微分特征列法在拟微分算子和Lax表示中的应用

微分特征列法用于拟微分算子和非线性发展方程Lax表示的计算.首先,利用微分特征列法和微分带余除法计算拟微分算子的逆和方根,由于不必求解常微分方程组,并将解代入,因此,使得计算得以简化.其次,利用微分特征列法,约化从广义Lax方程和Zakharov-Shabat推出的非线性偏微分方程,并得到相应的非线性发展方程.在Mathematica计算机代数系统上,编写了相关程序,从而可以利用计算机辅助完成一些非线性发展方程Lax表示的计算.     

无界时滞中立型微分大系统的不稳定性

本文采用Ｌｉａｐｕｎｏｖ函数法，研究了两类无界时滞的非线性中立型微分大系统的不稳定性，给出了一些简单、实用的代数判据，推广和改进了有关的研究。     

构造Lax表示的新算法

基于微分特征列法和微分带余除法,给出了利用拟微分算子构造非线性发展方程1+1维和2+1维Lax表示的新算法.新算法减少了运算步骤,简化了计算过程,是微分特征列法在可积系统领域一个新的应用.     

具有非线性边界条件的向量边值问题的奇摄动

该文利用微分不等式理论证明了具有非线性边界条件的非线性系统摄动解的存在，并给出了解的按分量直到O（εN 1）的一致有效的估计．     

二阶非线性微分方程解的Sturm比较定理

本文首先建立二个微分恒等式，然后利用它们研究了二类非线性微分方程与线性微分程之间解的Ｓｔｕｒｍ比较定理，所得结论包含了一些经典的结论     

非线性Robin边值问题的奇摄动

本应用微分不等式的方法，研究非线性Robin边值问题：     

二阶微分方程非振动的必要与充分条件

本文证明了一个微分恒等式，得到了二阶非线性微分方程非振动的一个充要条件，研究了一类二阶微分方程的振动性质，推广了现有的结果。     

二阶非线性微分方程解的Sturm比较定理

通过几个微分不等式建立了一类非线性微分方程解的Sturm比较定理，推广了一些经典的结论。     

一类微分代数系统的受控不变分布及其不变性

针对一类非线性微分代数系统,利用M导数方法,给出了受控不变分布的概念,并讨论了此类微分代数系统受控不变分布的一些性质.给出了一个计算包含在系统输出核(kerE(h))内的最大受控不变分布的算法,同时讨论了该算法的一些性质.最后,给出一个例子说明如何利用给出的算法计算微分代数系统的包含在系统输出核内的最大受控不变分布.     

微分连续正则化方法与一维声波方程系数反演问题求解

本文将求解非线性方程组的微分连续法与求解不问题的Ｔｉｋｈｏｎｏｖ正则化方法结合起来，形成了兼有大范围收性与稳定性的“微分连续正则化方法”，给出了方法的收敛性分析，文中最后给出的关于一维波动方程反问题的计算实例表明了方法的有效性。     

Lukasiewicz-based merging possibilistic networks

Possibility theory provides a good framework for dealing with merging problems when information is pervaded with uncertainty and inconsistency. Many merging operators in possibility theory have been proposed. This paper develops a new approach to merging uncertain information modeled by possibilistic networks. In this approach we restrict our attention to show how a “triangular norm” establishes a lower bound on the degree to which an assessment is true when it is obtained by a set of initial hypothesis represented by a joint possibility distribution. This operator is characterized by its high effect of reinforcement. A strongly conjunctive operator is suitable to merge networks that are not involved in conflict, especially those supported by both sources. In this paper, the Lukasiewicz t-norm is first applied to a set of possibility measures to combine networks having the same and different graphical structures. We then present a method to merge possibilistic networks dealing with cycles.     

Dynamic frictionless contact with adhesion

A model for the dynamic, adhesive, frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modeled by a bonding field on the contact surface. The contact is described by a modified normal compliance condition. The tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem is established, together with a partial regularity result. The existence proof proceeds by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space.     

Peters v. Roseau: Resolution of a conflict on the classical beach problem

A discrepancy is uncovered between two well documented solutions, to the uniquely solvable classical linearised sloping beach problem, by Peters in 1952 and independently by Roseau also in 1952 (though subsequently adjusted by personal correspondence from Roseau and Lehman to authors Wehausen & Laitone in 1960). The source of the main error (and other more minor errors) is identified, quantified and corrected and a consequence is that a study by Morris in 1976 (on a generalisation where the line source is no longer confined to the origin) will also have suffered from this deficiency. That problem therefore requires a re-visit.     

广义LQ最优控制问题的极小化序列

将经典LQ问题的评价泛函中关于控制变量的二次型推广为一类偶次多项式,证明了这类广义LQ无约束最优控制问题的一个等价扩张逼近可由一列半径递增的球约束最优控制问题加以实现.进而利用P0ntryagin极值原理建立相应的球约束最优控制问题的二次规划,并通过Canonical倒向微分流及不动点定理,求解常微分方程边值问题,得到球约束最优控制问题的最优值.随着约束球半径趋于无穷大,形成原广义LQ最优控制问题的一个极小化序列,从而得到原问题的最优值.     

Structural properties and recognition of restricted and strongly unimodular matrices

A (0, ±1) matrix A is restricted unimodular if every matrix obtained from A by setting to zero any subset of its entries is totally unimodular. Restricted unimodular matrices are also known as matrices without odd cycles. They have been studied by Commoner and recently Yannakakis has given a polynomial algorithm to recognize when a matrix belongs to this class. A matrix A is strongly unimodular if any matrix obtained from A by setting at most one of its entries to zero is totally unimodular. Crama et al. have shown that (0,1) matrix A is strongly unimodular if and only if any basis of (A, 1) is triangular, whereI is an identity matrix of suitable dimensions. In this paper we give a very simple algorithm to test whether a matrix is restricted unimodular and we show that all strongly unimodular matrices can be obtained by composing restricted unimodular matrices with a simple operation. Partially supported by a New York University Research Challenge Fund Grant.     

Piecewise monotone interpolation

In reaction to a recent paper by E. Passow in this Journal, it is shown that broken line interpolation as a scheme for piecewise monotone interpolation is hard to improve upon. It is also shown that a family of smooth piecewise polynomial interpolants, introduced by Swartz and Varga and noted by Passow to be piecewise monotone, converges monotonely, for fixed data, to a piecewise constant interpolant as the degree goes to infinity. Finally, piecewise monotone interpolation by splines with simple knots is discussed.     

A new model and hybrid approach for large scale inventory routing problems

This paper studies an inventory routing problem (IRP) with split delivery and vehicle fleet size constraint. Due to the complexity of the IRP, it is very difficult to develop an exact algorithm that can solve large scale problems in a reasonable computation time. As an alternative, an approximate approach that can quickly and near-optimally solve the problem is developed based on an approximate model of the problem and Lagrangian relaxation. In the approach, the model is solved by using a Lagrangian relaxation method in which the relaxed problem is decomposed into an inventory problem and a routing problem that are solved by a linear programming algorithm and a minimum cost flow algorithm, respectively, and the dual problem is solved by using the surrogate subgradient method. The solution of the model obtained by the Lagrangian relaxation method is used to construct a near-optimal solution of the IRP by solving a series of assignment problems. Numerical experiments show that the proposed hybrid approach can find a high quality near-optimal solution for the IRP with up to 200 customers in a reasonable computation time.     

Modeling and control of surface gravity waves in a model of a copper converter

Undesirable splashing appears in copper converters when air is injected into the molten matte to trigger the conversion process. We consider here a cylindrical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid dynamics in a transversal section of the converter is modeled by a 2-D inviscid potential flow involving a gravity wave equation with local damping on the liquid surface. Once the model is established, using a finite element method, the corresponding natural frequencies and normal modes are numerically computed in the absence of injection, and the solution of the system with injection is obtained using the spectrum. If a finite number of modes is considered, this approximation leads to a system of ordinary differential equations where the input is represented by the fluid injection. The dynamics is simulated as perturbations around a constant fluid injection solution, which is the desired operating state of the system, considering that the conversion process does not have to be stopped or seriously affected by the control. The solution is naturally unstable without control and the resulting increase of amplitude of the surface waves are assimilable to the splashing inside the converter. We show numerically that a variable flow around the operating injection is able to sensibly reduce these waves. This control is obtained by a LQG feedback law by measuring the elevation of the free surface at the point corresponding to the opposite extreme to where the nozzle injection is placed.     

Assessing problem complexity

The difficulty of objectively measuring the decision-making load imposed by a complex decision problem on a human decision maker is identified. It is suggested that a technique for such measurement would be useful in Operational Research. The secondary task technique, a method much used by psychologists and ergonomists to assess the mental processing load presented to subjects by a variety of tasks, is discussed. It is observed that the type of complex problem often of interest in Operational Research is characterised by the involvement of model building in the process of solution. An experiment is presented to compare the mental load presented by a number of different chess problems using a mental arithmetic secondary task, and it is shown that the method appears to be valid for the study of complex problems.