Nonlinear mappings associated with the generalized linear complementarity problem

We show that the Cottle—Dantzig generalized linear complementarity problem (GLCP) is equivalent to a nonlinear complementarity problem (NLCP), a piecewise linear system of equations (PLS), a multiple objective programming problem (MOP), and a variational inequalities problem (VIP). On the basis of these equivalences, we provide an algorithm for solving problem GLCP.Project partially supported by a grant from Oak Ridge Associated Universities, TN, USA.     

Tight-binding molecular dynamics study of the hydrogen-induced structural modifications in tetrahedral amorphous carbon

A tight-binding molecular dynamics study of the structural evolution in tetrahedral amorphous carbon networks under dynamic hydrogen saturation is presented. The incorporation of hydrogen results in higher degrees of network disorder in second-neighbour distances, and initiates orbital re-hybridization that relaxes network stress. Using the simulated structures, numerical tests are performed to verify the effectiveness of a new structural order parameter for tetrahedrally-bonded solids. It is found that the island of accessible information, within the order parameter field shows a linear dependence between the fluctuations in first- and second-nearest-neighbour distances at a preferred orientation of 36°. A comparison with similar studies on hydrogenated amorphous silicon suggests that the local network structure of tetrahedrally-bonded amorphous solids obey the same ordering rule irrespective of differences in chemical species.     

Production Equilibrium Point in Multi-Unit Manufacturing Systems and The Vertical Linear Complementarity Problem

A model that selects and produces products at an equilibrium point in multi-unit manufacturing systems is presented. It enables each business subsystem in the company to select and produce products so that the whole organization meets both internal and external demands at minimum inventory cost. Unlike previously proposed models, this model does not place any restrictions on the number of products or services that each business subsystem can provide. Proofs are provided to show existence of solutions and solvability, and a numerical example is given to demonstrate the utility of the model.     

Existence theory and Q-matrix characterization for the generalized linear complementarity problem: Revisited

We provide conditions under which a vertical block matrix is a Q-matrix if one or all representative sub-matrices are Q-matrices and vice versa. It is also shown, by means of counterexamples, that Eq. (3) of [A.A. Ebiefung, Existence theory and Q-matrix characterization for the generalized linear complementarity problem, Linear Algebra Appl. 223/224 (1995) 155-169] is incorrect.     

The Generalized Linear Complementarity Problem: Least Element Theory and Z-Matrices

Existence of solutions to the Generalized Linear Complementarity Problem (GLCP) is characterized when the associated matrix is a vertical blockZ-matrix. It is shown that if solutions exist, then one must be the leastelement of the feasible region. Moreover, the vertical block Z-matrixbelongs to the class of matrices where feasibility implies existence of asolution to the GLCP. The concept of sufficient matrices of class Z isinvestigated to obtain additional properties of the solution set.     

A support submatrix for the generalized linear complementarity problem

We provide an algorithm that selects, in a polynomial time, a representative submatrix whose appropriately defined LCP solution solves the GLCP. An algorithm based on support submatrices is also presented.     

Computational studies of the effect of hydrogen on the thermalized positron state in amorphous silicon

The two-component density functional theory is applied to the study of the thermalized positron state in simulated structures of hydrogenated amorphous silicon. Results show that positron properties in bulk and ad hoc defect structures are sensitive to the defect free-volume. Using the normalized positron density, it is determined that the thermalized positron state is weakly localized at hydrogen-decorated vacancy-like complexes, and not at microscopic open volume defects. These defect complexes form as clusters of hydrogen-passivated dangling bonds. It is also found that hydrogen enhances the delocalization of positron density in the simulated structures. The relevance of the present results to the interpretation of actual positron lifetime spectroscopy in real materials is discussed.     

Studies of the electronic and vibrational signatures of the unusual bonding geometries in melt-quenched amorphous silicon

Tight-binding molecular dynamics simulations have been performed to investigate the effect of quenching rate of the Si melt on the resulting local structure of amorphous silicon. Different quenching rates were used to cool liquid silicon in the simulations to demonstrate that the choice of quenching rates significantly influences the resulting local structure. The calculated pair correlation functions show that the local structure is sensitive to the thermal processing of the liquid silicon melt. The use of cooling rates higher than 10^?13 K s^?1 appears to prevent the activation of the required structural re-arrangements necessary to stabilise the networks, causing unexpected bonding geometries to develop. The electronic signatures of the defects show that only the triangular defect structure contributes resonance states to the conduction band tail. Also, the vibrational signature of the triangular structure shows a high energy transverse optical mode at 95 meV, indicating that the defect is likely to be unstable at 300 K, although both defects contribute minimal states to the mid-gap level.     

Design of a heuristic algorithm for the generalized multi-objective set covering problem

Computational Optimization and Applications - Set covering optimization problems (SCPs) are important and of broad interest because of their extensive applications in the real world. This study...     

The generalized Leontief input-output model and its application to the choice of new technology

The Leontief input-output model is generalized and formulated as a generalized linear complementarity problem. Conditions for existence of solutions are given, and solution techniques are reviewed. An application of the model to choosing new technologies is suggested.