Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

基于平行DEA模型的我国小学教育资源配置效率分析

小学教育是教育阶段的基础,也是我国强制教育的一部分。但如何在各省份性别比例相差较大的情况下,更加有效的提高各省份小学教育资源配置效率是一个值得思考的问题。为了避免性别带来的影响,可以通过平行结构DEA模型根据学生性别分为两个平行子系统,来衡量我国2012~2018年各省份小学教育的资源配置情况。研究发现大部分省份小学教育资源配置的总系统效率未达到有效边界,仍有需要改进的地方。男学生在小学教育阶段的效率通常优于女学生在小学教育阶段的效率,但随着近些年我国教育体制的日益完善,女学生在小学教育阶段的效率呈上升趋势。此外,我国西部地区的小学教育资源配置效率在一些年份普遍优于东部和中部地区,而中部地区和东部地区小学教育总系统效率相对稳定,西部地区小学教育总系统效率波动较大。     

Sur la détermination d'une relation binaire à partir d'informations locales

This paper deals with the problematic aspect of the reconstruction of binary relations: it includes all the questions raising the possibility or impossibility to determine a structure by gathering given substructures. It is the continuation of three studies: the first made by G. Lopez [9] in 1972 about the determination of a binary relation through the types of isomorphism of its restrictions, the second made by K. B. Reid and C. Thomassen [15] in 1976 about the strongly self-complementary tournaments (every subtournament is self-complementary), the third made by C. Thomassen [16] in 1989 about the cycle space of a tournament. In the second section, we use the notion of class of difference (which was introduced in [9]) to extend a study made in [16] to binary relations. Then, in the third section, we improve the result of this last study in the case of the tournaments. After noticing that the result of [15] inferred itself naturally from the approach developed in [9], we extend, in the fourth section, the study made in [15] to binary relations.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

On Potential Theoretic Skeletons of Polyhedra

We prove that any polyhedron in two dimensions admits a type of potential theoretic skeleton called mother body. We also show that the mother bodies of any polyhedron in any number of dimensions are in one-to-one correspondence with certain kinds of decompositions of the polyhedron into convex subpolyhedra. A consequence of this is that there can exist at most finitely many mother bodies of any given polyhedron. The main ingredient in the proof of the first mentioned result consists of showing that any polyhedron in two dimensions contains a convex subpolyhedron which sticks to it in the sense that every face of the subpolyhedron has some part in common with a face of the original polyhedron.     

Combinatorics of generalized q-Euler numbers

New enumerating functions for the Euler numbers are considered. Several of the relevant generating functions appear in connection to entries in Ramanujan's Lost Notebook. The results presented here are, in part, a response to a conjecture made by M.E.H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan's expansion for a generalization of the Rogers-Ramanujan series. Related generating functions appear in the work of H. Prodinger and L.L. Cristea in their study of geometrically distributed random variables. An elementary combinatorial interpretation for each of these enumerating functions is given in terms of a related set of statistics.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.     

Exponential dispersion relation and its effects on unstable propagating pulses in unidirectionally coupled symmetric bistable elements

The propagation of pulses in unidirectionally coupled symmetric bistable elements is studied. The speeds of unstable traveling pulse waves in a ring of elements increase with pulse width in an exponential manner. This dispersion relation causes exponential increases in the duration of transient propagating pulses and the noise-sustained propagation of pulses, which are qualitatively the same as those in a reaction-diffusion-convection equation and a ring of sigmoidal neurons. However, the speeds of pulse fronts in propagating pulses depend on the backward pulse width. Properties of pulse transmission in an open chain of elements then differ from those in the above two systems qualitatively.     

Bootstrap and empirical likelihood methods in extremes

One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domain of attraction of an extreme-value distribution and to predict rare events. In recent years, much effort in developing new methodologies has been made by many researchers in this area so as to diminish the impact of the bias in the estimation and achieve some asymptotic optimality in inference problems such as estimating the optimal sample fractions and constructing confidence intervals of various quantities. In particular, bootstrap and empirical likelihood methods, which have been widely used in many areas of statistics, have drawn attention. This paper reviews some novel applications of the bootstrap and the empirical likelihood techniques in extreme-value statistics. Dedicated to Professor Laurens de Haan on the occasion of his 70th birthday.     

Scan Statistics on Enron Graphs

We introduce a theory of scan statistics on graphs and apply the ideas to the problem of anomaly detection in a time series of Enron email graphs. Previous presentation: Workshop on Link Analysis, Counterterrorism and Security at the SIAM International Conference on Data Mining, Newport Beach, CA, April 23, 2005. Carey E. Priebe received the B.S. degree in mathematics from Purdue University in 1984, the M.S. degree in computer science from San Diego State University in 1988, and the Ph.D. degree in information technology (computational statistics) from George Mason University in 1993. From 1985 to 1994 he worked as a mathematician and scientist in the US Navy research and development laboratory system. Since 1994 he has been a professor in the Department of Applied Mathematics and Statistics, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland. At Johns Hopkins, he holds joint appointments in the Department of Computer Science and the Center for Imaging Science. He is a past President of the Interface Foundation of North America—Computing Science & Statistics, a past Chair of the Section on Statistical Computing of the American Statistical Association, and on the editorial boards of Journal of Computational and Graphical Statistics, Computational Statistics and Data Analysis, and Computational Statistics. His research interests are in computational statistics, kernel and mixture estimates, statistical pattern recognition, statistical image analysis, and statistical inference for high-dimensional and graph data. He was elected Fellow of the American Statistical Association in 2002. John M. Conroy received a B.S. in Mathematics from Saint Joseph's University in 1980 and a Ph.D. in Applied Mathematics from the University of Maryland in 1986. Since then he has been a research staff member for the IDA Center for Computing Sciences in Bowie, MD. His research interest is applications of numerical linear algebra. He is a member of the Society for Industrial and Applied Mathematics, Institute of Electrical and Electronics Engineers (IEEE), and the Association for Computational Linguistics. David J. Marchette received a B.A. in 1980, and an M.A. in mathematics in 1982, from the University of California at San Diego. He received a Ph.D. in Computational Sciences and Informatics in 1996 from George Mason University under the direction of Ed Wegman. From 1985–1994 he worked at the Naval Ocean Systems Center in San Diego doing research on pattern recognition and computational statistics. In 1994 he moved to the Naval Surface Warfare Center in Dahlgren Virginia where he does research in computational statistics and pattern recognition, primarily applied to image processing, text processing, automatic target recognition and computer security. Dr. Marchette is a Fellow of the American Statistical Society. Youngser Park received the B.E. degree in electrical engineering from Inha University in Korea in 1985, the M.S. degree in computer science from The George Washington University in 1991, and had pursued a doctoral degree there. From 1998 to 2000 he worked at the Johns Hopkins Medical Institutes as a senior research engineer. Since 2003 he is working as a research analyst in the Center for Imaging Science at the Johns Hopkins University. His research interests are clustering algorithm, pattern classification, and data mining.     

Chapter 8 Estimating production frontier shifts: An application of DEA to technology assessment

Evaluating the separate impacts of factors which affect the productive efficiency of organizations is difficult. This is because the impact of a factor is often contingent on other organizational, managerial or environmental characteristics. Standard econometric methods are limited in their ability to discriminate between efficient and inefficient units, and often impose considerable structure in parametrically specified functional forms. We show how a nonparametric data envelopment approach can be employed to focus on the best that can be achieved, with and without the key characteristic of interest. We illustrate the approach with real data from the service sector requiring the evaluation of the impact of a new information technology. The analytical technique estimates the annual savings in materials cost for an average store using the information technology to be over $4,000 (2.04% of materials cost), well in excess of the amortized annual cost for its installation. Establishing the separation in the production frontier in different regions, we show that the information technology had a substantially larger impact for the bigger stores. The savings were about 80% greater in the larger volume stores than in the smaller volume operations, an important consideration in setting the priorities for installation. The illustration underscores the flexibility of DEA in detecting different impacts of a new technology in different environments.     

On the Modeling of CO2 EUA and CER Prices of EU‐ETS for the 2008–2012 Period

Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions. One of the most important implications of carbon trading for industrial systems is the risk of uncertainty about the prices of carbon allowance permits traded in the carbon markets. In this paper, we consider stochastic and time series modeling of carbon market prices and provide estimates of the model parameters involved, based on the European Union emissions trading scheme carbon allowances data obtained for 2008–2012 period. In particular, we consider fractional Brownian motion and autoregressive moving average–generalized autoregressive conditional heteroskedastic modeling of the European Union emissions trading scheme data and provide comparisons with benchmark models. Our analysis reveals evidence for structural changes in the underlying models in the span of the years 2008–2012. Data‐driven methods for identifying possible change‐points in the underlying models are employed, and a detailed analysis is provided. Our analysis indicated change‐points in the European Union Allowance (EUA) prices in the first half of 2009 and in the second half of 2011, whereas in the Certified Emissions Reduction (CER) prices three change‐points have appeared, in the first half of 2009, the middle of 2011, and in the second half of 2012. These change‐points seem to parallel the global economic indicators as well. Copyright © 2016 John Wiley & Sons, Ltd.     

产能约束对闭环供应链回收渠道选择的影响

在制造商存在产能约束下,建立了再制造闭环供应链回收渠道决策的Stackelberg博弈模型,得出了三种回收渠道下的回收率、零售价以及制造商、零售商和供应链的利润,分析了制造商的生产能力对回收渠道决策的影响。研究表明:存在产能约束时,制造商回收渠道中的回收率总是最高的,这与无产能约束时零售商回收渠道中回收率最高的情况明显不同;同时,若废旧产品回收转移支付价格较低,制造商会选择自己回收,此时的零售价最低,制造商、零售商和供应链利润最高;若回收转移支付价格较高,制造商会选择零售商回收,此时的零售价最低,制造商和供应链利润最高。     

On slice hyperholomorphic fractional Hardy spaces

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.     

A Comparison of Two Sequential Metropolis-Hastings Algorithms with Standard Simulation Techniques in Bayesian Inference in Reliability Models Involving a Generalized Gamma Distribution

In this paper we consider the generalized gamma distribution as introduced in Gåsemyr and Natvig (1998). This distribution enters naturally in Bayesian inference in exponential survival models with left censoring. In the paper mentioned above it is shown that the weighted sum of products of generalized gamma distributions is a conjugate prior for the parameters of component lifetimes, having autopsy data in a Marshall-Olkin shock model. A corresponding result is shown in Gåsemyr and Natvig (1999) for independent, exponentially distributed component lifetimes in a model with partial monitoring of components with applications to preventive system maintenance. A discussion in the present paper strongly indicates that expressing the posterior distribution in terms of the generalized gamma distribution is computationally efficient compared to using the ordinary gamma distribution in such models. Furthermore, we present two types of sequential Metropolis-Hastings algorithms that may be used in Bayesian inference in situations where exact methods are intractable. Finally these types of algorithms are compared with standard simulation techniques and analytical results in arriving at the posterior distribution of the parameters of component lifetimes in special cases of the mentioned models. It seems that one of these types of algorithms may be very favorable when prior assessments are updated by several data sets and when there are significant discrepancies between the prior assessments and the data.     

A task that elicits reasoning: A dual analysis

This paper reports on the forms of reasoning elicited as fourth grade students in a suburban district and sixth grade students in an urban district worked on similar tasks involving reasoning with the use of Cuisenaire rods. Analysis of the two data sets shows similarities in the reasoning used by both groups of students on specific tasks, and the tendency of a particular task to elicit numerous forms of reasoning in both groups of students. Attributes of that task and ways that those attributes can be replicated in other domains may have implications in the teaching of early reasoning.     

The effect of the 4MAT method (learning styles and brain hemispheres) of instruction on achievement in mathematics

The purpose of this study was to determine the efficiency of 4MAT method of instruction in which learning style and cerebral hemispheres are taken into account in teaching the binary operation and its properties in mathematics. The sample of this study comprised 58 ninth grade students in two separate classes in a high school. One of the classes was selected as the experimental group in which 4MAT method of instruction was used; and the other class was selected as the control group in which the traditional teaching was given, and this selection was performed randomly. The data have been obtained primarily from three scales, namely ‘mathematical knowledge test’, ‘mathematical attitude scale’ and ‘knowledge test on binary operation and its properties’. It has been determined that 4MAT method of instruction was more efficient than the traditional method in teaching of the binary operation subject in mathematics.     

等参函数及相关问题研究

著名的Yau 猜想断言单位球面中的紧致嵌入极小超曲面的Laplace 算子的第一特征值等于其维数. 近年来有许多几何学家致力于对Yau 猜想的研究, 但是到目前为止, 已有的结论只是一些关于第一特征值估计的不等式. 作为本文的一个主要结果, 本文证明了对于单位球面中的等参极小超曲面,Yau 猜想是正确的. 进一步地, 对于等参超曲面的焦流形(实际上是球面的极小子流形), 本文还证明了在一定维数条件下, 它的第一特征值也是其维数.
作为本文的第二个主要结果, 以著名的Schoen-Yau-Gromov-Lawson 的关于数量曲率的手术理论为出发点, 本文在一个Riemann 流形的嵌入超曲面处作手术, 构造了一个新的具有丰富几何性质的流形, 称为double 流形. 特别地, 本文在单位球面的极小等参超曲面处实行了这一手术, 发现得到的double 流形不仅有很复杂的拓扑(但其示性类有精确描述), 还存在数量曲率为正的度量, 更重要的是保持了等参叶状结构.
比Willmore 曲面更广泛的定义是Willmore 子流形, 即Willmore 泛函在球面中的的极值子流形.单位球面中的Willmore 子流形的例子在已有文献中是非常罕见的. 作为本文的另外两个主要结果, 通过深入挖掘单位球面上的OT-FKM- 型等参函数的焦流形的性质, 本文发现其极大值对应的焦流形是单位球面的一系列Willmore 子流形; 之后, 本文用几何办法统一证明了单位球面中具有4 个不同主曲率的等参超曲面的焦流形都是单位球面的Willmore 子流形. 这些新的Willmore 子流形是极小的,但一般不是Einstein 的.     

Employing stochastic differential equations to model wildlife motion

The concern is with the properties of stochastic differential equations (SDEs) describing the motion of particles in 3 dimensional space, on the sphere or in the plane. There is consideration of the case where the drift function comes from a potential function. There is study of SDEs whose parameters are periodic in time. These are useful for incorporating circadian rhythm in the behavior. The cases of a seal in a frozen lake in Alaska, an elephant seal migrating a great distance in the Pacific Ocean and of a group of "free-ranging" elk in a reserve in Oregon are referred to. For the elk nonparametric estimates of the drift and variance terms of an SDE model are discussed and evaluated and the fit of the model assessed. One issue is how to include explanatories, beyond location and time, in the model. A number of questions motivated by the wildlife motion concerning diffusion processes of the type considered are posed at the end of the paper. Received: 25 April 2002     

Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs

This paper addresses the solution of parabolic evolution equations simultaneously in space and time as may be of interest in, for example, optimal control problems constrained by such equations. As a model problem, we consider the heat equation posed on the unit cube in Euclidean space of moderately high dimension. An a priori stable minimal residual Petrov–Galerkin variational formulation of the heat equation in space–time results in a generalized least squares problem. This formulation admits a unique, quasi‐optimal solution in the natural space–time Hilbert space and serves as a basis for the development of space–time compressive solution algorithms. The solution of the heat equation is obtained by applying the conjugate gradient method to the normal equations of the generalized least squares problem. Starting from stable subspace splittings in space and in time, multilevel space–time preconditioners for the normal equations are derived. In order to reduce the complexity of the full space–time problem, all computations are performed in a compressed or sparse format called the hierarchical Tucker format, supposing that the input data are available in this format. In order to maintain sparsity, compression of the iterates within the hierarchical Tucker format is performed in each conjugate gradient iteration. Its application to vectors in the hierarchical Tucker format is detailed. Finally, numerical results in up to five spatial dimensions based on the recently developed htucker toolbox for MATLAB are presented. Copyright © 2014 John Wiley & Sons, Ltd.