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We establish several results about the blowup of the solutions for the Cauchy problem of the 3D compressible Euler equations, under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities. Especially we prove the blowup results without the condition η ( 0 ) = ∫ [ ρ ( x , 0 ) e S ( x , 0 ) γ − ρ e S γ ] d x ≥ 0 , while it is an essential condition in the well-known result obtained by Thomas C. Sideris.

We establish several results about the blowup of the solutions for the initial–boundary value problem of the isentropic Euler equations with damping for a gas outside a ball, under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities.

In this paper we present several results about the blowup of the axis-symmetric solutions for the initial–boundary value problem of the isentropic Euler equations for a perfect gas, under some assumptions that the functionals of the initial data are large enough to develop singularities.

Measurement and variation control of geometrical Key Characteristics (KCs), such as flatness and gap of joint faces, coaxiality of cabin sections, is the crucial issue in large components assembly from the aerospace industry. Aiming to control geometrical KCs and to attain the best fit of posture, an optimization algorithm based on KCs for large components assembly is proposed. This approach regards the posture best fit, which is a key activity in Measurement Aided Assembly (MAA), as a two-phase optimal problem. In the first phase, the global measurement coordinate system of digital model and shop floor is unified with minimum error based on singular value decomposition, and the current posture of components being assembly is optimally solved in terms of minimum variation of all reference points. In the second phase, the best posture of the movable component is optimally determined by minimizing multiple KCs' variation with the constraints that every KC respectively conforms to its product specification. The optimal models and the process procedures for these two-phase optimal problems based on Particle Swarm Optimization (PSO) are proposed. In each model, every posture to be calculated is modeled as a 6 dimensional particle (three movement and three rotation parameters). Finally, an example that two cabin sections of satellite mainframe structure are being assembled is selected to verify the effectiveness of the proposed approach, models and algorithms. The experiment result shows the approach is promising and will provide a foundation for further study and application. © 2013 The Authors.

In this paper, the synchronization control of a general class of memristor-based recurrent neural networks with time delays is investigated. A delay-dependent feedback controller is derived to achieve the exponential synchronization based on the drive-response concept, linear matrix inequalities (LMIs) and Lyapunov functional method. Finally, a numerical example is given to illustrate the derived theoretical results.