Estimating HIV/AIDS incidence: Adjusting case reports for changes in definition

The purpose of this paper is to assess different procedures used in the modeling of the AIDS epidemic that account for changes in the definition of AIDS. Specifically, we assess three methods that adjust for the effect of definition changes on the modeling of HIV reconstructions. Our results suggest that how we account for definition changes is a critical influence on the severity and the shape of the estimated HIV/AIDS epidemic. Also, the scope of the recent (1993) definition change is sufficiently broad to limit approaches based on adjusting to a single, consistent definition. The most realistic approach appears to be one based on a dynamic disease progression model that accounts for AIDS definition changes via changes in disease incubation.     

Riemann积分的一个等价定义

本文给出了Ｒｉｅｍａｎｎ积分的一个等价定义，用该定义下的达布和的性质证明了Ｒ—可积的必要充分条件定理。并用两种方法证明了定义卫与定义２等价。     

Metaphor as a possible pathway to more formal understanding of the definition of sequence convergence

This study presents how the introduction of a metaphor for sequence convergence constituted an experientially real context in which an undergraduate real analysis student developed a property-based definition of sequence convergence. I use elements from Zandieh and Rasmussen's (2010) Defining as a Mathematical Activity framework to trace the transformation of the student's conception from a non-standard, personal concept definition rooted in the metaphor to a concept definition for sequence convergence compatible with the standard definition. This account of the development of the definition of sequence convergence differs from prior research in the sense that it began neither with examples or visual notions, nor with the statement of the formal definition. This study contributes to the Realistic Mathematics Education literature as it documents a student's progression through the definition-of and definition-for stages of mathematical activity in an interactive lecture classroom context.     

Constructing a mathematical definition: the case of the tangent

We analyze the process of constructing a definition within the theoretical framework of Abstraction in Context. Pairs of students were engaged in a task designed to engender a need for a definition of a tangent to a graph at a given point, and lead to constructing a definition following that need. The results of our analysis point to two characteristics of the process of constructing a definition: a. Constructing the concept does not necessarily include constructing its definition; in particular, students were able to use the concept before constructing its definition. b. Students’ language becomes more precise during the constructing process, not only as a characteristic of the process but also as a means of promoting the process.     

Measure-theoretic pressure for subadditive potentials

By using the definition of topological pressure for subadditive potentials, we introduce a new definition of measure-theoretic pressure for ergodic measures of subadditive potentials on a compact metric space. Under some assumption, we show that this definition has a similar formalism to the definition of measure-theoretic pressure for ergodic measures of additive potentials on a compact metric space. As an application, assume that the subadditive potential is Hölder continuous, then for an expansive homeomorphism with the specification property, we study the relationship between the measure-theoretic pressure and the periodic points.     

Some results on linear delay integral equations

Recently Borwein has proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone S is any nontrivial, closed convex cone. However, when S is the non-negative orthant, solutions may exist which are proper according to Borwein's definition but improper by Geoffrion's definition. As a result, when S is the non-negative orthant, certain properties of proper efficiency as defined by Geoffrion do not hold under Borwein's definition. To rectify this situation, we propose a definition of proper efficiency for the case when S is a nontrivial, closed convex cone which coincides with Geoffrion's definition when S is the non-negative orthant. The proposed definition seems preferable to Borwein's for developing a theory of proper efficiency for the case when S is a nontrivial, closed convex cone.     

A definition of information,the arrow of information,and its relationship to life

A new definition of information is proposed that is minimalistic and incorporates a lifetime requirement for conditions, (which we define here) applied to anything that can be considered to be information. The definition explicitly treats a state in thermodynamic equilibrium as an effectively zero information state. The definition includes the absolute requirement of selection for achieving information; the selection criterion being that the information directly or indirectly contributes to its own replication. The definition also explicitly incorporates the Laws of Thermodynamics, the Second Law leading to the requirement for replication. Finally, the definition explains the origin of information and predicts the monotonic increase of information with time. Published 2010 Wiley Periodicals, Inc. Complexity, 2011     

Sufficient conditions for optimality of threat strategies in a differential game

The problem of defining threat strategies in nonzero-sum games is considered, and a definition of optimal threat strategies is proposed in the static case. This definition is then extended to differential games, and sufficient conditions for optimality of threat strategies are derived. These are then applied to a simple example. The definition proposed here is then compared with the definition of threat strategies given by Nash.     

Turbulent chaos

A new definition of a chaotic invariant set for a continuous semi-flow in a metric space is given. This definition generalizes the known definition of Devaney and allows us to take into account a specific feature arising in a noncompact and infinite-dimensional case, the so-called turbulent chaos.     

建议一个角应变的新定义

本文建议了一个角应变的新定义.这个新定义和线应变的定义相类似,也是一种变化率(角位移的变化率).文中证明了这一新定义与原有定义是一致的,但在几何解释上却更为方便.文中还利用新的角应变定义证明了转轴公式,组成了应变张量和证明了剪切虎克定律.     

On the analogue of the Isidori relative degree definition for linear dynamical MIMO systems

This paper deals with the inversion problem for linear time-invariant dynamical systems. Earlier in this formulation the discussed issue has been addressed and solved for invertible systems that meet the definition of Isidori relative degree. But in fact, this problem is well-posed for a wider range of linear dynamical systems. In this paper we examine a particular case based on a definition that is similar to the definition of relative degree by Isidori. Presented here columnwise relative degree and its properties allow to consider and effectively solve the inversion problem for invertible systems that meet this definition.     

Topological entropy of maps on the real line

The aim of this paper is to introduce a definition of topological entropy for continuous maps such that, at least for continuous real maps, it keeps the following general philosophy: positive topological entropy implies that the map has a complicated dynamical behaviour. Besides, we pursue that our definition keeps some properties which are hold by the classic definition of topological entropy introduced for compact sets.     

一个全局最优化问题的填充函数

本文给出了一个非线性全局最优化问题的填充函数定义,此定义不同于以前已有的填充函数定义。根据此定义,本文提出了一簇单参数填充函数和相应的填充函数算法．对几个算例的数据测试表明,该填充函数法是可行和有效的．     

The many facets of a definition: The case of periodicity

This paper was triggered by an authentic conversation between two mathematics teacher educators who debated whether a constant function is a periodic function, within the framework of a professional development program for secondary mathematics teachers. Their initial conversation led to deep mathematical and pedagogical musing surrounding mathematical definitions. In this paper, we present various aspects of a mathematical definition, including the role and nature of definitions in school mathematics, critical versus preferable features of a definition, and the arbitrariness underlying the choice of definition. We discuss the interplay between logical and pedagogical considerations with respect to definitions, drawing on the definition of a periodic function as an example.     

基于一种新的集合插值的非凸紧集的细分概型

对A rtstein给出的度量平均的定义作了改进,给出一种新的集合插值,并基于这种新的集合插值,对相应的关于一般紧集的样条细分和插值细分分别作了研究,并给出了细分的收敛性性质.与此同时,将这种新的集合插值与基于度量平均的插值及基于M inkow sk i平均的插值分别作了比较,可以看出新的集合插值在某些方面具有更好的物理性质.     

关于Tuza和Voigt的(Dm,m)-可选择性刻画定理

给出一个不属于Non-D的图,但该图却不是(Dm,m)-可选择的.这表明在Tuza Zs和Voigt M的Non-D定义和(Dm,m)-可选择图的特征化定理中存在一定的冲突.针对如上冲突,对Tuza Zs和Voigh M所给出的Non-D的定义,以及(Dm,m)-可选择图的特征化定理的证明进行了修正.     

A filled function method for finding a global minimizer on global integer optimization

The paper gives a definition of the filled function for nonlinear integer programming. This definition is modified from that of the global convexized filled function for continuous global optimization. A filled function with only one parameter which satisfies this definition is presented. We also discuss the properties of the proposed function and give a filled function method to solve the nonlinear integer programming problem. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.     

直觉模糊数可能度的概率定义及其决策

发现直觉模糊数可能度的传统定义考虑的因素不全面,计算结果不太符合常理,提出基于均匀分布的直觉模糊数可能度定义,得到相对简单且精确的可能度计算公式;证明可能度的传统定义不稳定;探索多属性直觉模糊集利用可能度进行决策的方法.最后,运用多属性直觉模糊集决策实例,既验证基于均匀分布的可能度定义的优越性,又验证可能度传统定义的不稳定性和不能敏锐区别方案间的差别,难以得到最优决策,甚至可能导致错误决策.     

Reinventing the formal definition of limit: The case of Amy and Mike

Relatively little is known about how students come to reason coherently about the formal definition of limit. While some have conjectured how students might think about limits formally, there is insufficient empirical evidence of students making sense of the conventional ?-δ definition. This paper provides a detailed account of a teaching experiment designed to produce such empirical data. In a ten-week teaching experiment, two students, neither of whom had previously seen the conventional ?-δ definition of limit, reinvented a formal definition of limit capturing the intended meaning of the conventional definition. This paper focuses on the evolution of the students’ definition, and serves not only as an existence proof that students can reinvent a coherent definition of limit, but also as an illustration of how students might reason as they reinvent such a definition.     

Weakly convex sets and modulus of nonconvexity

We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order. Using the new definition of the weakly convex set with the given modulus of nonconvexity we prove a new retraction theorem and we obtain new results about continuity of the intersection of two continuous set-valued mappings (one of which has nonconvex images) and new affirmative solutions of the splitting problem for selections. We also investigate relationship between the new definition and the definition of a proximally smooth set and a smooth set.