L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

Managing differences by focusing on communication qualities: Pupils learning mathematics in pairs at a computer

The article presents a study of face-to-face verbal communication when pupils work with geometry in pairs and share a stand-alone computer with Geoboard software. The work sessions of pairs of 9th grade pupils are video recorded, and a screen recorder is used to capture their computer activity. The study focuses on identifying and characterizing good communication practices that enhance mathematics learning through joint research reflections between the pupils, the teacher, and the researcher. The major finding concerns how two of the pupils have diverging perspectives on how to communicate mathematics, yet they manage to have productive collaboration. The differences generate collaborative challenges for the pupils and an opportunity to discuss how pupils’ communication qualities can prove important in fruitfully managing such challenges.     

Determining matchdays in sports league schedules to minimize rest differences

Many sports leagues first announce the games to be played in each round and then determine their matchdays as the season progresses. This study focuses on the fairness criterion of minimizing the total rest difference among opposing teams to find the matchdays for an announced schedule. We show that the problem is decomposable into optimizing the rounds separately. We also provide a polynomial-time exact algorithm for canonical schedules.     

On log-normal convolutions: An analytical–numerical method with applications to economic capital determination

We put forward an efficient algorithm for approximating the sums of independent and log-normally distributed random variables. Namely, by combining tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums to a high precision and in a relatively short computing time. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation.     

Determination of Trimethylamine N-oxide and Betaine in Serum and Food by Targeted Metabonomics

Trimethylamine N-oxide (TMAO), as a gut-derived metabolite, has been found to be associated with enhanced risk for atherosclerosis and cardiovascular disease. We presented a method for targeted profiling of TMAO and betaine in serum and food samples based on a combination of one-step sample pretreatment and proton nuclear magnetic resonance spectroscopy. The key step included a processing of sample preparation using a selective solid-phase extraction column for retention of basic metabolites. Proton signals at δ 3.29 and δ 3.28 were employed to quantify TMAO and betaine, respectively. The developed method was examined with acceptable linear relationship, precision, stability, repeatability, and accuracy. It was successfully applied to detect serum levels of TMAO and betaine in TMAO-fed mice and high-fructose-fed rats and also used to determine the contents of TMAO and betaine in several kinds of food, such as fish, pork, milk, and egg yolk.     

Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings

An efficient scheme, called quasi-linearization finite differences, is developed for large-deflection analysis of prismatic and non-prismatic slender cantilever beams subjected to various types of continuous and discontinuous external variable distributed and concentrated loads in horizontal and vertical global directions. Simultaneous equations of highly nonlinear and linear terms are obtained when casting the derived exact highly nonlinear governing differential equation using central finite differences on the nodes along the beam. A quasi-linearization scheme is used to solve these equations based on successive corrections of the nonlinear terms in the simultaneous equations. The nonlinear terms in the simultaneous equations are assumed constant during each correction (iteration). Several representative numerical examples of prismatic and non-prismatic slender cantilever beams with different loading conditions are analyzed to illustrate the merits of the adopted numerical scheme as well as its validity, accuracy and efficiency. The results of the present scheme are checked using large-displacement finite element analysis by the MSC/NASTRAN program. A comparison between the present secheme, MSC/NASTRAN and available results from the literature reveals excellent agreement. The advantage of the new scheme is that the load can be applied in one step with few iterations (3–6 iterations).     

Notions of equivalence through ratios: Students with and without learning disabilities

Students with learning disabilities (LD) specific to mathematics historically underperform in foundational content such as rational number equivalence. This study examined the strategy usage and multiplicative thinking of three third grade children (i.e., Bill, a child identified as having a learning disability specific to mathematics, Carl, a child labeled as low achieving in mathematics, and Albert, a child labeled as typically achieving) before, during, and after participating in tutoring sessions consisting of student-centered pedagogy and equivalence tasks presented through an underutilized interpretation of rational number: namely, the ratio interpretation. Constant comparison analysis of the children's work during the tutoring sessions as well as responses to tasks during two clinical interviews seemed to indicate that all three children increased their use of viable strategies, with notable differences in the sophistication of the strategies as well as the level of multiplicative thinking utilized before and after the ratio-based tutoring sessions. Yet, Bill's continued use of rudimentary strategies reflects a need for continued research to investigate why the use of such strategies persists and how supporting the development of more sophisticated strategies (especially among children with LD) can be achieved.     

地面积水与装甲目标毫米波被动探测信号差异研究

以往毫米波被动探测中以平面金属目标代替立体金属目标(如装甲目标),而平面金属目标的探测信号又和地面积水的探测信号非常相似,所以导致这三种目标难以分辨。针对这一问题,从毫米波被动探测平面金属、积水、装甲目标探测信号的基本理论出发,通过建立目标模型、推导天线温度计算模型,仿真得到了这三种目标的探测信号,查找信号差异并分析总结了造成差异的根源。仿真结果证实了分析的正确性和有效性,为地面装甲目标识别算法的研究提供了必要的理论支撑和分析依据。