The Lagrange-Newton method for nonlinear optimal control problems

We investigate local convergence of the Lagrange-Newton method for nonlinear optimal control problems subject to control constraints including the situation where the terminal state is fixed. Sufficient conditions for local quadratic convergence of the method based on stability results for the solutions of nonlinear control problems are discussed.     

Non-unitary classification of molecular electronic structures and other atom clusters

Molecules or reacting assemblies of an isomeric set of atoms become related to each other regardless of any spatial symmetry by the principle of linear covariance and the valency dyad field introduced in two previous papers by the author. Crucial electronic indices characterize certain equivalence classes into which molecules get classified under transformations which are in general non-unitary.     

The Riemann Function for the Third-Order One-Dimensional Pseudoparabolic Equation

In this work, some classes of initial boundary-value problems are investigated in the Sobolev space for the third-order linear pseudoparabolic equation having, in general, nonsmooth coefficients. A new type of Riemann function concept is given for these problems, which is more natural than the classical Riemann-type function concept, and an integral form of the solutions of nonhomogeneous problems can be found more naturally using this concept.     

Optimal unity-magnitude input shaper duration analysis

Command profiles are required to move a dynamical system from rest to rest without residual vibration in a minimum time. The unity-magnitude (UM) input shaper is one of the faster input shaping techniques. However, analytical solution of the impulse time locations is impossible due to the dependent residual vibration constraint equations. Many researchers solve these by using curve fitting. In this paper, the characteristics of the UM shaping coefficients as a function of system parameters are investigated. An analysis procedure to obtain UM input shaper impulse time sequences is presented. Finally, the proposed technique is compared to the zero vibration (ZV) shaper in both response and robustness to modeling error.     

Linear and non-linear optical properties of some donor–acceptor oxadiazoles by ab initio Hartree-Fock calculations

The molecular hyperpolarizability of some donor–acceptor oxadiazoles was investigated using ab initio methods. Ab initio optimizations were performed at the Hartree-Fock level using different basis sets, starting with the minimal basis set, and then split valence sets. The first hyperpolarizabilities were calculated at the Hartree-Fock level employing the corresponding basis sets using Gaussian 98W. In general, the first hyperpolarizability is dependent on the choice of method and basis set. In order to understand this phenomenon in the context of molecular orbital picture, we examined the molecular HOMOs and molecular LUMOs generated via HF/6-31G level. It has also been calculated the polarizability, anisotropy of polarizability and ground state dipole moment of all the molecules. Several of these oxadiazoles display significant second-order molecular nonlinearity, β(8.57–195.05 × 10⁻³⁰ esu) and provide the basis for future design of efficient nonlinear optical materials having the oxadiazole core.     

Algorithm robust for the bicriteria discrete optimization problem

We apply Algorithm Robust to various problems in multiple objective discrete optimization. Algorithm Robust is a general procedure that is designed to solve bicriteria optimization problems. The algorithm performs a weight space search in which the weights are utilized in min-max type subproblems. In this paper, we experiment with Algorithm Robust on the bicriteria knapsack problem, the bicriteria assignment problem, and the bicriteria minimum cost network flow problem. We look at a heuristic variation that is based on controlling the weight space search and has an indirect control on the sample of efficient solutions generated. We then study another heuristic variation which generates samples of the efficient set with quality guarantees. We report results of computational experiments.     

On γ-semi-open sets

Summary We introduce the concepts of γ-semi-open set, γ_s-set, γ^s-set, generalized γ_s-set, generalized γ^s-set, semi-T₁^γspace and semi-R₀^γspace by using γ-open-sets.     

Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.