A well‐balanced upstream flux‐splitting finite‐volume scheme for shallow‐water flow simulations with irregular bed topography

This study extends the upstream flux‐splitting finite‐volume (UFF) scheme to shallow water equations with source terms. Coupling the hydrostatic reconstruction method (HRM) with the UFF scheme achieves a resultant numerical scheme that adequately balances flux gradients and source terms. The proposed scheme is validated in three benchmark problems and applied to flood flows in the natural/irregular river with bridge pier obstructions. The results of the simulations are in satisfactory agreement with the available analytical solutions, experimental data and field measurements. Comparisons of the present results with those obtained by the surface gradient method (SGM) demonstrate the superior stability and higher accuracy of the HRM. The stability test results also show that the HRM requires less CPU time (up to 60%) than the SGM. The proposed well‐balanced UFF scheme is accurate, stable and efficient to solve flow problems involving irregular bed topography. Copyright © 2009 John Wiley & Sons, Ltd.     

Algebraic obstructions and a complete solution of a rational retraction problem

For each compact smooth manifold containing at least two points we prove the existence of a compact nonsingular algebraic set and a smooth map such that, for every rational diffeomorphism and for every diffeomorphism where and are compact nonsingular algebraic sets, we may fix a neighborhood of in which does not contain any regular rational map. Furthermore is not homotopic to any regular rational map. Bearing in mind the case in which is a compact nonsingular algebraic set with totally algebraic homology, the previous result establishes a clear distinction between the property of a smooth map to represent an algebraic unoriented bordism class and the property of to be homotopic to a regular rational map. Furthermore we have: every compact Nash submanifold of containing at least two points has not any tubular neighborhood with rational retraction.

     

Integrable deformations of integrable Hamiltonian systems

We give new effective necessary conditions for the integrability of nonhomogeneous potentials which are sums of two homogeneous terms. These conditions were deduced from an analysis of the differential Galois group of variational equations. We apply the obtained result to polynomial perturbations of linear oscillator with two degrees of freedom.     

The value of polynomials represented by norm forms

Let P(t) be a product of(possibly repeated) linear factors over Q and K/Q an abelian extension. Under a strict condition, we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the only one for any smooth proper model of the variety over Q defined by P(t) = NK/Q(x).     

内设半球条栅形障碍物的可燃气云爆炸实验研究

以混合比为13.3%的乙炔 空气混合物为介质进行了内设半球条栅形障碍物的可燃气云爆燃实验研究。通过对实验数据进行曲线回归,并经方差分析检验,得到了描述可燃气云爆燃压力场的拟合关系式。应用多能模型构想对半球形可燃气云内设半球条栅形障碍物的爆燃实验结果进行分析,得到综合考虑边界条件、混合物活性和尺度比例因子的爆燃超压关系式,为其它可燃气云在其它形式障碍物约束下的爆燃超压提出估算方法。     

Strong Approximation for a Toric Variety

Let X be a toric variety over a number field k with k[X]~×=k~×.Let W ■ X be a closed subset of codimension at least 2.We prove that X \ W satisfies strong approximation with algebraic Brauer-Manin obstruction.     

Algebraic signatures of convex and non-convex codes

A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as they arise from the activity of neurons that have convex receptive fields. In this paper, we develop algebraic methods to determine if a code is convex. Specifically, we use the neural ideal of a code, which is a generalization of the Stanley–Reisner ideal. Using the neural ideal together with its standard generating set, the canonical form, we provide algebraic signatures of certain families of codes that are non-convex. We connect these signatures to the precise conditions on the arrangement of sets that prevent the codes from being convex. Finally, we also provide algebraic signatures for some families of codes that are convex, including the class of intersection-complete codes. These results allow us to detect convexity and non-convexity in a variety of situations, and point to some interesting open questions.     

Bak groups and equivariant surgery II

The previous paper showed that theG-surgery obstructions ofG-normal maps lie in the Bak groups. That paper remarked that in even-dimensional cases, theG-surgery obstruction is invariant under suitable cobordisms. This paper presents cobordism invariance theorems for theG-surgery obstruction not only in even-dimensional cases but also in odd-dimensional ones. We prove Theorems B-D by detaching equivariant issues from the singular sets and then by using arguments of C. T. C. Wall in ordinary surgery theory. We still need, however, to argue carefully, especially in the odd-dimensional cases. Actually, this paper contains details which are skipped over in Wall's work.Partially supported by Grant-in-aid for Development of Young Scientists.Dedicated to Kazutoshi Morioka on his 60th birthday     

煤气火焰传播规律及其加速机理研究

研究了煤气/空气预混气在两端封闭管道中的火焰传播加速现象和管道中有无障碍物时火焰的加速机理,认为火焰加速是由于火焰前未燃气体被前驱压缩波加热和障碍物诱导的湍流区对燃烧过程的正反馈造成的。实验结果表明,障碍物存在时,最大爆炸压力可提高20%,与理论计算一致;火焰传播特性随煤气浓度的变化而改变;障碍物阻塞比对火焰的速度和压力都有一定影响。