On nonlinear programming with support functions

Optimality conditions are derived for a nonliear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various dualityresults are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semidefinite quadratic form or anLp norm. It is pointed out that these special cases can easily be generated from our results.     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

An optical method and neural network for surface roughness measurement

The measurement of surface roughness using stylus equipment has several disadvantages. A non-contact optical method is needed for measuring the surface roughness of engineering metals with improved accuracy. One candidate for an optical method is the use of a laser source, where the laser light intensity reflected from the surface represents the surface roughness of the illuminated area. A relation can be developed between the reflected laser beam intensity and the surface roughness of the metal. The present study examines the measurement of the surface roughness of the stainless steel samples using a He-Ne laser beam. In the measurement a Gaussian curve parameter of a Gaussian function approximating the peak of the reflected intensity is measured with a fast response photodetector. In order to achieve this, an experimental setup is designed and built. In the experimental apparatus, fiber-optic cables are used to collect the reflected beam from the surface. The output of the fiber-optic system is fed to a back-propagation neural network to classify the resulting surface profile and predict the surface roughness value. The results obtained from the present study are then compared with the stylus measurement results. It is found that the resolution of the surface texture improves considerably in the case of optical method and the neural network developed for this purpose can classify the surface texture according to the control charts developed mathematically.     

Effect of γ-ray irradiation on the magnetic properties of NdFeB and Fe–Cr–Co permanent magnets

The effect of γ-ray irradiation on the magnetic properties of NdFeB and Fe–Cr–Co permanent magnets has been investigated. The magnetic flux loss of two kinds of magnets before and after irradiation was measured. Results show that the effect of γ-ray irradiation on the magnetic properties of sintered NdFeB is not so obvious as that on Fe–Cr–Co magnet. Irradiation-induced damage from γ-ray for the Fe–Cr–Co magnets was characterized for the first time. The decline of permanent magnetic properties of Fe–Cr–Co magnet induced by γ-ray irradiation is reversible except for the maximum energy product (BH)_max. The difference of coercivity mechanism between these two kinds of permanent magnets is responsible for the different dependence of magnetic properties loss induced by γ-ray irradiation.     

Characteristics of soft magnetic composite material under rotating magnetic fluxes

This paper reports the measurement of magnetic properties of the soft magnetic composite material SOMALOY^TM 500 in a square sample under different patterns of flux density with 2D magnetic excitations. The test system, principle of measurement, magnetic power loss calculation, and methods of correction for misalignment of H surface sensing coils are presented. The experimental results show that although nominally isotropic, the SOMALOY^TM 500 sample exhibits some anisotropy. The results are useful in the design and performance analysis of rotating electrical machines.     

Analogy of thermogravimetric measurements

Dimensionless number has been developed and introduced for quantitative analysis of the effect of thermogravimetric measuring factors like sample quantity, heating rate, etc. The TG, DTG and T data of different thermogravimetric measurements can be used directly for calculation of the three constants of analogy. TG data of CaCO₃ measured in very different conditions show the method of transformation and its applicability for calculation of the correlation of measurements.     

Numerical treatment of an asset price model with non-stochastic uncertainty

In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC ¹-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system for future contracts of the German DAX is suggested and developed. Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307.