具有遣赠动机的生命周期模型

本文研究遗赠动机对个人消费与储蓄的影响.利用解优化问题的一阶条件,得出在给定的条件下个人存在最优的消费流和遗产使得个人的终身效用达到最大化,当个人获得的收入或遗产增加时,个人将消费更多并留下更多的遗产.进一步,文中在四种具体的遗赠动机函数下研究了遗赠动机对个人消费与储蓄行为的影响,证明在后三种遗赠动机下,储蓄与遗产随遗赠动机的强度增加而赠加;在门槛动机下,随着门槛的提高,个人的消费上升,储蓄下降.     

ON THE VITALI-HAHN-SAKS-NIKODYM THEOREM

Abstract

The classical Vitali-Hahn-Saks-Nikodym Theorem [5, Thm. I.4.8] gives a limit criterion for when a sequence of strongly additive vector measures on a σ-field of sets having their range in a Banach space can be expected to be uniformly strongly additive. In [16, Cor. 8], Saeki proved that the limit condition on the sequence of vector measures could be substantially weakened as long as the Banach space in play is “good enough”. Saeki's result was based upon his work on a class of set functions too large to have Rosenthal's Lemma at his disposal. In Section 2, we prove Saeki's result with Rosenthal's Lemma at the basis of our work and then augment our characterization of Banach spaces enjoying Saeki's result in [1] with another natural equivalent condition. In Section 3 we extend Saeki's result to Boolean algebras having the Subsequential Interpolation property.     

关于可数点集的盒维数的一些探讨

本文研究了一类可数点集的盒维数的计算问题.通过构造双Lipschitz映射,把原可数点集的盒维数的求解问题转化为求解一类相对简单的可数点集的盒维数.获得了两个单调的可数点集在具有同阶间隔时具有相同的上盒维数和下盒维数的结论.该结论为计算一类可数点集的盒维数提供了方便.     

A SCALE FOR ASSESSING PROBABILISTIC THINKING AND THE REPRESENTATIVENESS TENDENCY

We report a study of children's probability conceptions and misconceptions using a diagnostic instrument developed from the literature on the representativeness heuristic. Rasch measurement methodology was used to develop the 13-item open response instrument with a sample (n=116) of 12-15 year olds. The result is that a hierarchy of responses at two levels is confirmed for this sample, and a third level is hypothesised. Each level is characterised by the ability to overcome typical 'representativeness' effects, namely 'recency', 'random-similarity' (at level 1), 'base-rate frequency' and 'sample size' (at level 2-3). The validity of our interpretations was tested and some anomalies were identified through clinical interviews with children making the errors (n=8). Another Rasch ability measure, which we named the 'representativeness tendency', was constructed from 11 multiple-choice errors.     

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.     

单纯形调优法的收敛性质

在非线性规划中,单纯形调优法是一种可信用的算法,然而却缺乏理论分析,本文对单纯形调优法的理论进行了一些研究,所考虑的方法类似于Spendley,Hext,Himsworth的正规单纯形调优法,但采用了不同的反映条件,其中带有某种下山门槛或具有三点下降形式,这里的基本思想是证明:上述单纯形调优法是定步长下山法的特殊情形,所以,此研究紧密联系着作者关于定步长下山法收敛定理的工作。     

THE CONVERSE OF HARTWICK'S RULE AND UNIQUENESS OF THE SUSTAINABLE PATH

ABSTRACT. We provide a constructive proof of the converse of Hartwick's rule for a generalization of Solow's model with one capital good and one exhaustible resource. We also show that the sustainable path is unique.     

MODELING THE EFFECT OF RARITY VALUE ON THE EXPLOITATION OF A WILDLIFE SPECIES SUBJECTED TO THE ALLEE EFFECT

The overexploitation of wildlife species is a serious problem in the field of biodiversity conservation. The species subjected to natural Allee effects are even more threatened by exploitation. Moreover, for many wildlife species, their rarity can fuel their exploitation by making them disproportionately desirable and consequently increasing their market price. In this paper, a mathematical model is proposed and analyzed to study how the value that consumers place on rarity can threaten the survival of a species subjected to natural Allee effects. It is assumed that the value of a species increases as its density declines. The analysis of model shows that the increase in the consumers' response to rarity can drive the system to admit Hopf‐bifurcation and heteroclinic bifurcation. The occurrence of the heteroclinic cycle indicates that the increase in consumers' response to rarity can cause the extinction of the species. It is found that an increase in the Allee threshold causes a decrease in the threshold value of consumers' response below which extinction is inevitable.     

THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS

Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple together the elementary uniform energy estimates of the global weak solutions and a well known Gronwall''s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980''s to study the optimal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay estimates with sharp rates of the global weak solutions of the Cauchy problems for $n$-dimensional incompressible Navier-Stokes equations, for the $n$-dimensional magnetohydrodynamics equations and for many other very interesting nonlinear evolution equations with dissipations can be established.     

THE COMPUTATION OF GREEN'S FUNCTION FOR THE LAPLACE OPERATOR IN A RECTANGLE

Abstract

The note gives an efficient method to compute Green's function for Laplace's operator in an arbitrary rectangle.     

一类Riccati矩阵方程广义自反解的双迭代算法

本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广义自反解的双迭代算法.拓宽了求解非线性矩阵方程的迭代算法.数值算例表明双迭代算法是有效的.     

ON THE ITERATED ω-RULE

Let Γ_n(φ) be a formula of L_PA (PA = Peano Arithmetic) meaning “there is a proof of φ from PA-axioms, in which ω-rule is iterated no more than n times”. We examine relations over pairs of natural numbers of the kind. (n, k) ≦_H (n', k') iff PA + RFN_n' (H_k') ? RFN_n (H_k). Where H denotes one of the hierarchies ∑ or Π and RFN_n(C) is the scheme of the reflection principle for Γ_n restricted to formulas from the class C(Γ_n(φ) implies “φ is true”, for every φ ∈ C). Our main result is that. (n, k) ≦H (n', k') if n ≦ n' and k ≦ max (k', 2n' + 1).     

A Teacher's Conception of Communication in Geometry Proofs

Mathematical proof has many purposes, one of which is communication of the reasoning behind a mathematical insight. Research on teachers' views of the role that proof plays as mathematical communication has been limited. This study describes how one teacher conceptualized proof communication during two units on proof (coordinate geometry proofs and Euclidean proofs). Based on classroom observations, the teacher's conceptualization of communication in written proofs is recorded in four categories: audience, clarity, organization, and structure. The results indicate differences within all four categories in the way the idea of communication is discussed by the teacher. Implications for future studies include attention to teachers' beliefs about learning mathematics in the process of understanding teachers' conceptions of proof as a means of mathematical communication.     

关于Fermat素数与L-函数的加权均值

本文研究了一类以Fermat素数为模的Dirichlet L-函数加权均值的计算问题. 利用初等方法以及Dirichlet 和的性质, 获得了一个有趣的计算公式.     

拟鞅的Fefferman不等式和对偶定理

本文讨论了拟鞅的Fefferman不等式和Hardy空间的对偶空间. 利用鞅的相关结果和Doob分解的方法, 把鞅的Fefferman不等式推广到拟鞅情形, 并描述了拟鞅的Hardy空间Ĥ_p在1 < p < ∞)时的对偶空间.     

THE Σλ-CALCULUS AND DERIVED PROGRAM FORMS

Abstract

The Σλ-calculus is an extension of an applied λ-calculus designed to abstract parallel and non-deterministic function application evaluation. The abstraction is extended to include Landin's closure, and constant terms and a special form of the conditional allows the regular logics to be developed along the lines of the Hilbert-Ackermann approach. The regular logics are used to characterize derived conditionals in extensions to Dijkstra's weakest preconditions. It is shown that various styles of programming—top-down, bottom-up, recursive and iterative—axe expressible in the Σλ-calculus. Lists and streams are found to be useful in expressing time-dependent behaviour of computational systems. An approximate Church-Rosser Theorem is given.     

ON ADJUNCTIONS INDUCING THE SAME MONAD

ABSTRACT

Consider an adjunction <F,U;n,c>: K. → A, T = <T,n,u> the monad it induces in K and ø: A → K^T the comparison functor, K^T being the category of T-algebras. By ø*: Proj U → Proj U^T we denote the restriction and co-restriction of ø to the subcategories of U-projective and U^T -projective objects, respectively. In this paper we deal with the following problem, raised by R.-E. Hoffmann in [5] 1.16 (b):

Assuming that ø* is an equivalence of categories when is it possible to find a category C and a right adjoint functor V: C → K inducing the same monad T in K, and a full reflective embedding E: A → K, such that:

(1) V.E = U.

(2) ø = ø'. E for the comparison functor ø': C → K^T .

(3) F'X is contained (via E) in A, for each K-object X, F' being the left adjoint of V.

(4) ø': C → K^T has a full and faithful left adjoint L'.

We prove that there exists a pair (C,V) satisfying the conditions of the problem, with A an isomorphism-closed subcategory of C, such that:

(5) For all C ? Obj C the reflection map r_C: C → A is ø'-initial.

We also prove that this pair (C,V) is the universal solution satisfying condition (5), i.e. if (C_i,V_i) is a pair satisfying conditions (1)-(5) with E_i: A → C₂ the embedding and L_i left adjoint to the comparison functor ø_i: C_i K^T then there exists a unique full and faithful functor H_i: C → C_i such that H. E = E_i and H_i. L'—L_i. Moreover the universal solution is uniquely determined up to isomorphisms of categories and natural isomorphisms of functors. Finally, we study a particular situation and find, within the solutions of the problem satisfying two further conditions, the lease and the largest element. We conclude the paper with an example of this situation.     

NOAH'S NONCONCAVITY: ON THE EXISTENCE OF NONTRIVIAL INTERIOR SOLUTIONS TO THE PROBLEM OF COST‐EFFECTIVE CONSERVATION PLANNING

Abstract The idea that species loss diminishes future information flows is a cornerstone of arguments for conservation planning. In his seminal work entitled The Noah's Ark Problem, Weitzman [1998] examines the problem of cost‐effective conservation planning from a theoretical perspective accounting for the affect planning has on the expected size of the biosphere's informative potential. This paper extends Weitzman's analysis by examining how his conclusions are altered by the introduction of a conservation authority that considers the value of information contained in the biosphere. Introducing nonquasiconcave preferences for the information contained in each species substantially modifies the characterization of a cost‐effective conservation plan. In particular, I find that a cost‐effective plan generally includes partial funding for many species and funds no species completely. This investigation is motivated by theoretical contributions to the information economics literature, a la Radner and Stiglitz [1984] , showing that the value function for information tends to exhibit increasing returns.     

NASH EQUILIBRIUM OF TWO GAME MODELS ON THE RANDOM SOCIAL NETWORK

A graph $G$ is $k$-triangular if each of its edge is contained in at least $k$ triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph $G$ is a sequence of distinct triangles $T_1 T_2\cdots T_k$ in $G$ such that for $1\leq i\leq k-1, |E(T_i )\cap E(T_{i+1})|=1$ and $E(T_i)\cap E(T_j)=\emptyset$ if $j>i+1$. Two edges $e,e''\in E(G)$ are triangularly connected if there is a triangle-path $T_1,T_2,\cdots, T_k$ in $G$ such that $e\in E(T_1)$ and $e''\in E(T_k)$. Two edges $e,e''\in E(G)$ are equivalent if they are the same, parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component. In this paper, we prove that every 4-edge-connected triangular graph $G$ is ${\mathbb Z}_3$-connected, unless it has a triangularly connected component which is not ${\mathbb Z}_3$-connected but admits a nowhere-zero 3-flow.     

LITTLEWOOD-PALEY THEOREM AND MULTIPLIERS ON THE QUANTUM TORUS＊

The Littlewood-Paley and Marcinkiewicz's multiplier theorems on the quantum torus are established.An key ingredient of the proof is vector-valued Littlewood-Paley and noncommutative Khinchin's inequali...