An iterative algorithm based on -proximal mappings for a system of generalized implicit variational inclusions in Banach spaces

In this paper, we give the notion of M-proximal mapping, an extension of P-proximal mapping given in [X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369–383], for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a system of generalized implicit variational inclusions in Banach spaces and show its equivalence with a system of implicit Wiener–Hopf equations using the concept of M-proximal mappings. Using this equivalence, we propose a new iterative algorithm for the system of generalized implicit variational inclusions. Furthermore, we prove the existence of solution of the system of generalized implicit variational inclusions and discuss the convergence and stability analysis of the iterative algorithm.     

格值命题逻辑系统L_(2n+1)P(X)中基于半正则广义文字的自动推理算法

在格值命题逻辑系统L2n+1P(X)上,提出了半正则的正广义文字和半正则的负广义文字的概念,进一步给出了半正则广义子句和半正则广义子句集的定义,详细地讨论了L2n+1P(X)上以中界元M为归结水平的半正则广义文字之间的M-归结性,最后,给出了L2n+1P(X)上基于半正则广义文字的归结水平为M的归结自动推理算法,并验证了其可靠性和完备性.     

Incommensurate modulated structure of the ferromagnetic shape-memory Ni2MnGa martensite

The ferromagnetic shape memory (MSM) alloy Ni₂MnGa undergoes a martensitic transformation (MT) at T=220 K on cooling. The structure of this phase is studied by powder X-ray diffraction experiment. The analysis of the experimental data combined with the huge information reported in literature allowed to conclude that the Ni₂MnGa martensite shows an incommensurate modulated structure closely related to a five-fold layered superstructure. The symmetry of the basic structure is found to be orthorhombic. The structure is refined by Rietveld method with superspace group Immm(00γ)s00 having a=4.2187(1) Å, b=5.5534(1) Å and c=4.1899(1) Å and modulation vector q=0.4248(3)c*. The results show that the modulation is mainly related to the periodic shuffling of the atomic layers perpendicular to the c-axis of the orthorhombic basic structure.     

Magnetic study of two isotypic manganese chloro-sulfides: MnSbS2Cl and the new compound MnBiS2Cl

Among the MnPnQ₂X compounds (Pn: pnictide; Q: chalcogen; X: halogen), two isotypic chloro-sulfides, MnSbS₂Cl and MnBiS₂Cl, have been studied. MnBiS₂Cl is a new compound synthesized by solid state reaction at 500 °C. It is orthorhombic, space group Pnma, with a=9.502(2), b=3.8802(8), , , Z=4. Its X-ray single crystal study shows (001) waved layers of MnS₄Cl₂ octahedra, opposite edge-sharing along b, and corner-sharing along a. Similar magnetic susceptibilities for both compounds have been recorded, indicating high spin Mn²⁺ with anti-ferromagnetic exchange. Correlatively, specific heat versus temperature shows a magnetic transition at for the Sb-bearing compound, and a two-steps magnetic transition at 28 and 32 K for the Bi isotype. The magnetic structure of MnSbS₂Cl has been determined by neutron diffraction, revealing a magnetic ordering at 1.5 K with an incommensurate wave-vector along b (k=[0, 0.3838, 0]). Two modulation models, sinusoidal and helicoidal, give quite equivalent reliability factors (R_mag=0.0573 and 0.0586, respectively).     

Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension

Standing wave solutions of the one-dimensional nonlinear Schrödinger equation

with are well known to be unstable. In this paper we show that asymptotic stability can be achieved provided the perturbations of these standing waves are small and chosen to belong to a codimension one Lipschitz surface. Thus, we construct codimension one asymptotically stable manifolds for all supercritical NLS in one dimension. The considerably more difficult -critical case, for which one wishes to understand the conditional stability of the pseudo-conformal blow-up solutions, is studied in the authors' companion paper Non-generic blow-up solutions for the critical focusing NLS in 1-d, preprint, 2005.

     

Optimum solutions for a system of differential equations via measure of noncompactness

New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’s fixed point theorems. In the last section, we apply such results to study the existence of optimum solutions to a system of differential equations.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.     

Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Sensitivity analysis for a system of generalized mixed implicit equilibrium problems in uniformly smooth Banach spaces

In this paper, a new system of parametric generalized mixed implicit equilibrium problems involving non-monotone set-valued mappings in real Banach spaces is introduced and studied. We first generalize the notion of the Yosida approximation in Hilbert spaces introduced by Moudafi to reflexive Banach spaces. Further, by using the notion of the Yosida approximation, we consider a system of parametric generalized Wiener-Hopf equation problems and show its equivalence to the system of parametric generalized mixed implicit equilibrium problems. By using a fixed point formulation of the system of parametric generalized Wiener-Hopf equation problems, we study the behavior and sensitivity analysis of a solution set of the system of parametric generalized mixed implicit equilibrium problems. We prove that, under suitable assumptions, the solution set of the system of parametric generalized mixed implicit equilibrium problems is nonempty, closed and Lipschitz continuous with respect to the parameters. Our results are new, and improve and generalize some known results in this field.     

A review of the recent contribution of systems thinking to operational research and management science

The systems approach, or systems thinking, has been intimately connected with the development of OR and management science initially through the work of founders such as Churchman and Ackoff and latterly through innovations such as soft systems. In this paper we have undertaken a review of the contribution that systems thinking has been making more recently, especially to the practice of OR. Systems thinking is a discipline in its own right, with many theoretical and methodological developments, but it is also applicable to almost any problem area because of its generality, and so such a review must always be selective. We have looked at the literature from both a theoretical and an applications orientation. In the first part we consider the main systems theories and methodologies in terms of their recent developments and also their applications. This covers: the systems approach, complexity theory, cybernetics, system dynamics, soft OR and PSMs, critical systems and multimethodology. In the second part we review the main domains of application: strategy, information systems, organisations, production and operations, ecology and agriculture, and medicine and health. Our overall conclusion is that while systems may not be well established institutionally, in terms of academic departments, it is incredibly healthy in terms of the quantity and variety of its applications.