We consider mainly the following version of set theory: “ZF+DC and for every λ,λℵ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda, \lambda^{\aleph_0}}$$\end{document} is well ordered”, our thesis is that this is a reasonable set theory, e.g. on the one hand it is much weaker than full choice, and on the other hand much can be said or at least this is what the present work tries to indicate. In particular, we prove that for a sequence δ¯=⟨δs:s∈Y⟩,cf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{\delta} = \langle\delta_{s}: s \in Y\rangle, {\rm cf}}$$\end{document} large enough compared to Y, we can prove the pcf theorem with minor changes.We then deduce the existence of covering numbers and define and prove existence of a class of true successor cardinals. Using this we give some diagonalization arguments on Abelian groups, chosen as a characteristic case.We end by showing that some such consequences hold even in ZF above. (shrink)

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A modest dc electric field markedly reduced the tensile flow stress at high temperatures in three polycrystalline oxides, i.e. MgO, Al2O3 and yttria-stabilized tetragonal ZrO2 (Y-TZP). The reduction in flow stress ΔσE in Y-TZP consisted of three components: (i) ΔσT due to Joule heating, (ii) a rapid, reversible component obtained in on-off and electric field step tests and (iii) the cumulative effect of the field on microstructure. Only ΔσT and occurred in MgO and Al2O3. It is concluded that results from (...) a reduction in the electrochemical potential for the formation of vacancies corresponding to the diffusion of the rate-controlling ion in the space-charge at the grain boundary. The calculated magnitude of the space-charge zone width and its temperature and solute composition dependence are in accord with theory and experiment; is attributed mainly to the retardation of grain growth by the field. The retardation could be due to one or more of the following effects of the field on the space-charge zone: (i) an increase in the segregated solute ions, (ii) a decrease in grain boundary energy and (iii) a decrease in solute ion mobility. (shrink)

In this study, the speed control of a DC motor with input delay and external disturbance is investigated. A delay-dependent memory state feedback robust predictor-based H ∞ controller that formerly has presented is utilized. Sufficient LMIs conditions provide the stabilizing gain of the predictor-based controller. The first-order model of a DC motor has been studied previously using PID and STA methods. However, in this paper, the delay-dependent robust H ∞ controller is used on both the first and second orders of (...) the DC motor. Finally, the predictor-based H ∞ controller is compared to the PID controller and the common H ∞ controller as well. The simulation results show that the proposed method has been more useful and efficient. (shrink)

This paper reports research concerning a suitable dialogue model for human computer debate. In particular, we consider the adoption of Moore's (1993) utilization of Mackenzie's (1979) game DC, means of using computational agents as the test-bed to facilitate evaluation of the proposed model, and means of using the evaluation results as motivation to further develop a dialogue model, which can prevent fallacious argument and common errors. It is anticipated that this work will contribute toward the development of human computer dialogue, (...) and help to illuminate research issues in the field of dialectics itself. (shrink)