一类二次问题的解法

以下一类系数含参变量的二次问题：已知二次函数在某闭区间上的最大（或最小）值，求参变量的值；已知二次不等式在某闭区间上为绝对不等式，求参变量的取值范围等，是常见的一类二次问题．解这一类问题，通常是通过考察相应的二次抛物线的开口方向以及与所给的闭区间的位置关系，按情况分类讨论，     

基于冷负荷需求的空调节能控制模型

针对商场中央空调的节能控制问题,首先建立了基于空调运行模式、经验值的冷负荷计算模型,给出了4种计算方法,并得出了人体冷负荷和照明电气设备冷负荷值的范围;然后对人流量分布进行合理假设,得出了商场冷负荷的函数表达式,讨论了冷负荷的误差范围,并用最小二乘方法对表达式进行了修正;再根据冷负荷的表达式建立了基于能量需求的空调节能模型,得出了制冷机组的控制策略,并给出了节能效果;最后计算出了基准冷负荷的值以及当商场温度升高1度基准冷负荷的减少比例.     

最小二乘问题及其研究

本文从理论上讨论了线性方程中最小二乘解的存在性及最小范数最小二乘解的唯一性，并给出求最小二乘解及最小范数最小二乘解的公式方法。     

定步长的连续极小化方法...

求解非线性方程组Ｆ（ｘ）＝０可转化为求非线性最小二乘问题ｍｉｎ１／２Ｆ（ｘ）＾ＴＦ（ｘ）的极小点。文章提出了一种求解上述非线性最小二乘问题的连续极小化方法，方法给出确定的步长，并证明具有整体和线性的收敛性。两个数值例子说明了方法的优越性。     

平面上的点-线选址问题

本文研究两类平面选址问题：（1）求一直线到n个给定点的加权距离和为最小；（2）求一点到n条给定直线的加权距离和为最小，对这两个非线性最优化问题，欠给出迭代次数为多项式的算法。     

平面上的min-max型点-线选址问题

本文研究两类平面选址问题：(1)求一直线到n个给定点的最大加权距离为最小；(2)求一点到n条给定直线的最大加权距离为最小．对这两个非线性优化问题，我们给出最优解的刻划及迭代次数为多项式的算法．     

最小p区间的定义及其应用

本文研究了 最小p区间的估计及应用.利用次序统计量得到了最小p区间的强相合估计,推广了求位置参数和刻度参数的估计方法.     

求三角函数最小正周期的一种方法

求三角函数最小正周期的一种方法２２４３００江苏射阳中学高一（８）班朱旭峰，匡建平指导老师钱军先有些求最小正周期问题，由于三角函数式较为复杂，用常规方法难以解决，但在许多资料和试题中又时有出现，本文介绍解这类问题的简便易行的方法─—运用函数的单调性化归...     

双矩阵变量Riccati矩阵方程对称解的迭代算法

研究一类双矩阵变量Riccati矩阵方程(R-ME)对称解的数值计算问题.运用牛顿算法求R-ME的对称解时,会导出求双矩阵变量线性矩阵方程的对称解或者对称最小二乘解的问题,采用修正共轭梯度法解决导出的线性矩阵方程约束解问题,可建立求R-ME的对称解的迭代算法.数值算例表明,迭代算法是有效的.     

双变量LMEs一种异类约束最小二乘解的MCG算法

借鉴求线性矩阵方程组(LMEs)同类约束最小二乘解的修正共轭梯度法,建立了求双变量LMEs的一种异类约束最小二乘解的修正共轭梯度法,并证明了该算法的收敛性.在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LMEs的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LMEs的极小范数异类约束最小二乘解.另外,还可求得指定矩阵在该LMEs的异类约束最小二乘解集合中的最佳逼近.算例表明,该算法是有效的.     

The study of structure optimization of blast furnace cast steel cooling stave based on heat transfer analysis

The three-dimensional mathematical model of temperature and thermal stress field of cast steel cooling stave in a blast furnace has been modeled. Kinds of the parameters optimization of cast steel cooling stave in a blast furnace are proposed based on the heat transfer analysis. The results indicate that the values of the parameters optimization for a cast steel cooling stave are 200 mm for cooling channels interdistance, 25 mm for inner radius of the water channel, 180 mm for thickness of the cooling stave body, 70 mm for thickness of inlaid brick and 1.5 m/s for speed of cooling water. Reducing the water temperature would be uneconomical. The water temperature can be chosen according to the local conditions. The best choice for lining material is silicon nitrogen bond silicon carbide brick or silicon carbide brick.     

On perturbed trapezoidal and midpoint rules

Explicit bounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.     

A cellular automaton model for boundary friction of PEEK and PEEK6

Nowadays a common material for journal bearings is PEEK (Polyetheretherketon) which is increasingly used under boundary friction. A Cellular Automaton model is developed to describe the boundary layer dynamics of PEEK and its composite PEEK6 sliding against a steel surface. Whereas PEEK is a homogeneous synthetic material, PEEK6 contains also carbon fibres for stability and fillers working as solid lubricants. The automaton shows a representative area of the real surface. The processes in the interface are described by a set of rules based on physical assumptions and measurements. Based on these rules the simulations show the dependency of friction and wear on the load spectrum. The discrete simulation allows to observe the topographic development of the PEEK and PEEK6 surface as well as the build-up of a transfer film on the steel surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The use of artificial intelligence technique for the optimisation of process parameters used in the continuous casting of steel

The productivity and quality of a continuous caster depend mainly on process parameters, i.e. casting speed, casting temperature, steel composition and cleanliness of the melt, water flow rates in the different cooling zones, etc. This work presents the development of an algorithm, which incorporates heuristic search techniques for direct application in metallurgical industries, particularly those using continuous casting process for the production of steel billets and slabs. This is done to determine the casting objectives of maximum casting rate as a function of casting constraints. These constraints are evaluated with the aid of a heat transfer and solidification model based on the finite difference technique, which has been developed and integrated with a genetic algorithm. The essential parts of continuous casting equipment, which must be subjected to monitoring, as well as a methodology of mathematical model and physical settlements in each cooling region, are presented. The efficiency of the intelligent system is assured by the optimisation of the continuous casting operation by maximum casting rate and defect-free products. This approach is applied to the real dimension of a steel continuous caster, in real conditions of operation, demonstrating that good results can be attained by using heuristic search, such as: smaller temperature gradients between sprays zones, reduction in water consumption and an increase in casting speed.     

THE MEASUREMENT OF WELFARE GAINS FROM GENETIC PROGRESS IN FORESTRY: GENERAL EQUILIBRIUM AND DISEQUILIBRIUM RESULTS

The paper contains an extension of existing results on the economics of tree improvement programs. The properties of the indirect utility function and the present value function are used to derive general equilibrium and disequilibrium cost–benefit rules for marginal projects resulting in an improved production function. Corresponding results for projects resulting in large second order effects in both prices and quantities are also provided, and indirect methods to estimate the net benefits are suggested. It is also briefly discussed how recreational and option values can be dealt with.     

Multiple crane scheduling in a batch annealing process with no-delay constraints for machine unloading

In this work, we focus on the scheduling of multi-crane operations in an iron and steel enterprise for a two-stage batch annealing process. The first stage is the heating process, and the second stage is the cooling process. To start the heating (cooling) stage, a special machine called a furnace (cooler) must be loaded. The real constraints of no-delay machine unloading are defined as follows: once the heating (cooling) is completed, the furnace (cooler) must be unloaded by crane immediately. The goal is to schedule limited machines (furnaces and coolers) operated by multiple cranes to minimize the completion time of the last annealed coil (makespan). We formulate a mixed-integer linear programming model to address this problem. Certain feasible properties are identified to avoid crane conflicts and ensure that the machine unloading no-delay constraints are met. Based on these necessary conditions, we then present a heuristic algorithm with running time in connection with the number of cranes, coils and machines. A lower bound to the problem is also developed. Through theoretical analysis, we show the worst-case bound of our heuristic algorithm. The average performances of the solution approaches are computationally evaluated. The computational results show that the proposed heuristic algorithm is capable of generating good quality solutions.     

First and second order sufficient conditions for strict minimality in nonsmooth vector optimization

In this paper we present first and second order sufficient conditions for strict local minima of orders 1 and 2 to vector optimization problems with an arbitrary feasible set and a twice directionally differentiable objective function. With this aim, the notion of support function to a vector problem is introduced, in such a way that the scalar case and the multiobjective case, in particular, are contained. The obtained results extend the multiobjective ones to this case. Moreover, specializing to a feasible set defined by equality, inequality, and set constraints, first and second order sufficient conditions by means of Lagrange multiplier rules are established.     

Convergence and Smoothness of Nonlinear Lane–Riesenfeld Algorithms in the Functional Setting

We investigate the Lane–Riesenfeld subdivision algorithm for uniform B-splines, when the arithmetic mean in the various steps of the algorithm is replaced by nonlinear, symmetric, binary averaging rules. The averaging rules may be different in different steps of the algorithm. We review the notion of a symmetric binary averaging rule, and we derive some of its relevant properties. We then provide sufficient conditions on the nonlinear binary averaging rules used in the Lane–Riesenfeld algorithm that ensure the convergence of the algorithm to a continuous function. We also show that, when the averaging rules are C ² with uniformly bounded second derivatives, then the limit is a C ¹ function. A canonical family of nonlinear, symmetric averaging rules, the p-averages, is presented, and the Lane–Riesenfeld algorithm with these averages is investigated.     

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.     

The Compatibility with Order of Some Subdifferentials

It is well known that elementary subdifferentials which are the simplest and the most precise among known subdifferentials do not enjoy good calculus rules, whereas more elaborated subdifferentials do have calculus rules but are not as precise and, in particular, do not preserve order. This paper explores an order preservation property for the subdifferentials of the second category. This property concerns the case in which a distance function is involved. It emphasizes the crucial role played by such functions in nonsmooth analysis. The result enables one to get in a simple, unified way the passage from the properties of subdifferentials for Lipschitzian functions to the same properties for the case of lower semicontinuous functions.