Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation

This paper is devoted to the testing and comparison of numerical solutions obtained from higher-order accurate finite difference schemes for the two-dimensional Burgers' equation having moderate to severe internal gradients. The fourth-order accurate two-point compact scheme, and the fourth-order accurate Du Fort Frankel scheme are derived. The numerical stability and convergence are presented. The cases of shock waves of severe gradient are solved and checked with the fourth-order accurate Du Fort Frankel scheme solutions. The present study shows that the fourth-order two-point compact scheme is highly stable and efficient in comparison with the fourth-order accurate Du Fort Frankel scheme.     

Half-width temperature dependence of nitrogen broadened lines in the ν2 band of H2O

Forty-seven N₂ broadened water vapor line-widths have been measured in the 1845-2140 cm⁻¹ spectral range with a Fourier Transform spectrometer in the 258-330 K temperature range at a spectral resolution of 0.005 cm⁻¹ for the lines with upper state rotational quantum number up to 16. The measured exponents of the temperature dependence of the width exhibit a large range of values from 1.60 to −0.86. Theoretical calculations were made using a semi-empirical technique based on the Anderson theory. The calculated broadening coefficients as well as the temperature exponents for the half-width agree satisfactory with measured values.     

地面附近的高空核爆电磁脉冲环境

 主要研究在高空核爆的双指数类型电磁脉冲平面波入射时，地面附近的电磁脉冲环境。计算给出了在不同入射波状态，不同地表介质电气特性和距地面不同高度等条件下的电磁脉冲环境参数，归纳了一些规律性认识。结果显示：地面附近的电场会随距地面高度的不同而发生显著的变化，对于水平场分量，其反射场总是试图抵消入射场，而对于垂直场分量，其反射场叠加在入射场上，使得地面附近的垂直场强幅值一般大于入射波场强幅值；当入射波仰角增大时，合成电场波形的脉冲宽度会变宽；地表介质的电气特性参数不同也会对地面附近电场的波形和幅值造成一定的影响。     

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

Determining radii of meromorphy via orthogonal polynomials on the unit circle

Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szeg functions.     

湖南省各市州经济发展水平评价

本文利用主成分分析法分析了湖南各市州的经济发展水平和经济综合实力,对湖南省14个市州的经济发展情况做出综合评价,得出了各市州在湖南省的经济地位.最后用系统聚类分析法进行了验证,结果表明用多元统计分析法来评价地区经济发展水平是可行的.     

负电子亲和势GaAs光电阴极中的三光子激发和发射的理论研究

将三阶微扰理论应用于单晶GaAs半导体,结合与实际相接近的能带结构,得到了GaAs中三光子吸收系数的解析式表达式,在考虑了激发电子的逃逸过程的情况下,进而推导了负电子亲和势GaAs光电阴极中三光子光电发射的发射系数的解析表达式.两表达式得到的理论数值分别与用ns量级脉宽、2.06μm波长的激光测得的GaAs中三光子吸收系数和GaAs(Cs,O)光电阴极中三光子发射系数的实验值相比较,吻合较好.     

Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions

For any Sturm-Liouville problem with a separable boundary condition and whose leading coefficient function changes sign (exactly once), we first give a geometric characterization of its eigenvalues λn using the eigenvalues of some corresponding problems with a definite leading coefficient function. Consequences of this characterization include simple proofs of the existence of the λn's, their Prüfer angle characterization, and a way for determining their indices from the zeros of their eigenfunctions. Then, interlacing relations among the λn's and the eigenvalues of the corresponding problems are obtained. Using these relations, a simple proof of asymptotic formulas for the λn's is given.     

Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

对期望理论的两个重要推进——损失厌恶系数λ及参考点研究

行为金融学是近20年来最为重要的新兴金融理论,期望理论更是其中的亮点,其运用领域之广超乎人们的想象,所以对它的完善改进具有非常重要的意义。本文对期望理论中的损失厌恶系数和参考点问题进行了深入研究,并且得出了创新性的结果:损失厌恶系数不是常数而是动态变量;得出了内生且纳入更多投资者行为特征的参考点。这些结果是对期望理论的重要改善和推进,对其在大量金融领域和涉及到财富偏好的问题的解决中都大有裨益。