Variational representations of Varadhan functionals

Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational ``rate function" representation.

     

Simple theoretical analysis of the thermoelectric power in quantum dot superlattices of non-parabolic heavily doped semiconductors with graded interfaces under strong magnetic field

We study theoretically the thermoelectric power in the presence of a large magnetic field (TPM) in heavily doped III–V, II–VI, PbTe/PbSnTe, strained layer and HgTe/CdTe quantum dot superlattices (QDSLs) with graded structures on the basis of newly formulated electron energy spectra and compare the same with that of the constituent materials. It has been found, taking heavily doped GaAs/Ga_1−xAl_xAs, CdS/CdTe, PbTe/PbSnTe, InAs/GaSb and HgTe/CdTe QDSLs as examples, that the TPM increases with increasing inverse electron concentration and film thickness, respectively, in different oscillatory manners and the nature of oscillations is totally band structure dependent. We have also suggested the experimental methods of determining the Einstein relation for the diffusivity–mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws.     

The rollon–rolloff waste collection vehicle routing problem with time windows

This study introduces a rollon–rolloff waste collection vehicle routing problem involving large containers that accumulate huge amounts of garbage at construction sites and shopping districts. In this problem, tractors move one container at a time between customer locations, a depot, disposal facilities, and container storage yards. The complicated constraints discussed in this study arise from having multiple disposal facilities, multiple container storage yards, seven service types of customer demands, different time windows for customer demands and facilities, various types and sizes of containers, and the lunch break of tractor drivers. In addition, real-world issues, such as changing service types, multiple demands at a customer’s location, and tractors with different work schedules, are dealt with. This study proposes a large neighborhood search based iterative heuristic approach consisting of several algorithms for the problem. The effectiveness of the proposed methods is demonstrated by computational experiments using benchmark data, some instances of which are derived from real-world problems.     

A goodwill model with predatory advertising

We investigate the dynamic advertising policies of two competing firms in a duopolistic industry, assuming a predatory phenomenon between their advertising campaigns. The resulting model is a differential game which is not linear-quadratic. We show that there exists a Markovian Nash equilibrium, and that it leads to time constant advertising strategies. According to this model, predatory advertising produces a negative externality: the interference between the advertising campaigns decreases the total demand of the market.     

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation （LES） to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale （SGS） model can correctly predict Lagrangian time correlations （LTCs）. Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation （DNS） and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid;scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.     

Suppression of Q-switching instabilities in broadened-waveguide monolithic mode-locked laser diodes

It is predicted theoretically that broadening the optical confinement layer in monolithic mode-locked semiconductor lasers may suppress Q-switching instability, by increasing the carrier transport time, and lead to emission of shorter, more stable optical pulses.     

Combinatorial analysis of Tetris-like games

We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion.     

Large sets of Hamilton cycle and path decompositions

The existence spectrums for large sets of Hamilton cycle decompositions and Hamilton path decompositions are completed. Also, we show that the completion of large sets of directed Hamilton cycle decompositions and directed Hamilton path decompositions depends on the existence of certain special tuscan squares. Several conjectures about special tuscan squares are posed.     

A General Vehicle Routing Problem

In this paper, we study a rich vehicle routing problem incorporating various complexities found in real-life applications. The General Vehicle Routing Problem (GVRP) is a combined load acceptance and generalised vehicle routing problem. Among the real-life requirements are time window restrictions, a heterogeneous vehicle fleet with different travel times, travel costs and capacity, multi-dimensional capacity constraints, order/vehicle compatibility constraints, orders with multiple pickup, delivery and service locations, different start and end locations for vehicles, and route restrictions for vehicles. The GVRP is highly constrained and the search space is likely to contain many solutions such that it is impossible to go from one solution to another using a single neighbourhood structure. Therefore, we propose iterative improvement approaches based on the idea of changing the neighbourhood structure during the search.     

A parallel search game

We answer in negative a question of Gál and Miltersen [Proc 30th Int Coll Automata, Languages, and Programming (ICALP) 2003, pp. 332–344] about a combinatorial game arising in the study of time‐space trade‐offs for data structures. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005