The 2‐Blocking Number and the Upper Chromatic Number of PG(2,q)

A twofold blocking set (double blocking set) in a finite projective plane Π is a set of points, intersecting every line in at least two points. The minimum number of points in a double blocking set of Π is denoted by τ₂(Π). Let PG(2,q) be the Desarguesian projective plane over GF(q), the finite field of q elements. We show that if q is odd, not a prime, and r is the order of the largest proper subfield of GF(q), then τ₂PG(2,q))≤ 2(q+(q‐1)/(r‐1)). For a finite projective plane Π, let denote the maximum number of classes in a partition of the point‐set, such that each line has at least two points in some partition class. It can easily be seen that (?) for every plane Π on v points. Let , p prime. We prove that for , equality holds in (?) if q and p are large enough.     

The Cartesian product of hypergraphs

We show that every simple, (weakly) connected, possibly directed and infinite, hypergraph has a unique prime factor decomposition with respect to the (weak) Cartesian product, even if it has infinitely many factors. This generalizes previous results for graphs and undirected hypergraphs to directed and infinite hypergraphs. The proof adopts the strategy outlined by Imrich and ?erovnik for the case of graphs and introduces the notion of diagonal‐free grids as a replacement of the chord‐free 4‐cycles that play a crucial role in the case of graphs. This leads to a generalization of relation Δ on the arc set, whose convex hull is shown to coincide with the product relation of the prime factorization. © 2011 Wiley Periodicals, Inc. J Graph Theory     

工件优先级图为非连接图且含环的单机总加权拖期调度问题

为满足实际生产环境对工件加工顺序和工件到达时间的要求,提出了具有新特征的单机总加权拖期调度问题,其特点体现在:工件有动态到达时间,且由工件优先级关系构成的优先级图为非连接图且存在环的情况,对该问题建立数学规划模型,在扩展Tang和Xuan等的基础上,提出了结合双向动态规划的拉格朗日松弛算法求解该问题。在该算法的设计中,提出双向动态规划算法求解拉格朗日松弛问题,使得它可处理优先级图中一个工件可能有多个紧前或紧后工件的情况,采用次梯度算法更新拉格朗日乘子,基于拉格朗日松弛问题的解设计启发式算法构造可行解。实验测试结果显示,所设计的拉格朗日松弛算法能够在较短的运行时间内得到令人满意的近优解,为更复杂的调度问题的求解提供了思路。     

非等温气固两相各向同性湍流的直接数值模拟

本文对非等温气固两相各向同性湍流中颗粒及颗粒所见流体温度的统计行为进行了直接数值模拟研究,系统地讨论了颗粒惯性的影响。对于Tp/Tk<1的颗粒,其温度脉动随惯性增大而减弱;对于Tp/Tk>1的颗粒,其趋势相反。颗粒及颗粒所见流体温度的自相关都随颗粒惯性的增加而减弱,而且随颗粒惯性的增加,颗粒所见流体温度的自相关比颗粒自身温度的自关联下降得快。     

球缺药型罩爆炸成型弹丸数值模拟

 利用LS-DYNA软件提供的二维轴对称拉格朗日计算编码,对钻地弹前级球缺形药型罩爆炸成型弹丸问题进行了数值模拟。讨论了计算方法的选取依据,考察了典型的射弹形成过程、壳体飞散过程以及射弹速度与动能,分析了不同模型的计算结果差异,实验结果与计算符合很好。     

The existence of regular self-complementary 3-uniform hypergraphs

A k-uniform hypergraph with vertex set V and edge set E is called t-subset-regular if every t-element subset of V lies in the same number of elements of E. In this paper we show that a 1-subset-regular self-complementary 3-uniform hypergraph with n vertices exists if and only if n≥5 and n is congruent to 1 or 2 modulo 4.     

A high‐order fully explicit flux‐form semi‐Lagrangian shallow‐water model

A new approach is proposed for constructing a fully explicit third‐order mass‐conservative semi‐Lagrangian scheme for simulating the shallow‐water equations on an equiangular cubed‐sphere grid. State variables are staggered with velocity components stored pointwise at nodal points and mass variables stored as element averages. In order to advance the state variables in time, we first apply an explicit multi‐step time‐stepping scheme to update the velocity components and then use a semi‐Lagrangian advection scheme to update the height field and tracer variables. This procedure is chosen to ensure consistency between dry air mass and tracers, which is particularly important in many atmospheric chemistry applications. The resulting scheme is shown to be competitive with many existing numerical methods on a suite of standard test cases and demonstrates slightly improved performance over other high‐order finite‐volume models. Copyright © 2014 John Wiley & Sons, Ltd.     

Schwinger’s effective lagrangian from reflection and transmission amplitudes

The reflection and transmission amplitudes are defined from the asymptotic form of the solution of Dirac equation of a charged fermion in the presence of uniform time independent external electromagnetic field (E, H). Schwinger’s effective lagrangian is derived from the reflection and transmission amplitudes. It is found that both the real and imaginary parts of the effective lagrangian agree with Schwinger’s expressions derived from the elegant method of proper time formalism.     

Lagrangian Particle Approach to Large Eddy Simulations of Hydrodynamic Turbulence

The flux of energy from large to small scales in hydrodynamic turbulence controls the dissipation of energy at a given scale in the fluid. An accurate parametrization of this flux is a prerequisite in order to devise reliable methods to simulate turbulent flows without resolving all the scales of motion. This problem is discussed in the context of a particle method based on the Smooth Particles Hydrodynamics algorithm. Motivated by the von Karman–Howarth–Kolmogorov exact relation for the energy flux, and by Lagrangian dynamics considerations we postulate an energy transfer term which is quadratic in the velocity and formally time reversal invariant. The numerical simulation of the model however is observed to spontaneously break the time reversal symmetry, demonstrating that the proposed term acts on average as the desired eddy damping.     

A Bernstein type theorem for minimal volume preserving maps

We show that any minimal volume preserving map from the Euclidean plane into itself is a linear diffeomorphism. We derive this from a similar result on minimal diffeomorphisms. We also show that the classical Bernstein theorem on minimal graphs is a corollary of our result.