A vertex‐centered linearity‐preserving discretization of diffusion problems on polygonal meshes

This paper introduces a vertex‐centered linearity‐preserving finite volume scheme for the heterogeneous anisotropic diffusion equations on general polygonal meshes. The unknowns of this scheme are purely the values at the mesh vertices, and no auxiliary unknowns are utilized. The scheme is locally conservative with respect to the dual mesh, captures exactly the linear solutions, leads to a symmetric positive definite matrix, and yields a nine‐point stencil on structured quadrilateral meshes. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Also, the relation with the finite volume element method is discussed. Finally, some numerical tests show the optimal convergence rates for the discrete solution and flux on various mesh types and for various diffusion tensors. Copyright © 2015 John Wiley & Sons, Ltd.     

具渐近线性无共振p(x)-Laplace方程的多解性

研究了如下p(x)-Laplace方程(?)多解的存在性问题,其中Ω是R~N上具有光滑边界的有界区域.我们以改进的山路引理为工具,获得了在给予f(x,u)某些条件的基础上,该问题具有多解性结果的结论.     

Linear Bayes and Optimal Estimation

In non-Bayesian statistics, it is often realistic to replace a full distributional assumption by a much weaker assumption about its first few moments; such as for instance, mean and variance. Along the same lines in Bayesian statistics one may wish to replace a completely specified prior distribution by an assumption about just a few moments of the distribution. To deal with such Bayesian semi-parametric models defined only by a few moments, Hartigan (1969, J. Roy. Statist. Soc. Ser. B, 31, 440-454) put forward linear Bayes methodology. By now it has become a standard tool in Bayesian analysis. In this paper we formulate an alternative methodology based on the theory of optimum estimating functions. This alternative methodology is shown to be more readily applicable and efficient in common problems, than the linear Bayes methodology mentioned above.     

非预解形式线性微分方程的解

通过几个实例给出解非预解形式线性微分方程的一般方法,并讨论了预解形式的线性微分方程与非预解形式的线性微分方程解集的差别.     

基于模式识别技术的色貌模型评价研究

选用Munsell新标数据集,采用基于模式识别技术的圆度、色相角偏差、明度线性度与空间投影点聚集度四个指标来分别评价目前八个典型色貌模型在彩度均匀性、色相预测准确性、明度均匀性、颜色的空间再现的能力。结果表明,不同的色貌模型在四个方面的颜色再现性上表现出不同的优势。八个色貌模型对彩度预测最好的是RLAB,每个色貌模型对红色和绿色预测比较好,CAM02在色相预测整体上占优势;明度的均匀性预测都比较好,尤其是CIELAB;LLAB的颜色的空间再现能力最好。     

Al掺杂浓度对ZnO陶瓷释能电阻材料性能的影响

为了制备ZnO释能电阻并研究Al掺杂浓度对ZnO释能电阻材料的影响,通过改进的制陶工艺制备了不同Al掺杂浓度的ZnO导电陶瓷。实验结果表明,Al掺杂浓度对ZnO释能电阻的导电性、能量密度和线性度均有较大的影响。Al的掺杂能较好地改善ZnO释能电阻的线性度,非线性系数可低至1.02;Al掺杂能很好地控制ZnO的电阻率,使其达到0.54 Ω·cm;Al掺杂还能较好地改善ZnO陶瓷的均匀性和密度,从而提高ZnO释能电阻的能量吸收密度,能量吸收密度高达720 J/cm³,较金属释能材料高出2~3倍。     

Dynamic range and linearity improvement for zero-field single-beam atomic magnetometer

Zero-field single-beam atomic magnetometers with transverse parametric modulation for ultra-weak magnetic field detection have attracted widespread attention recently. In this study, we present a comprehensive response model and propose a modification method of conventional first harmonic response by introducing the second harmonic correction. The proposed modification method gives improvement in dynamic range and reduction of linearity error. Additionally, our modification method shows suppression of response instability caused by optical intensity and frequency fluctuations. An atomic magnetometer with single-beam configuration is built to compare the performance between our proposed method and the conventional method. The results indicate that our method's magnetic field response signal achieves a 5-fold expansion of dynamic range from 2 nT to 10 nT, with the linearity error decreased from 5% to 1%. Under the fluctuations of 5% for optical intensity and ±15 GHz detuning of frequency, the proposed modification method maintains intensity-related instability less than 1% and frequency-related instability less than 8% while the conventional method suffers 15% and 38%, respectively. Our method is promising for future high-sensitive and long-term stable optically pumped atomic sensors.     

精细积分的非线性动力学积分方程及其解法

给出了非线性动力学积分方程的表达式,针对该方程提出了一个显式预测－校正的单步四阶精度的积分算法,适用于多自由度、强非线性,非保守系统。算例表明该方法精度高、计算量较少。     

Directly testing the linearity assumption for assay validation

The ICH Q2(R1) (International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use) guideline for testing linearity in validation of analytical procedures suggests that “linearity should be evaluated by visual inspection of a plot of signals as a function of analyte concentration or content.” The EP6‐A guideline recommends more quantitative methods that compare straight‐line and higher‐order polynomial curve fits. In this paper, a new equivalence test is proposed to compare the quality of a straight‐line fit to that of a higher‐order polynomial. By using orthogonal polynomials and generalized pivotal quantity analysis, one may estimate the probability of equivalence between a straight line and a polynomial curve fit either in the assay signal space (the Y values) or in the concentration space (the X values). In the special case of the linear‐to‐quadratic polynomial comparison, an equivalence test may be constructed via a two one‐sided T test. Copyright © 2013 John Wiley & Sons, Ltd.