MENTAL CALCULATION STRATEGIES

In the light of new post-16 mathematics qualifications (Free Standing Mathematics Qualifications) and their associated curriculum innovation, we report a case study that illustrates how the implementation of new qualifications in a sixth form college affects a teacher's classroom practices and her students’ perceptions of, and attitudes to, mathematics. In discussing the background to, and context of, the curriculum development at the centre of this case study, we highlight the current importance of such innovation to policy makers who are seeking to develop this area of the mathematics qualifications framework. Our findings suggest that these new qualifications, as implemented in this particular case, can effect the changes that were originally desired. However, we conclude that there is a need for further substantial research that builds on this study if proposed changes to post-14 qualifications in mathematics are to be informed by knowledge of how such innovation may be successfully implemented more widely.     

多目标决策优序法

不少多目标决策方法先提供非劣解集,然后从中选出选好解.但当要选的选好解有多个时单从非劣解集中去找就不一定合理.优序法是一类对所有方案加以排序的方法.然后根据需要选择那些序数优的解.这类方法对定性、定量目标都能应用.本文证明了优序法给出的好解的非劣性方面的几个定理.方法曾在实践中应用,并与其它方法作了对比.     

KKT系统结构条件数与条件数的比较

本文讨论Karush-Kuhn_Tucker(KKT)系统的条件数．首先利用单参数展开方法建立了Byers型不等式,然后讨论结构条件数与条件数的定性比较,结果表明,在极端情形,条件数与结构条件数之比可以任意大．     

EVALUATING ALTERNATIVE MANAGEMENT STRATEGIES FOR ABALONE

Industry participation in co‐management has become a cornerstone of assessing the blacklip abalone, Halitois rubra, fisheries of South‐Eastern Australia. Engaging industry in developing and implementing management strategies is aimed at stemming recent trends of stock depletion and reduced harvest. An alternative to the current strategy for determining harvests is under consideration. A central question is: which management strategy is most likely to maintain sufficient biomass to produce consistent harvest rates into the future? This question is addressed using a Systems Dynamics modeling approach. We evaluated the two strategies of harvest management planning under (i) unchanging environmental conditions and (ii) following a high‐mortality event. To assess the performance of each strategy, an existing abalone model was used to estimate yield and mature biomass over three decades (>5 generations). A strategy using mean length of commercial catch as a novel performance measure generally provided a better path to recovery from the high‐mortality event than the current harvest threshold strategy.     

Mycielski图的循环色数

通过引入一类点集划分的概念,研究了Mylielski图循环染色的性质,证明了当完全图的点数足够大时,它的Mycielski图的循环色数与其点色数相等.     

OPTIMAL TRAPPING STRATEGIES FOR DIFFUSING NUISANCE-BEAVER POPULATIONS

This paper examines dynamically optimal trapping strategies for a resident beaver population causing damage to privately-held timber land. An extreme elimination strategy does not account for the dispersive behavior of neighboring beaver populations in filling the resulting environmental vacuum. This negative externality is accounted for by embedding an ecological model of small-mammal dispersive dynamics into an optimization framework minimizing the sum of discounted timber damage and trapping costs. The optimal balance that timber producers must strike between the benefits of leaving sufficient resident numbers to deter foreign invasions and the costs of timber damage caused by these “protectors” is characterized.     

A THEORETICAL COMPARISON OF THE TEACHING OF MENTAL CALCULATION STRATEGIES IN ENGLAND AND THE NETHERLANDS

This comparative study aims to identify the philosophical underpinnings of the principles of two approaches to the teaching of primary mathematics, the English Numeracy Strategy and the Dutch Realistic Mathematics Education and to discuss pedagogical implications. Philosophical views of knowledge as personal'subjective' and culturally'constructed' are considered in relation to inter subjectivity as a state of shared knowledge within a community of mathematicians. The didactics of the teaching of mental calculation strategies from the two approaches are used to illustrate a key epistemological difference in the mathematics that is presented to children.     

CONDITION NUMBER FOR WEIGHTED LINEAR LEAST SQUARES PROBLEM

In this paper, we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem： minx ｜｜Ax- b｜｜2, where A is an m-by-n （m ≥ n） rank deficient matrix. We first derive an explicit expression for the condition number in the weighted Frobenius norm ｜｜ [AT,βb] ｜｜F of the data A and b, where T is a positive diagonal matrix and β is a positive scalar. We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.     

连通无向图Rabin数的一个界

可靠性和有效性是互连网络设计的重要标准,而Rabin数是度量网络容错性和传输延迟的重要参数.将通过图的容错直径给出2- 连通无向图和~3- 连通无向图的~Rabin 数r_2(G)和r_3(G)的界;同时也得到r_2(G) = D_2(G)成立的一个条件.     

树的四类控制参数的束缚数

图的束缚数是图的控制数研究中的一个重要方面，它在某种程度上反映了图的控制数对边数的敏感度．本文通过对图的结构特征的分析．研究了树的四类控制参数的束缚数，即控制数，强控制数，弱控制数．分数控制数的束缚数．分别给出了其紧的上界．     

OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

This paper concerns an optimal dividend-penalty problem for the risk models with surplus-dependent premiums. The objective is to maximize the difference of the expected cumulative discounted dividend payments received until the moment of ruin and a discounted penalty payment taken at the moment of ruin. Since the value function may be not smooth enough to be the classical solution of the HJB equation, the viscosity solution is involved.The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation and the optimal dividend-penalty strategy has a band structure. Finally,some numerical examples with gamma distribution for the claims are analyzed.     

高波数Helmholtz方程的有限元方法和连续内罚有限元方法

本文介绍高波数Helmholtz方程的有限元方法和连续内罚有限元方法.将以线性元情形为例,给出方法的明显依赖于波数k的预渐近稳定性和误差分析.我们将介绍三种证明方法.我们还讨论了内罚有限元方法的罚参数的选取以显著减少方法的污染误差·最后还给出数值例子验证理论结果.     

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

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高波数波动问题的多水平方法

本文主要讨论求解高波数Helmholtz方程的多水平方法,主要回顾了一些具有代表性的多重网格方法.如Erlangga等人的shifted Laplacian预处理的多重网格法;Elman等提出的修正的多重网格方法;以及我们的基于连续内罚有限元(CIP-FEM)离散代数系统的多水平算法.最后还介绍了求解高波数时谐Maxwell方程的CIP-FEM离散代数系统的多水平算法.     

几类图弱控制的广义束缚数

对任一图G,其弱控制的束缚数,广义束缚数分别定义为bw(G)=min{|E‖E(∪)E(G),且γw(G-E)＞γω(G)}.b'ω(G)=min{t|(A)E(∪)E(G),如果|E|=t,则有γω(G-E)＞γw(G)}.在本文中我们给出了几类图的弱控制的广义束缚数的精确值,称b'ω(G)=1图为弱控制去边临界图,并研究了正则图是弱控制去边临界图的充要条件,以及一般图和树的必要条件.     

一种基于支持向量域描述的区间数分类

研究了基于数据的区间数智能决策分析,提出了一种基于区间数的支持向量域多分类软计算方法,该方法可以直接处理特征空间为区间数的多分类问题,拓展了支持向量域多分类算法应用的范围.     

EXPECTED NUMBER OF ITERATIONS OF INTERIOR-POINT ALGORITHMS FOR LINEAR PROGRAMMING

We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the expected and anticipated number of iterations of theseTodd‘s probabilisticalgorithms is bounded above by O(n^1.5). The random LP problem is model with the Cauchy distribution.     

高波数问题的超收敛性

 本文考虑求解Helmholtz方程的有限元方法的超逼近性质以及基于PPR后处理方法的超收敛性质.我们首先给出了矩形网格上的p-次元在收敛条件k（kh）^2p+1≤C₀下的有限元解和基于Lobatto点的有限元插值之间的超逼近以及重构的有限元梯度和精确解之间的超收敛分析.然后我们给出了四边形网格上的线性有限元方法的分析.这些估计都给出了与波数k和网格尺寸h的依赖关系.同时我们回顾了三角形网格上的线性有限元的超收敛结果.最后我们给出了数值实验并且结合Richardson外推进一步减少了误差.     

OPTIMIZING SPATIAL AND DYNAMIC POPULATION-BASED CONTROL STRATEGIES FOR INVADING FOREST PESTS

This paper explores spatial optimization approaches to managing invading exotic forest pests. The relevant land planning area is divided into cells, and pest population growth and dispersal are modeled with linear, continuous-variable formulations. Management actions are limited to those that apply directly to pest extermination, as opposed to host-oriented management actions. A stylized case example is used to demonstrate the potential application of the model formulation and to show that simple spatial strategies such as “barrier zone” approaches to slowing an organism's invasion may not always be optimal.     

权益连结生存人寿保险合同的局部风险最小对冲策略

权益连结生存人寿保险合同是保险金依赖于某类特定股票的价格的保险合同 .本文主要利用Schweizer[3]引入的不完全市场的局部风险最小理论确定单位关联人寿保险合同的局部风险最小对冲策略 .