Planned lead time optimization in material requirement planning environment for multilevel production systems

This paper deals with the problem of planned lead time calculation in a Material Requirement Planning （MRP） environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered： multi-level serial-production and assembly systems. For the serial production systems （one type of component at each level）, a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and se＇~eral numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.     

Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus

Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Bj?rling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered.     

Structure and collaboration relationship analysis in a scientific collaboration network

We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network’s structure. The stability of the network’s structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.     

Direct evidence for atomic defects in graphene layers

Atomic-scale defects in graphene layers alter the physical and chemical properties of carbon nanostructures. Theoretical predictions have recently shown that energetic particles such as electrons and ions can induce polymorphic atomic defects in graphene layers as a result of knock-on atom displacements. However, the number of experimental reports on these defects is limited. The graphite network in single-walled carbon nanotubes has been visualized by transmission electron microscopy (TEM) and their chiral indices have been determined. But the methods used require a long image acquisition time and intensive numerical treatments after observations to find an 'average' image, which prevents the accurate detection and investigation of defect structures. Here we report observations in situ of defect formation in single graphene layers by high-resolution TEM. The observed structures are expected to be of use when engineering the properties of carbon nanostructures for specific device applications.     

Gains of glycosylation comprise an unexpectedly large group of pathogenic mutations

Mutations involving gains of glycosylation have been considered rare, and the pathogenic role of the new carbohydrate chains has never been formally established. We identified three children with mendelian susceptibility to mycobacterial disease who were homozygous with respect to a missense mutation in IFNGR2 creating a new N-glycosylation site in the IFNgammaR2 chain. The resulting additional carbohydrate moiety was both necessary and sufficient to abolish the cellular response to IFNgamma. We then searched the Human Gene Mutation Database for potential gain-of-N-glycosylation missense mutations; of 10,047 mutations in 577 genes encoding proteins trafficked through the secretory pathway, we identified 142 candidate mutations ( approximately 1.4%) in 77 genes ( approximately 13.3%). Six mutant proteins bore new N-linked carbohydrate moieties. Thus, an unexpectedly high proportion of mutations that cause human genetic disease might lead to the creation of new N-glycosylation sites. Their pathogenic effects may be a direct consequence of the addition of N-linked carbohydrate.     

Action de deux polybases sur la charge et l'agrégation des plaquettes

Summary The action of two polybases (polybren and DEAE Dextran) on the electrophoretic mobility of platelets is studied. These two substances induce a decrease of the mobility. An investigation of the aggregability with the help of a photometric test shows a correlation between the charge decrease and platelet aggregation.

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Ce travail a été réalisé avec l'aide de la D.R.M.E. (section Biologie), Contrat No. 71.34.010.00.480.75.01.     

Cauchy’s Infinitesimals,His Sum Theorem,and Foundational Paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.