格蕴涵代数中的扩张滤子

在格蕴涵代数中提出了扩张滤子的概念,讨论了扩张滤子与滤子,扩张滤子与素滤子,扩张滤子与滤子的根,扩张滤子与准素滤子,扩张滤子与最大滤子之间的关系.得到了扩张滤子的一些性质.最后,证明了在格H蕴涵代数中,扩张滤子与扩张滤子的根相等.     

A boundary integral formulation for elastically deformable particles in a viscous fluid

This paper reports a formulation and implementation of a mixed (both direct and indirect) boundary element method using the double layer and its adjoint in a form suitable for solving Stokes flow problems involving elastically deformable particles. The formulation is essentially the Completed Double Layer Boundary Element Method for solving an exterior traction problem for the surrounding fluid or solid phase, followed by an interior displacement, and a mobility problem (if required) for the elastic particles. At the heart of the method is a deflation procedure that allows iterative solution strategies to be adopted, effectively opens the way for large-scale simulations of suspensions of deformable particles to be performed. Several problems are considered, to illustrate and benchmark the method. In particular, an analytical solution for an elastic sphere in an elongational flow is derived. The stresslet calculations for an elastic sphere in shear and elongational flows indicate that elasticity of the inclusions can potentially lead to positive second normal stress difference in shear flow, and an increase in the tensile resistance in elongational flow.This work is supported by a grant from the Australian Research Grant Council. X-J F wishes to acknowledge the support of the National Natural Science Foundation of China.     

Ambient connections realising conformal Tractor holonomy

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal Tractor holonomy as affine holonomy of such a connection. We give an example of an ambient connection for which this is the case, and which is torsion free if we start the construction with a C-space, and in addition Ricci-flat if we start with an Einstein manifold. Thus, for a C-space this example leads to an ambient metric in the weaker sense of Čap and Gover, and for an Einstein space to a Ricci-flat ambient metric in the sense of Fefferman and Graham. Current address for first author: Erwin Schr?dinger International Institute for Mathematical Physics (ESI), Boltzmanngasse 9, 1090 Vienna, Austria Current address for second author: Department of Mathematics, University of Hamburg, Bundesstra?e 55, 20146 Hamburg, Germany     

Integrable Potentials by Darboux Transformations in Rings and Quantum and Classical Problems

We study a problem in associative rings of left and right factorization of a polynomial differential operator regarded as an evolution operator. In a direct sum of rings, the polynomial arising in the problem of dividing an operator by an operator for two commuting operators leads to a time-dependent left/right Darboux transformation based on an intertwining relation and either Miura maps or generalized Burgers equations. The intertwining relations lead to a differential equation including differentiations in a weak sense. In view of applications to operator problems in quantum and classical mechanics, we derive the direct quasideterminant or dressing chain formulas. We consider the transformation of creation and annihilation operators for specified matrix rings and study an example of the Dicke model.     

Minimising the number of gap-zeros in binary matrices

We study a problem of minimising the total number of zeros in the gaps between blocks of consecutive ones in the columns of a binary matrix by permuting its rows. The problem is referred to as the Consecutive Ones Matrix Augmentation Problem, and is known to be NP-hard. An analysis of the structure of an optimal solution allows us to focus on a restricted solution space, and to use an implicit representation for searching the space. We develop an exact solution algorithm, which is linear-time in the number of rows if the number of columns is constant, and two constructive heuristics to tackle instances with an arbitrary number of columns. The heuristics use a novel solution representation based upon row sequencing. In our computational study, all heuristic solutions are either optimal or close to an optimum. One of the heuristics is particularly effective, especially for problems with a large number of rows.     

A Hybrid Robust Adaptive Sliding Mode Controller for partially modelled systems: Discrete-time Lyapunov stability analysis and application

This work presents a new discrete-time Hybrid Robust Adaptive Sliding Mode Controller, developed from the union of a Robust Model Reference Adaptive Controller, an Adaptive Sliding Mode Controller, and an Adaptive One Sample Ahead Preview Controller in an unique control structure. Robust Model Reference Adaptive Controller is an adequate direct adaptive control strategy to control partially known plants, but can present slow closed-loop response to ensure global stability. Therefore, an adaptive One Sample Ahead Preview controller is incorporated to accelerate transient regimes, once it tries to track reference signal in one sample. Furthermore, an adaptive Sliding Mode Controller is also merged in the controller structure to help controller performance in transient regime and it also improves relevantly the steady state response in a scenario of several unmodelled dynamics Stability analysis of this controller using Lyapunov criterion and its robustness proof are provided, considering the plant subjected to unmodelled dynamics, which provides controller design constraints. These proofs show the controller is globally stable, and the tracking error tends to a residual set in steady state, even in the presence of matched and unmatched dynamics. Numerical simulations of the Hybrid Robust Adaptive Sliding Mode Controller applied on an unstable nonminimum-phase plant are presented, where only part of the overall plant is take into consideration for controller design. Results corroborate the feasibility and robustness of the developed control strategy and the performance superiority when compared to an adaptive One Sample Ahead Preview controller, with a 75% tracking error reduction in a scenario of several unmodelled dynamics.     

Enforced stability of an eigenvalue in the continuous spectrum of a waveguide with an obstacle

Perturbations of an eigenvalue in the continuous spectrum of the Neumann problem for the Laplacian in a strip waveguide with an obstacle symmetric about the midline are studied. Such an eigenvalue is known to be unstable, and an arbitrarily small perturbation can cause it to leave the spectrum to become a complex resonance point. Conditions on the perturbation of the obstacle boundary are found under which the eigenvalue persists in the continuous spectrum. The result is obtained via the asymptotic analysis of an auxiliary object, namely, an augmented scattering matrix.     

带鳍通道性能的遗传算法优化

与光滑通道相比,带鳍通道有更高的传热系数,附加的鳍,极大地增强了通道的传热.然而,传热的增强又与压降的升高相关联,这又导致泵动力需求的增加,因此应该寻求对该系统的优化设计.该文的主要目的是,通过如下方式来精确地确定鳍的位置和尺寸:利用遗传算法实现最小压降时达到最优传热.鳍的每种布局作为问题(遗传算法中的一个个体)的一个解.通常,首先随机地产生一个初始种群,然后该算法在所有这些解中搜索,利用布局函数迭代出新解,最后得到鳍的优化设计.     

Nonlocal diffusion,a Mittag-Leffler function and a two-dimensional Volterra integral equation

In this paper we consider a particular class of two-dimensional singular Volterra integral equations. Firstly we show that these integral equations can indeed arise in practice by considering a diffusion problem with an output flux which is nonlocal in time; this problem is shown to admit an analytic solution in the form of an integral. More crucially, the problem can be re-characterized as an integral equation of this particular class. This example then provides motivation for a more general study: an analytic solution is obtained for the case when the kernel and the forcing function are both unity. This analytic solution, in the form of a series solution, is a variant of the Mittag-Leffler function. As a consequence it is an entire function. A Gronwall lemma is obtained. This then permits a general existence and uniqueness theorem to be proved.     

An inner approximation method incorporating a branch and bound procedure for optimization over the weakly efficient set

In this paper, we consider an optimization problem which aims to minimize a convex function over the weakly efficient set of a multiobjective programming problem. From a computational viewpoint, we may compromise our aim by getting an approximate solution of such a problem. To find an approximate solution, we propose an inner approximation method for such a problem. Furthermore, in order to enhance the efficiency of the solution method, we propose an inner approximation algorithm incorporating a branch and bound procedure.     

政府花费改变对经济影响的理论分析

本文采用无限期内生时间偏好率模型,研究了政府花费对经济的影响.指出长期的政府花费增加可以使资本存量水平上升,消费水平下降和债券持有量上升;同时,短期分析表明政府花费增加可以减少初始投资率,增加政府债务率水平;但短期的政府花费增加同样导致资本存量水平上升,消费水平下降和债务水平的增加.     

Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics

The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.     

Revisiting a game theoretic framework for the robust railway network design against intentional attacks

This paper discusses and extends some competitive aspects of the games proposed in an earlier work, where a robust railway network design problem was proposed as a non-cooperative zero-sum game in normal form between a designer/operator and an attacker. Due to the importance of the order of play and the information available to the players at the moment of their decisions, we here extend those previous models by proposing a formulation of this situation as a dynamic game. Besides, we propose a new mathematical programming model that optimizes both the network design and the allocation of security resources over the network. The paper also proposes a model to distribute security resources over an already existing railway network in order to minimize the negative effects of an intentional attack. For the sake of readability, all concepts are introduced with the help of an illustrative example.     

Ovoids in finite uniform linear spaces

The concept of an ovoid is extended to linear spaces, and it is shown that a finite uniform linear space with an ovoid is either a trivial structure on a finite set, or else either two or three dimensional. In the three dimensional case, the ovoid is directly related to an inversive plane, in much the same way that an ovoid in a finite projective space is.Dedicated to Professor Tallini on the occasion of his 60th birthday     

Bifurcation of multimode flows of a viscous fluid in a plane diverging channel

The pattern of steady multimode flow of a viscous incompressible fluid in a plane diverging channel is constructed and investigated. It is shown that odd-mode flows have velocity profiles that are symmetrical about the axis of the channel and from one to three different flows with a fixed number of modes exist. The even-mode flows are asymmetric and exist as pairs. The existence of a denumerable set of finite ranges adjoining one another, in which a single-type of complex bifurcation of the flow occurs, is established in the case of an unbounded range of values of the Reynolds number. As the Reynolds number increases, transitions to flows with an increasing number of modes, containing domains of forward and backward flows, occur successively. Flow patterns with a smaller number of modes do not occur. An increase in the number of an range corresponding to an increase in the Reynolds number leads to an unlimited increase in the length of the range and the number of modes of permissible flows.     

Mathematic education in a cultural setting

The paper develops some proposals for curriculum development in mathematics based on an analysis of the intercultural transmission of mathematical knowledge. By introducing a concept of culture which calls for an analysis of individual and social behaviours, we are lead to recognize ‘ethnomathematics’ as a form of structured knowledge and to recognize ‘matheracy’ as a characteristic behaviour of human beings. Upon these two concepts, we introduce a theoretical framework for curriculum development in mathematics.

Curricular space is conceptualized as a three‐dimensional space with components, contents, methods and objectives considered solidarily. This relies upon an epistemology of action, based on an integration of episteme, techne and praxis. This allows for an approach in which theory and practice are in a dialectical relationship. Special reference is made to the problems of mathematical education for culturally differentiated groups, and in particular to the situation in third‐world countries.     

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.     

Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets

We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arbitrage assumption with a “no good-deal assumption” defined using an arbitrage-adjusted Sharpe ratio criterion we formulate the problem of computing the pricing and hedging of an American option in a financial market described by a multi-period, discrete-time, finite-state scenario tree as a large-scale mixed-integer conic optimization problem. We report computational results with off-the-shelf mixed-integer conic optimization software.     

Endogenous information acquisition in supply chain management

In this paper, we analyze an endogenous determination of efforts put into information acquisition and its impact on supply chain management. More specifically, we consider a supplier who sells a product to a buyer during a single selling season. Prior to placing an order with the supplier, the buyer has an option to acquire additional information about the demand by hiring experts (who are capable of providing forecasts). Because a commission fee must be paid to each hired expert, there exists a tradeoff between the cost and the value of the information, and the buyer needs to determine how much information to acquire. We derive the optimal information-acquisition level in an integrated setting and compare it with that determined in a decentralized setting. We also analyze several types of supply contracts to examine if they can coordinate the supply chain and allow an arbitrary division of system profit between the supplier and the buyer.     

非光滑泛函临界点理论的一个应用

本文利用局部Lipschitz泛函的临界点理论，来得到一个改进的半线性方程的Landesman Lazer型结果，问题来自于力学，称为变分不等式的特征值问题，在[3]中，D.Goeleven,D.Motreanu和P.D.Panagiotopoulos等人讨论了共振的情形，并得到了弱解的存在性的结果。但是，在他们结论中（见[3]中定理4．1），条件（H1）与（H2）却是互不相容的，本文得到了变分不等式的特征值问题在共振情形下的弱解存在性的相应结果。