Preservation of Lipschitz constants by Bernstein type operators

Summary We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces.     

A Novel Model for Protein Immobilization on Microspheres

The immobilization of proteins, especially receptor proteins commonly used in high through-put screening of drugs (HTS), have received great attention in recent years. There are many successful isothermal models for describing the adsorption of protein onto solid surface, such as Langmuir model, Bi-Langmuir model, Fowler model, Freundlich model, Freundlich-Langmuir model and Tekmin model etc. In all these models, Langmuir model was the most favorable one model accepted by many researchers, but the experimental results showed that it was not entirely fit to all adsorption behaviors. So new models were required for describing protein adsorption onto microspheres in different conditions.In our research, a novel isothermal model, including Langmuir and other adsorbing behaviors was presented basing on the holding degree of surface active sites and the interaction styles of protein immobilization. In Langmuir model, the adsorbing amount of protein was described as [PS] =Km[P]/1 + K[P], where [PS] was the concentration of adsorbed protein, [P] was the concentration of freeprotein at equilibrium state, and Km and K was constant. According to the interactions of protein and ligands, there were three patterns in the interactions of protein and ligands. On the similar assumption that the interaction of protein and microspheres were three styles, and based on the definition of the holding degree of surface active sites (Y), three adsorption behaviors could be described as Y K[ P ]φ/ K[P]φ+1 or ln K + φ ln[P] =ln(Y/1-Y) in which [P] was the concentration of free protein at equilibrium state, and φ and K was constant. Different scale of φ presented different adsorption behaviors, especially when φ was 1, the adsorption behavior was Langmuir adsorbing model. Figure I indicated the different adsorbing results in different adsorption behaviors (φ＞1, φ＜1,and φ=1).     

纯量反馈系统同时强镇定的充分条件

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定)．两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题．文中所作的基本假定是所有的对象具有相同的简单不稳定零点，在此条件下给出了n个对象同时强镇定的一个充分条件．当仅有一个不稳定零点时．容易检验是否同时强镇定，否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的，就能判定n个对象同时强镇定．因此是一个易于检验的充分条件．文章同时给出了n个对象同时强镇定的算法，丰富了同时强镇定的充分条件．     

Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

鲤鱼体中鱼腥味物质的提取和鉴定

采用同时蒸馏萃取法提取鲤鱼鱼体中的挥发和半挥发性有机物，用GC／MS从提取物中分析鉴定出鱼腥味和疑是鱼腥味物质16种。包括醛、烯醛、酮和呋喃4类化合物。其中己醛、庚醛和2，4-二烯癸醛被确认为鱼腥味的化合物。研究发现，这些物质总量在鲤鱼体的鱼鳞、鱼鳃和鱼肉的分布呈现下降趋势，且其总量与鱼腥味强度之间具有可比较的对应关系。     

Optimizing in the class of Fuller modified limited information maximum likelihood estimators

A general class of Fuller modified maximum likelihood estimators are considered. It is shown that this class possesses finite moments. Asymptotic bias and asymptotic mean squared error are derived using small-σ expansions. A simulation study is carried out to compare different estimators in this class with standard estimators.