Dynamics of the Friedmann universe with boundary terms added to the action

Theoretical and Mathematical Physics - We consider the dynamics of the universe following from the variational principle with boundary terms added to the action. We calculate a scalar function that...     

基于顾客排队的服务供应链协调策略研究

现阶段对于服务供应链的研究仍受限于传统产品供应链的研究框架,专门针对服务特性的供应链研究是该领域的核心议题。基于服务供应链面向顾客的独有特性,首先分析了服务供应链中服务提供商、集成商与顾客之间的服务关系,然后构建了基于顾客排队的服务供应链模型,其次探讨了集中式和分散式服务供应链下双方的决策问题。研究结果表明,服务提供商、服务集成商通过选择合理的成本共担系数,制定相应的成本共担契约,是协调分散式服务供应链、实现帕累托最优的最佳策略。研究结论对于开拓和深化服务供应链研究具有一定的启示意义。     

Measures of pseudorandomness for finite sequences: typical values

Mauduit and Sárközy introduced and studied certainnumerical parameters associated to finite binary sequences E_N {–1, 1}^N in order to measure their ‘level of randomness’.Those parameters, the normality measure (E_N), the well-distributionmeasure W(E_N), and the correlation measure C_k(E_N) of order k,focus on different combinatorial aspects of E_N. In their work,amongst others, Mauduit and Sárközy (i) investigatedthe relationship among those parameters and their minimal possiblevalue, (ii) estimated (E_N), W(E_N) and C_k(E_N) for certain explicitlyconstructed sequences E_N suggested to have a ‘pseudorandomnature’, and (iii) investigated the value of those parametersfor genuinely random sequences E_N. In this paper, we continue the work in the direction of (iii)above and determine the order of magnitude of (E_N), W(E_N) andC_k(E_N) for typical E_N. We prove that, for most E_N {–1,1}^N, both W(E_N) and (E_N) are of order N, while C_k(E_N) is oforder for any given 2 k N/4.     

Seeing chance: perceptual reasoning as an epistemic resource for grounding compound event spaces

The mathematics subject matter of probability is notoriously challenging, and in particular the content of random compound events. When students analyze experiments, they often omit to discern variations as distinct events, e.g., HT and TH in the case of flipping a pair of coins, and thus infer erroneous predictions. Educators have addressed this conceptual difficulty by engaging students in actual experiments whose outcomes contradict the erroneous predictions. Yet whereas empirical activities per se are crucial for any probability design, because they introduce the pivotal contents of randomness, variance, sample size, and relations among them, empirical activities may not be the unique or best means for students to accept the logic of combinatorial analysis. Instead, learners may avail of their own pre-analytic perceptual judgments of the random generator itself so as to arrive at predictions that agree rather than conflict with mathematical analysis. I support this view first by detailing its philosophical, theoretical, and didactical foundations and then by presenting empirical findings from a design-based research project. Twenty-eight students aged 9?C11 participated in tutorial, task-based clinical interviews that utilized an innovative random generator. Their predictions were mathematically correct even though initially they did not discern variations. Students were then led to recognize the formal event space as a semiotic means of objectifying these presymbolic notions. I elaborate on the thesis via micro-ethnographic analysis of key episodes from a paradigmatic case study.     

Normalising geometrical figures: dynamic manipulation and construction of meanings for ratio and proportion

Enlarging-shrinking geometrical figures by 13 year-olds is studied during the implementation of proportional geometric tasks in the classroom. Students worked in groups of two using ‘Turtleworlds’, a piece of geometrical construction software which combines symbolic notation, through a programming language, with dynamic manipulation of geometrical objects by dragging on sliders representing variable values. In this paper we study the students’ normalising activity, as they use this kind of dynamic manipulation to modify ‘buggy’ geometrical figures while developing meanings for ratio and proportion. We describe students’ normative actions in terms of four distinct Dynamic Manipulation Schemes (Reconnaissance, Correlation, Testing, Verification). We discuss the potential of dragging for mathematical insight in this particular computational environment, as well as the purposeful nature of the task which sets up possibilities for students to appreciate the utility of proportional relationships.     

Exact lower bound for proportion of maximally embedded beamlet

We prove that the maximal inscribed beamlet is at least 1/7 of an arbitrary line segment (i.e., beam). The implication of this result is addressed.     

Coordinating Theories of Learning to Account for Second-Grade Children's Arithmetical Understandings

This article coordinates social constructivism and socioculturalism orientations to explain 2nd-grade children's reasoning with 2-digit quantities. From a social constructivist position, we illustrate how the classroom teacher and the students constituted what counted as an acceptable mathematical explanation. As children offered informal and conventional ways of interpreting problem situations, they were expected to reason with quantities in sensible ways. From a sociocultural position, we explain how the teacher's and students' contributions were situated within the mathematical ways of knowing constituted by the community at large. Particular children's contributions were clarified in terms of the ways in which they participated in socially organized activities. By coordinating these lenses, we argue the local classroom mathematical practices constrained and enabled the mathematical practices of the wider society.     

Coordinating Theories of Learning to Account for Second-Grade Children's Arithmetical Understandings

This article coordinates social constructivism and socioculturalism orientations to explain 2nd-grade children's reasoning with 2-digit quantities. From a social constructivist position, we illustrate how the classroom teacher and the students constituted what counted as an acceptable mathematical explanation. As children offered informal and conventional ways of interpreting problem situations, they were expected to reason with quantities in sensible ways. From a sociocultural position, we explain how the teacher's and students' contributions were situated within the mathematical ways of knowing constituted by the community at large. Particular children's contributions were clarified in terms of the ways in which they participated in socially organized activities. By coordinating these lenses, we argue the local classroom mathematical practices constrained and enabled the mathematical practices of the wider society.     

Weighted values for non-atomic games: an axiomatic approach

Weighted values of non-atomic games were introduced by Hart and Monderer. These values have been studied by using three approaches: the potential, the asymptotic and the random order approach. In this study we analyze the axiomatic approach for one class of weight functions: the set of players is partitioned into a finite number of types, with each type having different weight.     

On the action of permutations on distances between values of rational functions mod p

For the finite field Fp one may consider the distance between r₁(n) and r₂(n), where r₁, r₂ are rational functions in Fp(x). We study the effect to such distances by applying all possible permutations to the elements.     

The use of interactive visualizations to foster the understanding of concepts of calculus: design principles and empirical results

Calculus and functional thinking are closely related. Functional thinking includes thinking in variations and functional dependencies with a strong emphasis on the aspect of change. Calculus is a climax within school mathematics and the education to functional thinking can be seen as propaedeutics to it. Many authors describe that functions at school are mainly treated in a static way, by regarding them as pointwise relations. This often leads to the underrepresentation of the aspect of change at school. Moreover, calculus at school is mainly procedure-oriented and structural understanding is lacking. In this work, two specially designed interactive activities for the teaching and learning of concepts of calculus based on dynamic geometry software are presented. They accentuate the aspect of change and the object aspect of functions using a double stage visualization. Moreover, the activities allow the discovery and exploration of some concepts of calculus in a qualitative-structural way without knowing or using curve-sketching routines. The activities were used in a qualitative study with 10th grade students of age 15–16 in secondary schools in Berlin, Germany. Some pairs of students were videotaped while working with the activities. After transcribing, the interactions of the students were interpreted and analyzed focusing to the use of the computer. The results show how the students mobilize their knowledge about functions working on the given tasks, and using the activities to formulate important concepts of calculus in a qualitative way. Also, some important epistemological obstacles can be detected.     

Additive comparisons of stopping values and supremum values for finite stage multiparameter stochastic processes

This paper concerns the optimal stopping problem for discrete time multiparameter stochastic processes with the index set Nd. In the classical optimal stopping problems, the comparisons between the expected reward of a player with complete foresight and the expected reward of a player using nonanticipating stop rules, known as prophet inequalities, have been studied by many authors. Ratio comparisons between these values in the case of multiparameter optimal stopping problems are studied by Krengel and Sucheston (1981) [9] and Tanaka (2007, 2006) [14] and [15]. In this paper an additive comparison in the case of finite stage multiparameter optimal stopping problems is given.     

Analysis of complementary methodologies for the estimation of school value added

This paper analyses the value added (VA) of a sample of Portuguese schools using two methodologies: data envelopment analysis (DEA) and the methodology used presently by the UK Department for Children, Schools and Families (DCSF). The VA estimates obtained by the two methods are substantially different. This reflects their different focus: DEA emphasizes on best-observed performance, whereas the DCSF method reveals average performance. The main advantage of the methodology used by the DCSF is its simplicity, although it confounds pupil effects with school effects in the estimation of school VA. In contrast, the DEA methodology can differentiate these effects, but the complexity may prevent its use in a systematic way. This paper shows that the two methods provide complementary information regarding the VA of schools, and their joint use can improve the understanding of the relative effectiveness of schools regarding the progress that pupils make between educational stages.     

Approximations for the values of american options

The solution of the American option valuation problem is the solution of a parabolic partial differential equation satisfying free boundary conditions. The free boundary represents the critical price, at which the option should be exercised. In this paper the free boundary is determined by an algebraic relation and an approximate solution derived. A suitable modification of the approximate solution gives the exact solution. The uniqueness of the free boundary implies the expression determined by the algebraic relation is the true critical price     

Special values of L-functions for orthogonal groups

This is an announcement of certain rationality results for the critical values of the degree-2n L-functions attached to ${\mathrm{GL}}_1\times \mathrm{SO}(n,n)$ over $\mathbb{Q}$ for an even positive integer n. The proof follows from studying the rank-one Eisenstein cohomology for $\mathrm{SO}(n+1,n+1)$.