An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Condensed Cramer rule for some restricted quaternion linear equations

In this paper, we derive an alternative more condensed Cramer rule for the unique solution of some restricted left and right systems of quaternion linear equations. The findings of this paper extend some known results in the literature.     

The rotational dimension of a graph

Given a connected graph G = (N, E) with node weights s∈? and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of G: Find v_i∈?^|N|, i∈N so that distances between adjacent nodes do not exceed prescribed edge lengths, the weighted barycenter of all points is at the origin, and is maximized. In the case of a two‐dimensional optimal solution this corresponds to the equilibrium position of a quickly rotating net consisting of weighted mass points that are linked by massless cables of given lengths. We define the rotational dimension of G to be the minimal dimension k so that for all choices of lengths and weights an optimal solution can be found in ?^k and show that this is a minor monotone graph parameter. We give forbidden minor characterizations up to rotational dimension 2 and prove that the rotational dimension is always bounded above by the tree‐width of G plus one. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:283‐302, 2011     

Trigonometric Widths and Best N-Term Approximations of the Generalized Periodic Besov Classes BΩp,θ

In this paper,we determine the estimates exact in order for the trigonometric widths and the best n-term trigonometric approximations of the generalized classes of periodic functions BΩp,θ in the space Lq for some values of parameters p,q.     

An accurate theory for the square-well potential: from long to short well width

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.     

衍射光强取样分析法测定划痕宽度：实验部分

根据衍射光强取样分析法理论部分的测量原理设计了一套实验方案，比较了该方法一义、显痛实际宽度的测试结果，给出了其对测量误差，并分析了误差的主要来泊，该方法速度快，精度高，有推广和应用的价值。     

塞曼效应与边缘离子温度的光谱测量

通过理论推导得到了谱线实际宽度和塞曼展宽之间的关系。在磁感应强度分别为1、2、2．5和3T的情况下，用数值方法进行了求解，用得到的结果拟合出了校正因子随离子温度变化的经验公式和拟合曲线，结果表明：离子温度较低时，塞曼效应对谱线宽度的影响很大，温度较高时，塞曼效应对谱线宽度的影响可以忽略。