recently introduced extension of the classical Vehicle Routing Problem with Time Windows which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment so as to minimize a function comprising fuel, emission and driver costs. This paper presents an adaptive large neighborhood search for the PRP. Results of extensive computational experimentation confirm the efficiency of the algorithm.     

On classification of four-dimensional nilpotent Leibniz algebras

Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Heterograft copolymers via double click reactions using one‐pot technique

The double click reactions (Cu catalyzed Huisgen and Diels–Alder reactions) were used as a new strategy for the preparation of well‐defined heterograft copolymers in one‐pot technique. The synthetic strategy to the various stages of this work is outlined: (i) preparing random copolymers of styrene (St) and p‐chloromethylstyrene (CMS) (which is a functionalizable monomer) via nitroxide mediated radical polymerization (NMP); (ii) attachment of anthracene functionality to the preformed copolymer by the o‐etherification procedure and then conversion of the remaining ? CH₂Cl into azide functionality; (iii) by using double click reactions in one‐pot technique, maleimide end‐functionalized poly(methyl methacrylate) (PMMA‐MI) via atom transfer radical polymerization (ATRP) of MMA and alkyne end‐functionalized poly (ethylene glycol) (PEG‐alkyne) were introduced onto the copolymer bearing pendant anthryl and azide moieties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6969–6977, 2008     

The bi-objective Pollution-Routing Problem

The bi-objective Pollution-Routing Problem is an extension of the Pollution-Routing Problem (PRP) which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment. The two objective functions pertaining to minimization of fuel consumption and driving time are conflicting and are thus considered separately. This paper presents an adaptive large neighborhood search algorithm (ALNS), combined with a speed optimization procedure, to solve the bi-objective PRP. Using the ALNS as the search engine, four a posteriori methods, namely the weighting method, the weighting method with normalization, the epsilon-constraint method and a new hybrid method (HM), are tested using a scalarization of the two objective functions. The HM combines adaptive weighting with the epsilon-constraint method. To evaluate the effectiveness of the algorithm, new sets of instances based on real geographic data are generated, and a library of bi-criteria PRP instances is compiled. Results of extensive computational experiments with the four methods are presented and compared with one another by means of the hypervolume and epsilon indicators. The results show that HM is highly effective in finding good-quality non-dominated solutions on PRP instances with 100 nodes.     

Monotonicity of input-output mappings in inverse coefficient and source problems for parabolic equations

This article presents a mathematical analysis of input-output mappings in inverse coefficient and source problems for the linear parabolic equation ut=(kx(x)ux)+F(x,t), (x,t)∈ΩT:=(0,1)×(0,T]. The most experimentally feasible boundary measured data, the Neumann output (flux) data f(t):=−k(0)ux(0,t), is used at the boundary x=0. For each inverse problems structure of the input-output mappings is analyzed based on maximum principle and corresponding adjoint problems. Derived integral identities between the solutions of forward problems and corresponding adjoint problems, permit one to prove the monotonicity and invertibility of the input-output mappings. Some numerical applications are presented.     

Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

A rigorous solution is presented for the problem of diffraction of plane harmonic sound waves by a cavity formed by a terminated rigid cylindrical waveguide of finite length whose interior surface is lined by an acoustically absorbent material. The solution is obtained by a modification of the Wiener-Hopf technique and involve an infinite series of unknowns, which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.Received: December 12, 2001     

Coerciveness of the discontinuous initial-boundary value problem for parabolic equations

In this paper, the mixed problem for parabolic equations is investigated with the discontinuous coefficient at the highest derivative and with nonstandard boundary conditions. Namely, the boundary conditions contain values of the solution not only on the boundary points, but also on the inner points of the considered domain as well. Moreover, abstract functionals are involved in the boundary conditions. We single out a class of functional spaces in which coercive solvability occurs for the investigated problem.     

Curvature and closed trapped surfaces in 4-dimensional space-times

The way a spacelike surfaceH sits in a 4-dimensional space-timeM may be measured by the average null curvature function _H and the shape function _H ofH. Relations between the shape function _H of a spaceiike surfaceH and curvature of a 4-dimensional space-time obeying the Einstein equation are investigated. Some relations between the shape functions of compact spacelike surfaces and infinite curvature are obtained and discussed. Assuming some curvature conditions, some results concerning the evolution of closed trapped surfaces from a restricted type of marginally trapped surfaces diffeomorphic toS ² are obtained.Based on Chapter 4 of the author's Ph.D. thesis.     

Measurement of angular dependencies of M X-ray differential cross sections and production cross sections using 5.96 keV photons

The differential cross sections of the emission of M-shell fluorescence X-rays from Tl and Pb have been measured by 5.96 keV photons at seven angles ranging from 50° to 110°. The differential cross section is found to decrease with the increasing emission angle, showing an anisotropic spatial distribution of M-shell fluorescence X-rays. Furthermore, M-shell fluorescence cross sections and the average fluorescence yields were measured for Pt, Au, Hg, Tl, Pb, Bi, Th, and U at an excitation energy of 5.96 keV using a Si(Li) detector. The experimental results of the total M X-ray fluorescence cross sections and M-shell fluorescence yields were compared with the theoretical values.This revised version was published online in November 2005 with corrections to the Cover Date.