Enumeration of the doubles of the projective plane of order 4

A classification of the doubles of the projective plane of order 4 with respect to the order of the automorphism group is presented and it is established that, up to isomorphism, there are 1 746 461 307 doubles. We start with the designs possessing non-trivial automorphisms. Since the designs with automorphisms of odd prime orders have been constructed previously, we are left with the construction of the designs with automorphisms of order 2. Moreover, we establish that a 2-(21,5,2) design cannot be reducible in two inequivalent ways. This makes it possible to calculate the number of designs with only the trivial automorphism, and consequently the number of all double designs. Most of the computer results are obtained by two different approaches and implementations.     

Duality of a Nonconvex Sum of Ratios

For mathematical programs with objective involving a sum of ratios of affine functions, there are few theoretical results due to the nonconvex nature of the program. In this paper, we derive a duality theory for these programs by establishing their connection with geometric programming. This connection allows one to bring to bear the powerful theory and computational algorithms associated with geometric programming.     

生态系统的参数确定问题

通过不同观测数据研究捕食者—被捕食者生态系统参数确定问题.研究了四种情形1.观察数据无误差,并已知一个参数值.这种情况下,参数可由其相轨线和最小二乘法精确确定.2.观察数据无误差,但所有参数未知.此时仅靠相轨线的研究,无论给出多少组精确数据,都无法精确确定这些参数.通过原非线性模型的数值计算和网格搜索法,至少需要4组数据,同样得到了精度较高的参数值.3.当观测数据有误差时,根据解的周期性,引入标准周期的概念,在一个标准周期里讨论参数的确定问题,并利用标准周期内的捕食者与被捕食者的数量均值与系统的平衡点的关系对参数进行修正,然后使用网格法进行搜索,进一步提高了参数的精度.4.当观测时间也有误差时,先选取相对最优的随机正态数对观测时刻进行修正,然后再利用3.的方法估计参数.     

Investigation of velocity dependence of rolling frictions as a means of studying adhesion

Investigation of the rolling of two cylinders on the device described in this paper has shown that a study of the rolling friction of bodies coated with polymer films offers a means of investigating adhesion processes. It has been found that the resistance to rolling of bodies coated with nonadhesive polymers has a tendency to increase with increase in velocity, in accordance with the electrical theory of adhesion. The resistance to rolling of bodies coated with adhesive polymers passes through a maximum as the velocity increases and then decreases, in accordance with the diffusion theory of adhesion.Mekhanika Polimerov, Vol. 1, No. 4 pp. 117–122, 1965     

Partial stability analysis of some classes of nonlinear systems

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.     

The effect of discretization on the numerical simulation of the vibrations of the impacting cantilever beam

We study the dynamics of a cantilever beam with an unnegligible large mass and with a concentrated mass fixed at the end, which impacts on the base during motion. Generally to model such a system, the finite element method with appropriate number of degrees of freedom has to be employed. However, to analyse some selected aspects of its dynamic behaviour, particularly to predict if the motion with impacts will be periodic, lower-dimensional substitutive models with one degree or two degrees of freedom can be employed. The way to determine the parameters of such models and their applicability limits are discussed.     

Measurability of automorphisms of topological groups

Relations between the measurability and continuity of algebraic automorphisms of topological groups depending on the types of groups are examined. Various cases are considered and theorems on the continuity of measurable automorphisms are proved; for instance, such theorems are proved for separable locally compact groups and automorphisms measurable with respect to nonnegative Haar measures. On the other hand, examples of nonmetrizable nonseparable compact groups with Haar measures and of non-locally-compact separable metrizable groups with measures μ quasi-invariant with respect to dense subgroups admittings μ-measurable discontinous automorphisms are given. Translated fromMatenmaticheskie Zametki, Vol. 68, No. 1, pp. 105–112, July, 2000. An erratum to this article can be found online at .     

Stabilization of the stationary motions of non-holonomic mechanical systems

The possible stabilization of the unstable stationary motions of a non-holonomic system is studied from the standpoint of general control theory /1, 2/. As distinct from the case previously considered /3/, when forces of a certain structure are applied with respect to both positional and cyclical coordinates, the stabilization is obtained here by applying control forces only with respect to the cyclical coordinates /4/; the control forces may be applied with respect to some or all of the cyclical coordinates, and depend on the positional coordinates, the velocities, and the corresponding cyclical momenta. It is shown that, just as in the case of holonomic systems /5, 6/, depending on the control properties of the corresponding linear subsystem, the stationary motions, whether stable or unstable, can be stabilized, up to asymptotic stability with respect to all the phase variables, or asymptotic stability with respect to some of the phase variables and stability with respect to the remaining variables. The type of stabilization with respect to the given phase variables depends on the Lyapunov transformations which are needed in order to reduce the critical cases obtained to singular cases /7, 8/.     

Existence of periodic solutions of sublinear Hamiltonian systems

The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.     

Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications

A survey is given of old and new results on the sensitivity of solutions to systems of optimality conditions with respect to parametric perturbations. Results of this kind play a key role in subtle convergence analysis of various constrained optimization algorithms. General systems of optimality conditions for problems with abstract constraints, Karush-Kuhn-Tucker systems for mathematical programs, and Lagrange systems for problems with equality constraints are examined. Special attention is given to the cases where the traditional constraint qualifications are violated.     

Measure of noninvertibility of minimal maps

Minimal maps in compact metric spaces are known to be almost one-to-one. Thus, the set of points with more than one preimage is of first category. In the present paper we study the measure of this set with respect to the invariant measures of the considered minimal map. Among others, we give an example of a minimal self-mapping of a continuum such that the set of points with more than one preimage has positive measure for every invariant measure.     

A heuristic approximation of the worst case of Shellsort

A heuristic algorithm is presented to construct permutations which require as many moves in sorting by Shellsort as possible. The approximations obtained are compared with those found by other known methods. Experiments were performed with up ton=2047 elements to be sorted, and the results show the distinct superiority of the heuristic approximations. The actual times needed by Shellsort to sort the worst permutations achieved were determined and compared with the corresponding times of Shellsort in the average case, as well as with the times of quicksort and heapsort in their worst cases.     

波纹壳的格林函数方法

应用轴对称旋转扁壳的基本方程,研究了在任意载荷作用下具有型面锥度的浅波纹壳的非线性弯曲问题·　采用格林函数方法,将扁壳的非线性微分方程组化为非线性积分方程组·　再使用展开法求出格林函数,即将格林函数展成特征函数的级数形式,积分方程就成为具有退化核的形式,从而容易得到非线性代数方程组·　应用牛顿法求解非线性代数方程组时,为了保证迭代的收敛性,选取位移作为控制参数,逐步增加位移,求得相应的载荷·　在算例中,研究了具有球面度的浅波纹壳的弹性特征·　结果表明,由于型面锥度的引入,特征曲线发生显著变化,随着荷载的增加,将出现类似扁球壳的总体失稳现象·　本文的解答符合实验结果·     

Scaling Properties of Flood Peaks

The scaling behavior of flood peak distributions is examined using a statistical model of the spatio-temporal distribution of rainfall and a hydrological model that describes the transformation of rainfall to discharge within a drainage network. Of particular interest is the empirical observation made by a number of investigators that the coefficient of variation (CV) of annual flood peaks for a region increases with drainage area up to drainage areas of approximately 100 km², and decreases with drainage area for larger drainage basins. This observation is neither consistent with simple scaling models, in which the coefficient of variation does not vary with drainage area, nor multiscaling models, in which the coefficient of variation decreases monotonically with drainage area. Model analyses illustrate that knowledge of the spatial and temporal organization of the rainfall, together with the details of the network structure of the drainage basin, is sufficient information with which to explain the observed behavior of sample CV. The interaction between the temporal variability of rainfall, relative to basin size, and the network structure is shown to be of particular importance.     

Systems of partial differential equations of mixed hyperbolic-parabolic type

We prove the global existence and uniqueness of solutions of certain mixed hyperbolic-parabolic systems of partial differential equations in one space dimension with initial data that is assumed to be pointwise bounded with possibly large oscillation and with small total energy. The systems we consider are general enough to include the Navier-Stokes equations of compressible flow, the equations of compressible MHD, models of chemical combustion, and others. In particular, the application of our results to the MHD system gives an existence result which is new.     

货物列车的编组调度问题

研究的是货物列车的编组和调度问题.通过对问题的深入研究,设计了一种车辆编组调度方案的算法.按照这种算法,在数据处理的基础上利用VC编写每个问题的处理程序,实现了对列车的快速安全高效的调度.对每个问题进行处理,都得到符合要求的结果.问题一首先对整个车辆编组调度的问题进行分析,在尽量保证新组装列车满载的基础上,使每班的中时尽可能少.为此,本文解决了两个关键问题:一是选车问题,二是拆解重组的问题.采用梯形方案对列车车辆进行编队重组,对选车问题主要采用按照时间先后顺序的选车方案,然后通过启发式算法配合遗传算法的选车方案对按时间先后顺序的方案进行检验.从编写的VC程序的运行结果来看,两种方案都可得到满意的结果,遗传算法得到的结果更为合理.另外,为了达到中时最短,采用双推双滑的方式利用驼峰线,提高了调度效率,并在驼峰线和编组道之间加入了碰撞检验模块,保证了列车调度时的安全性.问题二的求解是在问题一的基础上对待拆列车按优先级进行分类.对优先级高的列车先进行拆解.救灾车辆最高,其次是军列和发往S1的车辆,最后是一般车辆.问题三的处理主要是在问题二的基础上,通过提前获得列车的相关信息来决定编组场的列车离开编组场的时刻,从而缩短车辆的中时.问题四在原有模型基础上对编组方案进行了修改,利用编写的VC程序重新计算了每班的中时和列车的调度方案.问题五主要分析了整个系统瓶颈所在,分析了提高资源利用率的可行性.最后,通过对站名的调整,达到了对地质灾害等对铁路系统的破坏突发情况的有效处理,并且进一步分析了如何提高车站的效率的调度方案和建议.     

Continuity of the feasible solution sets of probabilistic constrained programs

In this paper, we show the continuity of the feasibility set with respect to the reliability levels and with respect to the distribution of the random elements of a stochastic program with probabilistic constraints. Continuity is then used to obtain stability results for this type of stochastic program. An easy criterion is given for checking the conditions which guarantee the continuity of the feasibility set.The author wishes to thank Professor R. Wets for his comments.     

Existence and uniqueness of solutions of differential equations with respect to non-additive measures

By taking Sugeno-derivative into account, first, we investigate the existence of solutions to the initial value problems (IVP) of first-order differential equations with respect to non-additive measure (more precisely, distorted Lebesgue measure). It particularly occurs in the mathematical modeling of biology. We begin by expressing the differential equation in terms of ordinary derivative and the derivative with respect to the distorted Lebesgue measure. Then, by using the fixed point theorem on cones, we construct an operator and prove the existence of positive non-decreasing solutions on cones in semi-order Banach spaces. In addition, we also use Picard–Lindelöf theorem to prove the existence and uniqueness of the solution of the equation. Second, we investigate the existence of a solution to the boundary value problem (BVP) on cones with integral boundary conditions of a mix-order differential equation with respect to non-additive measures. Moreover, the Krasnoselskii fixed point theorem is also applied to both BVP and IVP and obtains at least one positive non-decreasing solution. Examples with graphs are provided to validate the results.     

基于现金流量的虚拟企业协同增值评估模型研究

虚拟企业是个开放性的复杂系统,其本质是协调成员企业的管理,提高和协调其有序性以达到协调增值的目的.基于现金流,通过黑箱理论与投入产出模型分别建立了成员企业、虚拟企业以及信息共享下的虚拟企业价值评估模型,通过比较三者的差值评估虚拟企业的协同增值效应.