What is a proof?

To those brought up in a logic-based tradition there seems to be a simple and clear definition of proof. But this is largely a twentieth century invention; many earlier proofs had a different nature. We will look particularly at the faulty proof of Euler's Theorem and Lakatos' rational reconstruction of the history of this proof. We will ask: how is it possible for the errors in a faulty proof to remain undetected for several years-even when counter-examples to it are known? How is it possible to have a proof about concepts that are only partially defined? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they offer a possible cognitive model for the human construction of proofs in mathematics. In particular, we show how they can account for persistent errors in proofs.     

What is negative refraction?

We review various published definitions associated with the phenomenon of negative phase velocity propagation of electromagnetic waves in meta-media, as observed through negative refraction. For the principal definition, based on the Poynting vector and the wave vector having negative scalar product, we summarise the various material constraints that have been derived. The distinction between criteria based on the Poynting vector and the group velocity are considered, both in respect of causality, and in the context of moving media. Instances where a fully covariant definition is necessary are also identified, and compared with other results from the extant literature. Satisfaction of the NPV propagation criterion is also considered for surface plasmons.     

What is Simulated Annealing?

Beginning in 1983, simulated annealing was marketed as a global optimization methodology that mimics the physical annealing process by which molten substances cool to crystalline lattices of minimal energy. This marketing strategy had a polarizing effect, attracting those who delighted in metaphor and alienating others who found metaphor insufficient at best and facile at worst. In fact, the emotional outbursts that accompany many discussions of simulated annealing are an unfortunate distraction. Whatever its pros and cons, simulated annealing can be grounded in rigorous mathematics. Here we provide an elementary, self-contained introduction to simulated annealing in terms of Markov chains.     

What is Middle Maintenance Policy?

The main purpose of this paper is to propose several new maintenance policies that can be performed at suitable middle times for trivariate preventive maintenance scenarios. Firstly, characteristics and limitations for the approaches of whichever occurs first and whichever occurs last are analyzed, and their respective maintenance models, which are called first maintenance and last maintenance, are given directly. Secondly, a combined approach of first and last is employed and middle maintenance is proposed. Thirdly, the aforementioned policy is modified to be performed at discrete working cycles, using the method of overtime maintenance. Finally, a new approach of whichever occurs middle is proposed for modelings. We give the analyses of how to formulate the middle maintenances and obtain their expected maintenance cost rates, using the technique of cumulative damage models. Numerical examples are given to compare the optimal policies among first, last, and middle maintenances. Finally, a potential application of middle maintenance is provided for future studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Myocardial stunning in hemodialysis: What is the overall message?

Heart failure and cardiovascular events are common in chronic renal failure. Hemodialysis (HD) causes significant hemodynamic changes and hypotension. New evidence based on intradialytic echocardiography demonstrates transient cardiac dysfunction or stunning in majority of chronic HD patients. Over time, this group may progress to chronic heart failure and appears to predict higher cardiovascular events and mortality. Although the exact etiology is unclear, alterations in HD technique and cardiac medications may reduce this complication. We review the current understanding of acute cardiac stunning during HD and present a systematic management algorithm to optimizing overall outcomes in this high-risk population.     

Influence of magnesium on hydrogenated ScAl1−xMgx alloys: A theoretical study

Ab initio total energy calculations, based on the projector augmented wave method and the exact muffin-tin orbitals method in combination with the coherent-potential approximation, are used to examine the effect of magnesium on hydrogen absorption/desorption temperature and phase stability of hydrogenated ScAl_1?xMg_x (0 ? x ? 0.3) alloys. According to the experiments, ScAl_1?xMg_x adopts the CsCl structure, and upon hydrogen absorption it decomposes into ScH₂ with CaF₂ structure and Al–Mg with face centered cubic structure. Here we demonstrate that the stability field of the hydrogenated alloys depends sensitively on Mg content and on the microstructure of the decomposed system. For a given microstructure, the critical temperature for hydrogen absorption/desorption increases with Mg concentration.     

Strengthening mechanisms in magnesium alloys containing ternary Ⅰ,W and LPSO phases

This study was aimed at identifying underlying strengthening mechanisms and predicting the yield strength of as-extruded Mg-Zn-Y alloys with varying amounts of yttrium(Y) element. The addition of Y resulted in the formation of ternary I(Mg_3 YZn_6), W(Mg_3 Y_2 Zn_3) and LPSO(Mg_(12) YZn) phases which subsequently reinforced alloys ZM31 + 0.3 Y, ZM31 + 3.2 Y and ZM31 + 6 Y, where the value denoted the amount of Y element(in wt%). Yield strength of the alloys was determined via uniaxial compression testing, and grain size and second-phase particles were characterized using OM and SEM. In-situ high-temperature XRD was performed to determine the coefficient of thermal expansion(CTE), which was derived to be 1.38 × 10~(-5 K~(-1) and 2.35 × 10~(-5) K~(-1) for W and LPSO phases, respectively. The individual strengthening effects in each material were quantified for the first time, including grain refinement, Orowan looping, thermal mismatch, dislocation density, load-bearing, and particle shearing contributions. Grain refinement was one of the major strengthening mechanisms and it was present in all the alloys studied,irrespective of the second-phase particles. Orowan looping and CTE mismatch were the predominant strengthening mechanisms in the ZM31 + 0.3 Y and ZM31 + 3.2 Y alloys containing I and W phases, respectively, while load-bearing and second-phase shearing were the salient mechanisms contributing largely to the superior yield strength of the LPSO-reinforced ZM31 + 6 Y alloy.     

What is Different in Mixtures? From Critical Point to High Pressures

It is well known that the properties of mixtures may be very different from those of the pure constituent components, due to the unlike forces. Even for mixtures composed of simple molecules, this behavior can be rather complicated at high pressures, where the system may exhibit gas–gas equilibrium, a critical double point and density inversions. A few mixtures such as He–H₂ and He–N₂ are discussed. It is demonstrated that Raman spectroscopy is an important tool not only for obtaining knowledge about the dynamical behavior of mixtures but also for determining phase equilibria at high pressures. The frequency shift, the linewidth, and the line shape provide information about the solubility, the state of aggregation, and other conditions of the system. Recently, a new type of compound has been found, the so-called van der Waals compound. The results obtained in simple mixtures, such as Ne–N₂ and Xe–N₂, are compared with the results of molecular dynamics (MD) simulations of hard sphere mixtures. It is pointed out that energy, and not a geometrical effect (or entropy), is the driving force for compound formation.     

Effect of aluminium on the microstructure and mechanical properties of as-cast magnesium–manganese alloys

In this paper, the effect of aluminium on microstructure and mechanical properties of as-cast magnesium–manganese alloy has been investigated by means of X-ray diffraction, optical microscopy and scanning electron microscopy. The results reveal that various Al–Mn intermetallic compounds form with an increase of Al content. As a result, microstructure of AM11 alloy has been effectively refined due to the formation of Al₈Mn₅ phase along the grain boundary, while Al addition is explained as the main reason on refining the microstructure of AM91 alloy due to its higher grain growth restriction factor value of ～4.32. The tensile yield strength (TYS) has been improved steadily from 27.4 to 122.9?MPa with increasing Al content, because of the combined effects of grain boundary strengthening, solid solution strengthening and precipitation hardening behaviours.     

Grain growth in perovskites: What is the impact of boundary transitions?

Several perovskite ceramics are known to have non-Arrhenius type grain growth and to show grain growth transitions instead. These growth transitions are coupled to bimodal microstructures and seem to be caused by the existence, coexistence and transition of two different grain boundary types. This paper gives a review on the details of the grain growth transitions in perovskite ceramics. A simple mean field approach and standard grain growth experiments are used for quantification. However, this approach is far too simple to understand bimodal anisotropic grain growth completely as apparent in perovskites. Important parameters such as atomistic boundary structure, segregation effects, wetting transitions, faceting, grain boundary stoichiometry, space charge and interfacial drag effects are discussed with respect to their impact on grain growth in perovskites. A summary of open questions and future directions is given.     

Effect of magnesium content on thermal and structural parameters of Al–Mg alloys directionally solidified

In this study, the influence of magnesium content on thermal and structural parameters during the unsteady-state unidirectional solidification of Al–Mg alloys is analyzed. Using a special device, Al–Mg alloys containing 5, 10, and 15 wt% Mg were submitted to unidirectional solidification. Using a data acquisition system, the temperature variations along the casting during solidification were measured. From these results, the variations of solidification parameters as growth rate of dendrite tips, thermal gradient, cooling rate, and local solidification time were determined. The variation of global heat transfer coefficient at metal/mould interface was estimated through the adjustment of experimental temperature variation close to the interface and numerical predictions. Primary and secondary dendrite arms spacing variations during solidification were measured by optical microscopy. From these results, comparative analysis were developed to determine the influence of magnesium content.     

Precipitation and aging in high-conductivity Cu–Cr alloys with additions of zirconium and magnesium

Abstract

The precipitation reactions responsible for age hardening in a high-conductivity Cu–Cr–Zr–Mg alloy have been investigated by analytical transmission electron microscopy and compared briefly with the processes that occur in simpler Cu–Cr and Cu–Cr–Mg alloys. Aging at low temperatures (400°C) results in the formation of Guinier–Preston zones. Peak hardness, obtained by aging for 24 h at 450°C, is found to be a result of the fine scale precipitation of an ordered compound, possibly of the Heusler type, with the suggested composition CrCu₂(Zr, Mg). Overaging results in the formation of coarse precipitates of Cr and CU₄Zr. The intergranular precipitate which forms in the Cu–Cr–Zr–Mg alloy is Cu₄Zr. This phase precipitates both as discrete particles on the grain boundaries and as thin ( ~ 5 nm) continuous intergranular films.

MST/89     

What is the role of value-added service in a remanufacturing closed-loop supply chain?

While the previous literature overlooks value-added service in a closed-loop supply chain (CLSC), we consider new research problems with embedding value-added service into remanufacturing models. In this paper, we mainly study the role of value-added service in a CLSC and investigate how the value-added service influences profits and other decision variables. Then, we evaluate the performance of the CLSC in different service structures, where a manufacturer or a retailer provide the value-added service. Systematic comparisons and numerical studies show that the supply chain is more effective when service is provided by a manufacturer rather than by a retailer. Also, value-added service improves the whole supply chain performance and plays a regulatory role in a CLSC and influences the decisions of supply chain members. We also show that while a service cost-sharing mechanism can only optimise rather than achieve the supply chain coordination, and the degree of optimisation depends on cost-sharing percentage, the two-part tariff contract can be an effective mechanism to coordinate decentralised service scenarios by generating the same supply chain performance in a centralised service architecture model.