局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

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.     

相对性区域创新指数与经济周期挖掘

提出了一类新的相对性区域创新指数,并采用世界专利申请数据对其进行了具体计算.基于区域创新同经济发展水平之间的超线性关系,该指数消除了经济发展水平对创新能力的影响,可以实现对不同发展水平的经济体之间进行有效的创新能力横纵对比.该创新指数尽管极其简单,却揭示出一系列迥异于传统认知的现象,例如中国大陆地区的技术创新能力在1980年代就已经位居世界前列.采用该指数,不但可以在较高水平上解释世界各国的经济增长,还发现它同经济增长率之间的相关性存在一个20年的经济周期.这些结果显示,该指数作为一个单一性指标,以极小的数据依赖就实现了较高程度的解释性,不但重新定位了世界各经济体的创新能力,对深入理解创新同经济发展之间的关系提供了新的角度,而且暗示着这类相对性经济指标的发展潜力与应用空间.     

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.     

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.     

NUMERICAL SIMULATION WITH A COMPREHENSIVE CHEMICAL TRANSPORT MODEL OF NITRATE, SULFATE, AND AMMONIUM AEROSOL DISTRIBUTIONS OVER EAST ASIA

The transport and chemical production processes of nitrate, sulfate, and ammonium aerosols over East Asia were investigated by use of the Models-3 Community Multi-scale Air Quality （CMAQ） modeling system coupled with the Regional Atmospheric Modeling System （RAMS）. For the evaluation of the model＇s ability in depicting their 3-dimensional concentration distributions and temporal variations, modeled concentrations of nitrate, sulfate, and ammonium aerosols are compared with the observations obtained at a ground station in Japan in March 2001 and onboard of an aircraft DC-8 on 18 and 21 March 2001 during the Transport and Chemical Evolution over the Pacific （TRACE-P） field campaign. Comparison shows that simulated values of nitrate, sulfate, and ammonium aerosols are generally in good agreement with their observed data, and the model captures most important observed features, and reproduces temporal and spatial variations of nitrate, sulfate, and ammonium aerosol concentrations reasonably well, e.g., the timing and locations of the concentration spikes of nitrate, sulfate, and ammonium aerosols are well reproduced, but large discrepancies between observed and simulated values are also clearly seen at some points and some times due to the coarse grid resolution and uncertainties of the emissions used in this study. This comparison results indicate that CMAQ is able to simulate the distributions of nitrate, sulfate, and ammonium aerosols and their related species in the troposphere over East Asia reasonably well.     

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).