Applying Stochastic Algorithms to a Locomotive Scheduling Problem

This paper addresses a problem common to all railway networks. Given a fixed train timetable and locomotives (or other forms of traction) of various types, each train must be allocated a locomotive. This paper examines the use of stochastic algorithms for such a problem. Two types of algorithm are used—a simple ‘local improvement’ method, performed successively from randomly chosen starting points, and a ‘simulated annealing’ approach. Both are found to give considerably better results than a deterministic method in current use, and the annealing approach is probably the better stochastic method.     

Dissociative excitation cross sections of the lead atom in collisions between electrons and PbI2 molecules

Dissociative excitation of the lead atom in e-PbI₂ collisions has been studied experimentally. 27 excitation cross sections were measured for an energy of the exciting electrons equal to 100 eV. Nine optical excitation functions were recorded with variation of the electron energy in the range 0–100 eV. The most probable reaction channels for low electron energies are discussed, as well as the ratio of the dissociative excitation cross sections for the lead atom in e-PbI₂ and e-PbCl₂ collisions. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 6, pp. 701–706, November–December, 2006.     

Relativistic shift of the linear Zeeman effect

The efficiency with which a magnetic field acts on sublevels of the first and second doublets of a hydrogen-like atom is shown to vary because of relativistic effects by a factor of 1 ? 2γ(l + 1)/(2l + 3) and 1 ? 2γl/(2l ? 1), respectively, where γ is the ratio of the electron binding energy to the rest energy and l is the quantum number of the orbital angular momentum.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

The application of a vehicle routing model to a waste-collection problem: two case studies

In this paper we suggest a unique model for estimating the operating cost of each of three waste-collection systems. Under the traditional system, which is widely used, waste is typically collected in plastic bags and a three-man crew is needed on each vehicle. The other two systems require a one-man crew for vehicle collecting street containers. The side-loader system with fixed body automatically empties street containers into the vehicle body and empties the load at the disposal site. The side-loader system with demountable body allows the separation of the waste collection phase from transport to the disposal site, since the vehicle body can be demounted. We also present two case studies and show how the estimation of operating costs is a critical issue in decisions regarding the type of system to be used for waste collection.     

The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis

In this paper necessary and sufficient conditions of null-controllability and approximate null-controllability are obtained for the wave equation on a half-axis. Controls solving these problems are found explicitly. Moreover, bang-bang controls solving the approximate null-controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band (−a,a) for this equation and the Markov power moment problem.     

Characterization and Computation of Canonical Tight Windows for Gabor Frames

Let (\gnm)_{n,m ? \Zst}(\gnm)_{n,m\in\Zst} be a Gabor frame for \LtR\LtR for given window gg. We show that the window \ho = \SQI g\ho=\SQI g that generates the canonically associated tight Gabor frame minimizes ||g-h||\|g-h\| among all windows hh generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in each domain the canonical \ho\ho is expressed using functional calculus for Gabor frame operators. Furthermore, we derive a Wiener--Levy type theorem for rationally oversampled Gabor frames. Finally, a Newton-type method for a fast numerical calculation of \ho\ho is presented. We analyze the convergence behavior of this method and demonstrate the efficiency of the proposed algorithm by some numerical examples.     

A simple electronic speckle shearing interferometer

A new speckle shearing interferometer with simple setup is proposed. The interferometer can be converted easily from a speckle referenced speckle pattern interferometer into a speckle shearing interferometer and vice versa. A beamsplitter and a mirror are used to generate the shear. The amount of shear can be adjusted by simply rotating the mirror. The costs involved are low and it is particularly useful for fast inspection in non-destructive testing of structural integrity. Both the theoretical studies of the method of measurement and the experimental results are presented.