Commuting and stable feedback design for switched linear systems

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.     

Fixed-point theorems for families of weakly non-expansive maps

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.     

Nonlinear modelling and control of a common rail injection system for diesel engines

Modern trends in designing mechatronic systems call for a synergic design of the separated subsystems (mechanic, electronic parts, control modules, etc.) concurring to the overall performance. Following this point of view, this paper presents a control oriented model and a nonlinear control design for a Common Rail injection system. First a model is developed, which is tuned in a virtual simulation environment, representing the injection system in details in a reliable replication of reality. Then a sliding mode control is developed. Both the model of the injection process and of the control law are validated by a virtual detailed simulation environment. The prediction capability of the model and the control efficiency are clearly shown.     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

A New 4.0-Generation Dendrimer Phosphorescence Labeling Reagent and Its Application to Determination of Trace Alkaline Phosphatase by Affinity Adsorption Solid Substrate-room Temperature Phosphorimetry

A Triton X-100-4.0G-D （4.0G-D refers to a 4.0-generation dendrimer） was brought forward as a new phosphorescence labeling reagent. Two types of specific affinity adsorption （AA） reactions （direct method and sandwich method） were carried out between the labeling product of Triton X-100-4：0G-D-Wheat germ agglutinin （WGA） and alkaline phosphatase （ALP）, the product of AA reaction preserved the good characteristics of room temperature phosphorescence （RTP） of 4.0G-D and △Ip of the product was proportional to the content of ALP. According to the fact stated above, a new method for the determination of trace ALP by affinity adsorption solid substrate-room temperature phosphorimetry （AA-SS-RTP） was established on the basis of WGA labeled with the Triton X-100-4.0G-D. The detection limits were 0.20 ag·spot^-1 （corresponding concentration： 5.0×10^-16 g·mL^-1, namely 5.0×10^-18 mol·L^-1） for a direct method and 0.14 ag·spot^-1 （corresponding concentration： 3.5×10^-16 g·mL^-1, namely 3.5×10^-18 mol·L^-1） for a sandwich method, respectively. For their high sensitivity, good repeatability and high accuracy, the direct method and sandwich method have been successfully appfied to determine the content of ALP in human serum, and the results were coincided with the clinical detection results of the enzyme-linked immunosorbent assay method by the Zhangzhou Hospital of Traditional Chinese Medicine. Meanwhile, the mechanism for the determination of trace ALP by AA-SS-RTP was discussed.     

Fermentation characteristics and the dynamic trend of chemical components during fermentation of Massa Medicata Fermentata

As a representative of traditionally fermented Chinese medicine, Massa Medicata Fermentata (MMF) shows the functions of invigorating the spleen and stomach and promoting digestion, which plays an important role in the treatment of gastrointestinal diseases. The fermentation mechanism and the key factors that affect the quality of MMF have not been revealed yet, which has become an urgent issue that limits its clinical application. This article aims to systematically and comprehensively reveal the transformation of physical properties and the dynamic trend of chemical components including substrate components, volatile components, and lactic acid as anaerobic fermentation product during MMF fermentation. Along with obvious hyphae growth observed for MMF, the weight of MMF decreased, and the moisture and temperature increased. Through the quantified 14 components from substrate, ferulic acid increased from 45.53 ± 6.94 to 141.89 ± 78.40 μg/g, while glycosides and phenolic acids declined except caffeic acid. Also, within the 66 volatile components analyzed, alcohols and acids increased, while aldehydes and ketones decreased. Lactic acid was not detected in the fermentation substrate, but an apparent increase in lactic acid content was observed along with the increased fermentation days, resulting in 2.54 ± 0.15 mg/g on day 8. Based on the tested components, the fermentation process of MMF was discriminated into three distinct stages by principal component analysis, and an optimal fermentation time of four days was proposed. The results of this study will be of great significance to clarify the characteristics of fermentation and conduce to improving quality standards of MMF.     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

DIRECT SOMATIC EMBRYOGENESIS AND PLANT REGENERATION FROM PROTOPLAST-DERIVED CELLS OF WHEAT (Triticum aestivum L.)

Protoplasts were isolated from embryogenic calli derived from immature embryos ofwheat (Triticum aestivum L. cv. Jinan 177). The protoplasts were cultured in NMB mediumsupplemented with 1mg/L 2,4- D and 500mg/l casein hydrolysate (CH). The regenerated cellsfrom protoplasts divided to form somatic embryos directly. The somatic embryos grown to1.5- 2 mm in size directly developed into complete plants on solid MB medium without hor-mones.     

THE ESTABLISHMENT OF TWO SETS OF ALIEN ADDITION LINES OF WHEATWHEATGRASS

The procedure and method for the transfer of two sets of 14 pairs of wheatgrass (Agropyron interrnedium) chromosomes into common wheat to establish two sets of wheat-wheatgrass alien addition lines are reported. Meanwhile, observations and analyses have been made on the phenotypicaI characters of all the 14 alien addition lines established. It is determined that wheatgrass chromosomes in some of the established addition lines carry the rustresistant genes. In addition, questions concerning the location and distribution of certain agriculturally important genes of wheatgrass chromosomes have been discussed.     

Kinetic determination of trace levels of selenium(IV) and total selenium by Nile Blue A/hydrogen peroxide method

A kinetic method for the determination of selenium(IV) traces is proposed, based on its inhibitory action on the oxidation of Nile Blue A by hydrogen peroxide in phosphate buffer (pH 10.5). A linear dependence was established between the rate of the proposed indicator reaction and selenium concentration in the range 9.5 × 10^–2-1.58 ng cm^–3. The experimental conditions of maximal selenium effect were established. Selenium, determined by the tangent method, was determined at concentrations over the range 0.22–1.26 ng cm^–3, with relative standard deviations up to 4.5%. The reaction rate was followed spectrophotometrically. The effect of foreign ions on the accuracy of this method was also investigated. The method was applied to the determination of selenium in pharmaceutical preparations and wheat flour.