培养学生科学思维和创新能力的研究与实践——谈大学数学研究型教学

通过从一个导数值等式的证明谈起,探讨教师在课堂教学中如何根据教学内容创设能激起学生新异感的问题情景,启发和引导学生发散思考,类比、联想、猜想,探索和发现新问题并给出解答.使学生思维不断攀升,丰富教学内容,激发学生兴趣,培养学生科学思维方法和创新能力.     

Mexican high school students' social representations of mathematics,its teaching and learning

This paper reports a qualitative research that identifies Mexican high school students’ social representations of mathematics. For this purpose, the social representations of ‘mathematics’, ‘learning mathematics’ and ‘teaching mathematics’ were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students’ social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.     

On the relation of abstract and concrete in scientists’ graph interpretations: A case study

The notions of abstract and concrete are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how engagement with some object leads to the working out of existing, concrete practical understanding and the articulation of categorical statements (“generalizations”); because the scientist knew something at the end of his interpretive work that he did not prior to it, the event is understood to constitute an episode of learning. The analysis shows that rather than being a movement from concrete to abstract or from abstract to concrete, development occurs in a movement that appears to be simultaneously from concrete to abstract and from abstract to concrete.     

Self-converse mixed graphs are extremely rare

A mixed graph is cospectral to its converse, with respect to the usual adjacency matrices. Hence, it is easy to see that a mixed graph whose eigenvalues occur uniquely, up to isomorphism, must be isomorphic to its converse. It is therefore natural to ask whether or not this is a common phenomenon. This note contains the theoretical evidence to confirm that the fraction of self-converse mixed graphs tends to zero.     

随机数学教学设计与实践——关注理解、掌握与应用

本文通过分析教学案例并总结课程教学交流体会,探讨在大学《概率论与数理统计》课程教学中如何引导学生理解概念、掌握方法并灵活应用以解决相关实际问题;培养学生善学睿思,增强其自主创新实践能力。     

A study of leveraged ETF based on geometric return

Leveraged (inverse) exchange-traded funds (LETFs) seek to deliver multiples (opposite) of the performance of the index or benchmark they track. LETFs typically are designed to achieve their stated performance objectives on a daily basis. Many real-life and hypothetical examples have been given to show that the performance of these ETFs over a period longer than one day can differ from their stated daily performance objectives. Formulae have been found using both continuous method and discrete method. A discrete method was used to find a formula linking the return of a leveraged fund with the corresponding multiple of the return of the unleveraged fund and its realized variance but the method needs to use some assumptions and statistical properties to create the volatility term. A CME report finds a very simple way to include volatility in their formula but fails to link to the return of the corresponding unleveraged product. In this paper, we find a natural way to link a leveraged fund with its corresponding unleveraged product and its realized variance in a discrete manner. Our derivation process is similar to that in the CME report, so we do not need to use assumptions and statistical properties to create the volatility term. Unlike the CME method, we use geometric return as opposed to arithmetic return. So, we are able to connect with the return of the corresponding unleveraged product.     

Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions

The previous attempts to launch liquid and standardized longevity derivatives in the market failed because banks do not seem to be ready to take longevity risk. Therefore, instead of trying to transfer longevity risk to investors, it could be interesting for financial institutions to propose interest rate hedges adapted to longevity portfolios, in the spirit of liability driven investments. In this paper, we introduce a new structured financial product: the so-called Longevity Nominal Chooser Swaption. Thanks to such a contract, insurers could keep pure longevity risk and transfer to financial markets a great part of interest rate risk underlying annuity portfolios.We use a population dynamics longevity model and a classical two-factor interest rate model to price this product. Numerical results show that the option offered to the insurer (in terms of choice of nominal) is not too expensive in many real-world cases. We also discuss the pros and the cons of the product and of our methodology.     

Perturbation theory for mathematical programming problems

Mathematical programming (MP) problems depending on a small parameter are investigated. Attention is paid to the cases where the solutions to the reduced program and/or the solutions to the dual reduced program are not unique. Conditions are given for the convergence of perturbed solutions to a point of the reduced problem solution set, if the small parameter tends to zero. It is shown how to find this point and how to construct an approximate solution to the perturbed program. A singular situation may appear if the dual solution set is unbounded. In this case, a gap between perturbed and reduced solutions may arise. However, it is shown that the perturbed solutions are close to the solutions of some modified reduced problem. The practical usefulness of perturbation theory is demonstrated by considering the two LP problems. Decomposition and aggregation procedures are constructed on the base of general results to find suboptimal solutions of these problems.     

出租车司机社会贡献评价方法研究

出租车司机的社会贡献对于促进城市经济发展和社会进步具有重要的作用,评价出租车司机的社会贡献是激励出租车司机多做社会贡献的重要手段。为了评价出租车司机的社会贡献,本文提出了一种基于实际出租车运营数据的评价方法。本文设计了运营特性、重点区域、恶劣天气、大事件四个体现司机社会贡献的指标,以此构建了出租车司机社会贡献评价指标体系,进而选用了主观赋权法G1法和客观赋权法拉开档次法相结合的赋权方式对指标赋权,并选择四种评价信息集结方法建立了出租车司机社会贡献评价模型。最后,通过实际的出租车运营数据验证了本方法的可行性。本文为评价出租车司机社会贡献提供了一种研究思路和方法,并对政府政策的制定和企业策略的实施具有一定的启示。     

Learning to Ignore Online Help Requests

Email discussion groups provide a useful way of organizing email communities with a common interest in a certain topic. Emails submitted to the discussion group are sent automatically to each individual member, thereby eliminating the need to send multiple emails. This method may present unexpected difficulties however, when it comes to cooperation between members. An experimental study shows that email requests for help sent through discussion groups received less responses than emails sent individually to members of a group. Furthermore, subscribers to large discussion groups responded less often to help requests, whether they were sent to the group as a whole or to individuals. These results are discussed in terms of the separate roles of social cues and experience on the diffusion of responsibility effect.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

Promise as Practice Reason

Acta Analytica - To promise someone to do something is to commit oneself to that person to do that thing, but what does that commitment consist of? Some think a promissory commitment is an...     

Scheduling of road vehicles in sugarcane transport: A case study at an Australian sugar mill

Pressure to remain internationally competitive has forced Australian sugar mills to reduce capital and operational costs. Improved scheduling of road transport vehicles provides one such opportunity, as it would reduce vehicle queue and mill idle times and hence the number of vehicles needed. It is difficult for mill traffic officers to produce good transport schedules manually due to the need to service a large number of harvesters in different locations. To address this issue, research was undertaken participatively with a sugar milling company in Australia to produce and implement a mixed integer programming model that represents the road transport operations. Two meta-heuristics were applied to find a solution to the model, leading to potential cost savings of AU$240,000 per year versus schedules produced manually by the mill traffic officer. The model was also applied to explore regional planning options for a more integrated harvesting and transport system.     

An automotive bulk recycling planning model

The automotive recycling infrastructure successfully recovers 75% of the material weight in end-of-life vehicles primarily through ferrous metal separation. However, this industry faces significant challenges as automotive manufacturers increase the use of nonferrous and nonmetallic materials. As the nonferrous content in end-of-life vehicles rises, automotive shredders need to evaluate to what extent to separate nonferrous metals. We propose a recycling planning model for automotive shredders to make short-term tactical decisions regarding to what extent to process and to reprocess materials through multiple passes. In addition, the mixed integer programming model determines whether to combine materials for shipment. In a case study for automotive shredding decisions for the current composition and more polymer-intensive end-of-life vehicles, we use our model to show the sensitivity of the decision to reprocess light nonferrous metal to low and high metal prices. Contrary to observations in practice to mix light and heavy nonferrous metals for shipment, we show multiple scenarios where the model chooses to reprocess and ship separated light and heavy nonferrous metals.     

The transportation problem with exclusionary side constraints and two branch-and-bound algorithms

The transportation problem with exclusionary side constraints, a practical distribution and logistics problem, is formulated as a 0–1 mixed integer programming model. Two branch-and-bound (B&B) algorithms are developed and implemented in this study to solve this problem. Both algorithms use the Driebeek penalties to strengthen the lower bounds so as to fathom some of the subproblems, to peg variables, and to guide the selection of separation variables. One algorithm also strongly exploits the problem structure in selecting separation variables in order to find feasible solutions sooner. To take advantage of the underlying network structure of the problem, the algorithms employ the primal network simplex method to solve network relaxations of the problem. A computational experiment was conducted to test the performance of the algorithms and to characterize the problem difficulty. The commercial mixed integer programming software CPLEX and an existing special purpose algorithm specifically designed for this problem were used as benchmarks to measure the performance of the algorithms. Computational results show that the new algorithms completely dominate the existing special purpose algorithm and run from two to three orders of magnitude faster than CPLEX.     

The effects of immunity and resistance on the development of AIDS

We incorporate basic genetics into an AIDS model. We illustrate that if a homozygote is immune to the disease or is resistant to the effects of the disease, the corresponding allele goes to fixation. On the other hand, if the heterozygote is immune to the disease or is resistant to the effects of the disease, polymorphism usually occurs.     

Stability study and control of helicopter blade flapping vibrations

The response of a two-degree-of-freedom, controlled, autoparametric system to harmonic excitations is studied and solved. The objective of this research is to investigate the effect of linear absorber on the vibrating system and the saturation control of a linear absorber to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to obtain the periodic response equation near the primary resonance in the presence of internal resonance of the system. The stability of the obtained numerical solution is investigated using both phase plane methods and frequency response equations. Variation of some parameters leads to the bending of the frequency response curves and hence to the jump phenomenon occurrence. The reported results are compared to the available published work.     

研究式教学:初等代数研究教学模式引探

探索初等代数研究教学改革之路是适应时代发展,培养新型师范生的需要,是实现"教育以学生发展为本"新教育观的必由之路.在高师数学系开展研究式教学是一项十分有意义的实践,它是对传统教学模式的反思,对培养学生创新能力,启迪学生走上教育和科研之路具有方法论意义.研究式教学的基本模式有目标探究、过程探究和模型探究等,自由探究为其最高境界.     

Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge.In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches.The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus.This revised version was published online in September 2005 with corrections to the Cover Date.     

The use of the linear sampling method for obtaining super-resolution effects in Born approximation

A two-step reconstruction scheme is introduced to solve fixed frequency inverse scattering problems in Born approximation conditions. The aim of the approach is to achieve super-resolution effects by constraining the inversion method to exploit some a priori knowledge on the scatterer. Therefore, the first step is to apply the linear sampling method to the far-field data in order to obtain an estimate of the support of the inhomogeneity. The second step is to apply the projected Landweber method to the linearized scattering equation in order to obtain super-resolution effects via out-of-band extrapolation. The effectiveness of the approach, which has a rather wide applicability power, is tested in the case of a two-dimensional problem for some scatterers of simple geometry.