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.     

Hermitian阵的 Hadamard积的Schur补的一些不等式（英文）

本文得到了正定Hermitian阵的Hadamard积的Schur补的一些不等式，进而，给出了他们的一些应用，这些改进了近期的一些结束．     

广义Schur补的广义逆

对四分块矩阵A=A(︿) A(︿,︿′)A(︿′,︿) A(︿′)来说 ,如果 A和 A(︿)都是非奇异的 ,则A- 1 (︿′) =(A/︿) - 1 ,这里 A/ ︿=A(︿′) -A(︿′,︿) A(︿) - 1 A(︿,︿′)是 A(︿)在 A中的 Schur补 .王伯英教授指出上述等式 ,对半正定的 Hermitian矩阵而言 ,一般也是不能推广到 Moore-Penrose逆上去的 .在某些限制条件下 ,我们证明了广义逆的主子矩阵与广义 Schur补的关系是密切的 ,它使经典结果成为特例     

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.     

Tumor cell detection method using complement-mediated cytolytic reaction and imaging sensor system

A novel tumor-detection system consisting of complementmediated cytolytic reaction and an image processing system was developed for the simple and rapid determination of tumor cells. The present system consists of a CCD image sensor, image memory board, personal computer, and microscope. When monoclonal antibody 3C4, which is specific to the guinea pig hepatoma L-10, was added to cell suspension, only L-10 cytolysis occurred. Cytolysis caused a decrease in brightness of the cells observed by phase-contrast microscopy. The phase contrast image of the cells before cytolysis was converted to a digitalized signal and stored in computer memory. After cytolysis, a brightness threshold above that of lysed cells was subtracted from the digitalized signal and compared to the signal stored before reaction. L-10 cells in mixed cell suspension were determined specifically by the system. Measurement time was only 2 sec and overall time, including reaction time, was approximately 30 min. Since this method does not require a cell washing process, automation of the whole system is possible.     

LIGHT-SCATTERING STUDY OF POLYELECTROLYTE HOLLOW CAPSULES

Silver halide (AgX) microcrystal was used as template to synthesize hollow polyelectrolyte capsules. These hollow capsules were characterized by laser light scattering (LLS) used to measure the size of the capsules in solution. The ratio of hydrodynamic radius (Rh) from dynamic LLS to the radius of gyration (Rg) from static LLS is almost unity, revealing that the entities are hollow in solution. The results suggest that the LLS method can be regarded as a good complement to the confocal laser scanning microscopy (CLSM) method for the characterization of small hollow capsules, and it possesses the advantage of not needing fluorescence labeling.     

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.

     

Methods for research on immune complement activation on modified sensor surfaces

We have developed a methodological system consisting of a new surface sensitive quartz crystal microbalance with dissipation monitoring (QCM-D) sensor surfaces together with different surface modification methods for the investigation of surface associated complement activation in human sera. The QCM-D surface, 10 mm in diameter, was modified by spin-coating of poly(urethane urea) (PUUR) and polystyrene (PS). Some sensor surfaces were also sputtered with titanium (Ti) or modified by hydrophobic self-assembled monolayer (SAM) of an 18-carbon alkane thiol with a ---CH₃ end group. The amount of surface deposited complement protein was investigated by incubation of the modified sensor surfaces in human sera, followed by incubation with antibodies directed against complement factor 3c (C3c). The amounts of bound anti-C3c were then used as an arbitrary measure of surface induced complement activation. The order of complement activation of the different surfaces, as judged by three separate measurements per surface modification, was PUUR>PS=SAM>Ti. The Ti surface had a similar low degree of anti-C3c binding as the negative controls (heat inactivated sera). The novel QCM-D methodology was found to be very simple, accurate, sensitive and well suited as a screening method for complement activation and protein adsorption on different materials. We also compared the sensitivity of QCM-D method with surface plasmon resonance (SPR) for the quantification of protein adsorption and complement activation on gold sensor surfaces. The QCM-D method was equally sensitive as the SPR for the detection of protein adsorption from a solution independently if low flow rate (5 μl/min) was used. A slight increase in sensitivity was found at higher flow rate (30 μl/min). However, we found it difficult to use the SPR method on the Ti, PS and PUUR surfaces due to decreased light penetration of the modified SPR sensor chip.