One for all, all for one---von Neumann, Wald, Rawls, and Pareto

Applications of the maximin criterion extend beyond economics to statistics, computer science, politics, and operations research. However, the maximin criterion---be it von Neumann's, Wald's, or Rawls'---draws fierce criticism due to its extremely pessimistic stance. I propose a novel concept, dubbed the optimin criterion, which is based on (Pareto) optimizing the worst-case payoffs of tacit agreements. The optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but it also generalizes (iii) Nash equilibrium in $n$-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy. Moreover, every Nash equilibrium satisfies the optimin criterion in an auxiliary game

Influence of Rayleigh-Doppler broadening on the selection of H2O dial system parameters

Computer simulations have enabled the performance of a H2O Differential Absorption Lidar (DIAL) system to be studied by spectrally analyzing the forward propagating and backscattered laser energy. The simulations were done for a high altitude (21 km) DIAL system operating in a nadir-viewing mode. The influence of Rayleigh Doppler broadening on DIAL measurement accuracies were evaluated and show that the Rayleigh broadening influence, which can be corrected to first order in regions free of large aerosol gradients, reduces the sensitivity of DIAL H2O measurement errors in the upper tropospheric region. The ability to correct the Rayleigh broadening and the selection of H2O DIAL parameters when all the systematic effects are combined, were discussed

Modelling the Effects of Friction on Tool-Chip Interface Temperature During Orthogonal Cutting of Al6061-T6 Aluminium Alloy

© IEOM Society International - IEOM 2019In this work, finite element simulations based on the analytical model derived with the MATLAB software were used to establish the temperature fields within the cutting tool and tool-chip interface. The average tool-chip interface temperature model was simulated and the simulation results were compared with experimental results for validation. At a maximum cutting speed of 90 m/min, the maximum temperature obtained from the experiment was 410 oC, at same rake angle of 0o. However, the developed model predicted 490 oC under the same conditions. The higher value obtained by the model can be attributed to the negligence of heat losses to the surrounding by both convection and radiation modes, as an assumption in the formulated model. A similar trend of these results was also recorded for the case of rake angle and feed rate of 30o and 0.0635 mm/rev, respectively. It was observed that the simulation results and experimental measurements for the average tool-chip interface temperature agreed significantly.Final Published versio

Experimental Characterization of Electrical Discharge Machining of Aluminum 6061 T6 Alloy using Different Dielectrics

Electrical discharge machining is a non-traditional machining method broadly employed in industries for machining of parts that have typical profiles and require great accuracy. This paper investigates the effects of electrical parameters: pulse-on-time and current on three performance measures (material removal rate, microstructures and electrode wear rate), using distilled water and kerosene as dielectrics. A comparison between dielectrics for the machining of aluminum 6061 T6 alloy material in terms of performance measures was performed. Aluminum 6061 T6 alloy material was selected, because of its growing use in the automotive and aerospace industrial sectors. The experimental sequence was designed using Taguchi technique of L9 orthogonal array by changing three levels of pulse-on-time and current, and test runs were performed separately for each dielectric. The results obtained show that greater electrode wear rate (EWR) and higher material removal rate (MRR) were achieved with distilled water when compared with kerosene. These greater EWR and MRR responses can be attributed to the early breakage of the weak oxide and carbide layers formed on the tool and alloy material surfaces, respectively. The innovative contributions of this study include, but are not limited to, the possibility of machining of aluminum 6061 T6 alloy with graphite electrode to enhance machinability and fast cutting rate employing two different dielectrics.Peer reviewe

Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle.Comment: 27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74