Delay-independent stability of homogeneous systems

A class of nonlinear systems with homogeneous right-hand sides and time-varying delay is studied. It is assumed that the trivial solution of a system is asymptotically stable when delay is equal to zero. By the usage of the Lyapunov direct method and the Razumikhin approach, it is proved that the asymptotic stability of the zero solution of the system is preserved for an arbitrary continuous nonnegative and bounded delay. The conditions of stability of time-delay systems by homogeneous approximation are obtained. Furthermore, it is shown that the presented approaches permit to derive delay-independent stability conditions for some types of nonlinear systems with distributed delay. Two examples of nonlinear oscillatory systems are given to demonstrate the effectiveness of our results.     

粘性导电流体在磁场作用下流过多孔通道时传热传质振荡流的数值解——用于病理状态动脉中血液的流动

当血管内壁出现多孔性结构时,流过多孔性血管的血液将作不稳定的MHD流动.研究血液在其中的传热传质问题,考虑了与时间相关的渗透率和振荡引起的吸入速度,并数值地求解该问题.对分析中出现的参数取不同数值时,图形给出了速度、温度、浓度场,以及表面摩擦因数、Nusselt数和Sherwood数的计算结果.研究表明,血液流动受磁场和Grashof数的影响明显.     

On the calculation of highly oscillatory integrals with an algebraic singularity

In this paper we explore the evaluation of highly oscillatory integrals containing an algebraic singularity based on the change of variable t = x^−r, where r is a positive real number, and the analytical continuation. Robust numerical results demonstrate the accuracy and effectiveness of the proposed approach.     

非线性中立型时滞方程解的全局渐近稳定性和振动性

本文研究非线性中立型时滞微分方程N( t) =N( t) [a( t) -b( t) N ( t-τ) -c( t) N( t-σ) -d( t) N ( t) ],t≥ t0 ,( E)其中τ,σ∈ [0 ,∞ ) ,a( t) ,b( t) ,d( t)∈ C1( [t0 ,∞ ) ,R+) ,c( t)∈ C( [t0 ,∞ ) ,k) ,得到方程 ( E)的正解关于正常数平衡点全局渐近稳定和振动的充分条件 .本文所用方法与其他文献不同 ,所得结果发展了一些文献的结果 ,其中定理 ( 2 .3)回答了由 Y.Kuang and A.Feldstein所提出的一个公开问题 .     

Fast directional algorithms for the Helmholtz kernel

This paper presents a new directional multilevel algorithm for solving N-body or N-point problems with highly oscillatory kernels. We address the problem by first proving that the interaction between a ball of radius r and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of O(1/r) and is at a distance which is at least O(r²) away from the ball. Based on this representation, our algorithm organizes the high frequency computation using a multidirectional and multiscale strategy. Our algorithm is proved to have an optimal O(NlogN) computational complexity for any given accuracy when the points are sampled from a two-dimensional surface.     

非理想性对B-Z反应体系时间自组织的影响

从理论和实验上研究了非理想性对B Z反应体系时间自组织行为的影响 ,重点考察了加入惰性电解质对B Z反应体系振荡周期的影响 ,按照Oregonator模型 ,通过小寄生参数法动力学理论分析表明 ,非理想性对B Z反应体系振荡周期的影响体现在振荡周期与铈离子的活度系数成反比 ,而且惰性电解质的加入使得振荡周期进一步加长 .通过一系列实验观测 ,原则上得到了与理论分析一致的结论     

不同湿化状态下压实红黏土的压缩特征

为模拟路基土体在不同湿度状态下的压缩特征,以湖南长沙－韶山－娄底高速公路的红黏土路基填料为研究对象,开展吸水自由膨胀、吸水限制膨胀和不浸水等三种湿化状态下的压缩实验研究。本文根据实际应力与固结屈服应力的关系提出确定土体压缩系数的改进方法,并与目前规范中推荐的压缩系数(a_1-2)进行了比较,验证了改进方法更加合理。然后,对比分析不同湿化状态下的压缩指标。结果表明：吸湿后的土体压缩性均大于不浸水土的压缩性;但浸水吸湿限制膨胀和浸水吸湿自由膨胀后再压缩,前者的压缩性要大于后者的压缩性。最后,从孔隙结构的细观角度探讨了固结应力对土体孔隙结构的作用模式,发现固结作用主要影响孔径d>10μm范围内的孔隙分布。     

Numerical modeling of the turbulent viscous-gas flow past a cylinder with a circular vortex cell in the presence of suction from the central body surface

The compressibility effect on the cylinder drag reduction due to air suction through the surface of a central body in a circular vortex cell is estimated on the basis of the solution of the steady Reynolds equations closed by the shear stress transfer model, together with the continuity, energy, and state equations.     

The rheology of bread dough made from four commercial flours

 A selection of four commercial flours has been subjected to extensive rheological measurements as part of a comprehensive program of wheat improvement. The results have been used to determine which of the many types of rheological measurements provide significant discrimination between various types of modern baker's flours (including biscuit flours) and to procure data suitable for use in mathematical models describing the dough rheology. The rheological measurements undertaken include oscillatory shear at low amplitude, steady shear at a low shear rate, stress relaxation and extensional viscosity testing. Although oscillatory shear data show minor differences between these flours, the other tests show significant variations and these provide very good discrimination between the different flour types in comparison with conventional dough testing (e.g. by the extensograph). The current dough rheological measurements provide further insight into molecular structure. In the future, mathematical (constitutive) models are expected to provide a means of predicting processing and baking behaviour of bread dough. Received: 27 June 2001 Accepted: 28 August 2001