Existence of optimal solutions of two-directionally continuous linear repetitive processes

In the paper, an existence theorem for a Lagrange optimal control problem connected with a two-directionally continuous variant of a linear autonomous repetitive process is derived. As a corollary, existence of an optimal solution in the case of cost functional depending on a fixed ??end-function?? is obtained.     

New friction welding technology for joining tubes with lids

The article presents the results of research on the use of the new technology of friction welding with a non-wearing tool for welding pipe ends with lids. The pipes and lids were made of aluminium alloy EN AW 2017A, non-weldable by conventional methods. The aim of the study was to verify the possibility of welding the lid to the pipe using the FSW method as well as a new method with a tool with specially profiled friction surface. The article presents the results of structural tests and strength tests of the weld joints obtained using the new technique.     

Quasilinearized Regression

Estimation in nonlinear regression usually requires a considerable amount of computational work. If it is possible to linearize the original formulas, the linear regression is sometimes applied to transformed linear relations. The method of quasilinearized regression (first order approximation of nonlinear regression), comparable to linear regression, with respect to computational effort, is described in this paper. This method gives substantially better results than linear regression of linearized formula.     

The Effect of Implanted Al and/or Y on the Scale Formation on Low-Al Fe20Cr2Al Alloy

The very early stages of the oxidation of an Fe20Cr2Al alloy, unmodified and ion-implanted by aluminium, yttrium and a combination of both elements, Al and Y, were studied at 1100 °C in oxygen using two-stage-oxidation exposures with ¹⁸O₂ as a tracer and subsequent characterisation of the scales using SIMS analyses of distribution of oxygen isotopes and oxide-related negative ion clusters, SEM observations of the surface morphology and photoluminescence spectroscopy analysis of the phase composition. The scales formed in all cases, except for the Al-implanted alloy, exhibited layered structures, with the outer part comprising Fe- and Cr-rich oxide, and the inner part being Al₂O₃, which grew due to a mixed outward–inward mechanism . The alumina sub-layers contained the transient oxides and α-Al₂O₃. Implanted Al significantly affected the mechanism of the scale growth, providing that the scale consisted essentially of α-Al₂O₃, and grew via a mixed inward-outward mechanism typical for scales on alumina formers.