Almost diagonal systems of linear difference equations

Linear homogeneous difference systems of equations on an infinite interval are considered. Conditions are given which allow to represent a fundamental solution as a product of two square matrices. The product is made of a diagonal matrix and a matrix which is a perturbation of the identity. The diagonal matrix being on the left in the proposed product rather than on the right as it has been traditionally represented. A self contained theorem of asymptotic approximation is provided which is applied to a special family of difference systems. A theorem, utilizing a linear transformation, which is best possible in a certain sense, is also given.     

A Simulation Model for Production/Inventory Decisions

The paper describes initial simulation work on various factors associated with production and inventory decisions. The machine shop model which was used comprised one machine only on which a small product range is manufactured. The effects of variations in output mix and demand levels on the rate of return on investment is examined. The necessary adjustments in stocking policy for an economic level of capacity utilization are indicated, and a "capacity profile" is produced which reveals the efficient operating frontier for the different cases. The direction of further experiments is indicated.     

Dynamic and static loss in stability of flexible spherical shells made out of a composite material

The dynamic and static stability of shallow spherical shells which are rectangular in a plane are investigated. It is assumed that the shell is made out of a composite material which is weakly shear resistant and hence the refined theories which allow for transverse shear deformations and rotational inertia are applied. The solutions which were obtained are compared with solutions founded on the basis of the Kirchhoff-Love theory. It is shown that the results which are obtained on the basis of the classical theory are high for both the static and dynamic loss in stability, and are qualitatively different from the results obtained using the refined theory. The solutions were obtained using the Bubnov-Galerkin method in the higher approximations.     

Multiphase free discontinuity problems: Monotonicity formula and regularity results

The purpose of this paper is to analyze regularity properties of local solutions to free discontinuity problems characterized by the presence of multiple phases. The key feature of the problem is related to the way in which two neighboring phases interact: the contact is penalized at jump points, while no cost is assigned to no-jump interfaces which may occur at the zero level of the corresponding state functions. Our main results state that the phases are open and the jump set (globally considered for all the phases) is essentially closed and Ahlfors regular. The proof relies on a multiphase monotonicity formula and on a sharp collective Sobolev extension result for functions with disjoint supports on a sphere, which may be of independent interest.     

Double-pulse cotangential transfers between coplanar elliptic orbits

The geometric characteristics of double-impulse cotangential transfers between coplanar elliptic orbits, which are used to investigate of such transfers, are given. Each argument is accompanied by the development of a corresponding geometric algorithm which illuminates the mechanical problem from a geometric point of view, imparting the clarity to it which is characteristic of a geometric concept. A general method of investigation is developed based on a comparison of the behaviour of a cotangential transfer with an excentre of the transfer orbit which is joined to the excentres of the given elliptic orbits (an excentre is a circle constructed on the major axis of the ellipse which is its diameter). The cotangential transfer trajectory parameters and the values of the velocity pulses controlling the motion of the spacecraft during the transfer are determined in explicit form and depend on the parameters of the specified orbits and the true anomaly of the point of application of the first velocity pulse.     

Parallel block preconditioning based on SSOR and MILU

Two kinds of parallel preconditioners for the solution of large sparse linear systems which arise from the 2-D 5-point finite difference discretization of a convection-diffusion equation are introduced. The preconditioners are based on the SSOR or MILU preconditioners and can be implemented on parallel computers with distributed memories. One is the block preconditioner, in which the interface components of the coefficient matrix between blocks are ignored to attain parallelism in the forward-backward substitutions. The other is the modified block preconditioner, in which the block preconditioner is modified by taking the interface components into account. The effect of these preconditioners on the convergence of preconditioned iterative methods and timing results on the parallel computer (Cenju) are presented.     

Second-order elliptic integro-differential equations: viscosity solutions' theory revisited

The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen–Ishii's lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The proof of this result, which is of course a key ingredient to prove comparison principles, relies on a new definition of viscosity solution for integro-differential equation (equivalent to the two classical ones) which combines the approach with test-functions and sub-superjets.     

Preconditioned implicit solution of linear hyperbolic equations with adaptivity

This paper describes a method for solving hyperbolic partial differential equations using an adaptive grid: the spatial derivatives are discretised with a finite volume method on a grid which is structured and partitioned into blocks which may be refined and derefined as the solution evolves. The solution is advanced in time via a backward differentiation formula. The discretisation used is second-order accurate and stable on Cartesian grids. The resulting system of linear equations is solved by GMRES at every time-step with the convergence of the iteration being accelerated by a semi-Toeplitz preconditioner. The efficiency of this preconditioning technique is analysed and numerical experiments are presented which illustrate the behaviour of the method on a parallel computer.     

准时制下非核心企业最佳生产数学模型研究

通常,研究订单生产企业的生产计划求解模型往往只解决排产问题,制作的计划不能顾及各个方面的生产成本.其主要原因在于两个方面:一是,没有对由计划引发的成本作全面的考虑;二是,缺乏有效的成本表达方式,尤其是任意时间段内的各个产品的负荷总和以及能力波动费用的数学表达.研究了一种特殊的订单生产——准时制下非核心企业的生产,分析了计划范围内的成本,并分别就各种成本给出求解公式,尤其在能力波动费用的求解上,引进了符号函数,解决了在任意单位时间段内能力累计的数学表达以及能力波动费用的数学求解,在以上基础上给出了最佳生产的数学模型,给出了求解方法,讨论了最优解的存在条件,最后,讨论了在APS(A dvance P lan System)中的应用前景.     

Real-time Model Predictive Control of a Pendulum

In this work, a model predictive approach is applied on a mechanical system with a view on a real-time capable implementation. The mechanical system is represented by a pendulum, which consists of a sphere at the end of a long, thin rod. The rod is mounted on gimbals on a cross table, which can be moved by two DC motors. The control objective is trajectory tracking of the sphere, which can be realized by the control of these motors. In this work, linear model predictive control techniques are designed for the pendulum and are simulatively compared with regard to an accurate trajectory tracking and a real-time capable algorithm. A linear time-invariant approach is implemented on the experiment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A decomposition algorithm for the single machine total tardiness problem

The problem of sequencing jobs on a single machine to minimize total tardiness is considered. An algorithm, which decomposes the problem into subproblems which are then solved by dynamic programming when they are sufficiently small, is presented and is tested on problems with up to 100 jobs.     

基于关键因素的国家重大区域规划实施效果评价

以国家重大区域规划中的长三角为实证研究对象,利用加权灰色关联度筛选出与政策效果评价关联性高度相关的政策指标:中央财政专项拨款、中央补助收入、中央固定资产投资额,进而建立政策指标与规划目标的第三产业增加值的对数回归函数,通过过去的数据预测某一特定年份第三产业增加值,并与该年份的实际值进行对比、评价国家重大区域规划的政策效果。本文的特色与创新一是通过灰色关联度剔除与政策效果评价关联度小的指标,筛选出对重大区域规划政策效果有显著影响的关键因素。二是通过时间权向量对政策指标的关联度进行加权,体现时间越近的年份、加权灰色关联度越大,指标越应该保留的思路,保证年份越近的指标数据、对评价结果影响越显著。三是通过历史数据的预测,得到在没有规划政策下、区域自然发展的目标效果,并把其与同一时点、政策实施后的实际效果进行对比,得到政策实施后的政策绩效。实证结果表明应该增大对上海和浙江影响显著的中央财政专项拨款的政策投入,减少对上海和浙江影响不显著的中央固定资产投资额的投入。     

线性方程组的多维投影算法

本文分析了求解线性方程组的一维投影算法即最小剩余法。定义了长轴陷阱及陷阱深度，用它们刻划了该算法迭代过程中锯齿现象的几何特征。本文给出了基于残差序列的避开长轴陷阱的扰动技巧，即多维投影算法。数值试验表明，投影算法要优于现在流行的主要算法。     

基于信息熵的属性约简在多属性决策中的应用

属性约简是在信息系统中的一个重要操作.分类是属性约简的基础,且直接在大数据集上进行属性约简往往存在效率低下的问题.以分类为基础提出了一种基于信息熵的信息系统属性约简算法.算法通过信息熵的计算,在属性约简的同时对原信息系统逐层分解,从而实现了属性的约简并缩小了搜索空间.提出了依据信息熵来确定属性的不必要性及简约属性集,应用在多属性决策中所带来的优势.     

On the reduction (mod 1) of completely monotone functions (0, ∞)

Summary The Euler-Maclaurin summation formula and its harmonic analysis (Poisson) are applied to the case of functions which are completely monotone on an open half-line. What thus results is a curious class of Fourier series, which can be determined explicitly and which represent completely monotone functions on the first half of the period. A by-product is the complete monotony (on the first half-period) of the Bernoulli functions, whether the index is integral or fractional.     

Critical temperature of soliton state stability in quasi-one-dimensional systems

The temperature effect on soliton state formation in quasi-one-dimensional systems is considered in the self-consistent field approximation. The critical temperature above which soliton states are nonstable is shown to exist. The crirical temperature dependence on nonlinearity parameter and system dimension is found. Soliton density at which the critical temperature is maximal is calculated.     

Simulation of electrochemical machining using the boundary element method with no saturation

The simulation of electrochemical machining (ECM) is based on determining the surface shape at each point in time. The change in the shape of the surface depends on the rate of the electrochemical dissolution of the metal (conducting material), which is assumed to be proportional to the electric field strength on the boundary of the workpiece. The potential of the electric field is a harmonic function outside the two domains—the tool electrode and the workpiece. Constant potentials are specified on the boundaries of the tool electrode and the workpiece. A scheme with no saturation in which the strength of the electric field created by the potential difference on the boundary of the workpiece is proposed. The scheme converges exponentially in the number of grid elements on the workpiece boundary. Given the rate of electrochemical dissolution, the workpiece boundary, which depends on time, is found. The numerical solutions are compared with exact solutions, examples of the ECM simulation are discussed, and the results are compared with those obtained by other numerical methods and the ones obtained using ECM machines.     

Boolean Functions With Low Average Sensitivity Depend On Few Coordinates

. The sensitivity of a point is dist, i.e. the number of neighbors of the point in the discrete cube on which the value of differs. The average sensitivity of is the average of the sensitivity of all points in . (This can also be interpreted as the sum of the influences of the variables on , or as a measure of the edge boundary of the set which is the characteristic function of.) We show here that if the average sensitivity of is then can be approximated by a function depending on coordinates where is a constant depending only on the accuracy of the approximation but not on . We also present a more general version of this theorem, where the sensitivity is measured with respect to a product measure which is not the uniform measure on the cube. Received: November 12, 1996     

The maximum return-on-investment plant location problem

The standard plant location problem determines which plants to open from a set of potential sites in order to satisfy the demands at a set of customer vertices at a minimum total cost. However, the optimal solution may exceed a limit on investment costs imposed on the enterprise in a practical setting. This paper examines the plant location problem in an environment in which the investment in plant and equipment is also an objective to be minimised. The problem is posed as a bicriterion model which examines the tradeoff between the sum of operational and investment costs and investment cost (or total cost vs sunk cost). A weighting method is used to generate efficient solutions, one of which is shown to maximise the return on investment. The integer-friendliness of the LP relaxation is investigated.