Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.     

A CLASS OF NEW NONCONFORMING FINITE ELEMENTS

A class of new nine-parameter nonconforming finite elements with convergent prop-erties are constructed in terms of the approach of interpolation methods in this paper. All of those finite elements can be viewed as the generalization of Zienkiewicz's finite element by dis-lurbing its parameters.     

The course scheduling problem at Lufthansa Technical Training

Lufthansa Technical Training GmbH (LTT) performs training courses for Lufthansa Technik AG as well as for several other international airlines. Courses of about 670 different types are offered of which several hundred take place each year. The course scheduling problem faced by LTT is to construct a yearly schedule which maximizes the profit margin incurred while meeting a variety of complex precedence, temporal, and resource-related constraints. A “good” operational schedule should also meet a number of additional subordinate objectives. We formalize the problem and develop a heuristic scheme along with several priority rules, as well as a local search algorithm to determine well-suited weights for weighted composite rules. The operational planning situation of 1996 served as our major test instance; additional test instances were constructed by modifying this data. Several computational experiments were carried out to evaluate the performance of the algorithms. It turned out that the best so-found schedule is substantially better in terms of the profit margin incurred than the solution manually constructed by LTT.     

A decomposition heuristics for the container ship stowage problem

In this paper we face the problem of stowing a containership, referred to as the Master Bay Plan Problem (MBPP); this problem is difficult to solve due to its combinatorial nature and the constraints related to both the ship and the containers. We present a decomposition approach that allows us to assign a priori the bays of a containership to the set of containers to be loaded according to their final destination, such that different portions of the ship are independently considered for the stowage. Then, we find the optimal solution of each subset of bays by using a 0/1 Linear Programming model. Finally, we check the global ship stability of the overall stowage plan and look for its feasibility by using an exchange algorithm which is based on local search techniques. The validation of the proposed approach is performed with some real life test cases. This work has been developed within the research area: “The harbour as a logistic node” of the Italian Centre of Excellence on Integrated Logistics (CIELI) of the University of Genoa, Italy     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Numerical comparison of methods for solving second-order ordinary initial value problems

In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C²-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented.     

Freedom from the interpolation property for tense calculi associated with Ershov spaces

We study into the question whether calculi associated with Ershov topological spaces possess Craig’s interpolation property. Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-4787.2006.1. __________ Translated from Algebra i Logika, Vol. 46, No. 6, pp. 745–762, November–December, 2007.     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.     

Likelihood estimation of soft-core interaction potentials for Gibbsian point patterns

The likelihood method is developed for the analysis of socalled regular point patterns. Approximating the normalizing factor of Gibbs canonical distribution, we simultaneously estimate two parameters, one for the scale and the other which measures the softness (or hardness), of repulsive interactions between points. The approximations are useful up to a considerably high density. Some real data are analyzed to illustrate the utility of the parameters for characterizing the regular point pattern.