自然光入射时反射及折射光的偏振态与入射角之关系

应用菲涅耳公式对自然光入射时反射及折射光的偏振态与入射角之关系进行了讨论。发现对于反射光来说,在布儒斯特角两侧平行入射面的光振动与垂直入射面的光振动振幅之比不是一个对称关系;对于折射光来说,平行入射面的光振动与垂直入射面的光振动振幅之比是单调上升的。     

泰勒公式的应用

给出泰勒公式在证明不等式及在求极限中的应用     

不饱和度的计算方法及通用公式的推导

介绍了几种常见不饱和度的计算方法并扩展了相应烃法,推导了一个适合包括多元有机复合物在内的所有有机物的不饱和度通用计算公式．     

我国公司并购成功率的预测方法探析

公司并购成功与否的预测,不仅关系到并购双方以及并购标的物的利益,而且也是众多中小投资者判断投资价值的重要标准,且一次错误的预测往往带来不可计量的经济损失.在剔除了诸多因素变量后,最终选取了对并购成功率起重要作用的3个因素作为自变量,分别用logistic回归模型和前馈神经网络模型来建立两种并购成功率预测模型,对近三年来的2 611个并购案例有效样本进行分析,结果表明两种模型在并购成功率预测应用中各有优劣,为未来参与并购的企业以及投资者的预测提供有力的借鉴.     

一种神经网络结构优化算法研究

提出一种广义自适应前馈网络算法,通过调节参数 ,若满足预先设置的范围,那么输入层和各隐节点规模被认为是合适的,即令网络结构按精度和推广能力来综合考虑,且将输入层中一些无关因素删除,以避免维数灾难。     

梯形修正公式及其余项“中间点”的渐近性

给出了一种带端点导数的梯形修正公式,并给出了该公式的截断误差。分析了相应的复化求积公式的收敛阶,其收敛阶比复化梯形法提高了2阶;并通过对梯形修正公式余项的研究。讨论了该求积公式余项中间点的渐近性,使求积公式的代数精度得到进一步提高。     

关于正整数的k次方部分数列均值研究

研究了数列ak(n)和bk(n)的性质,其中ak(n)表示不超过n的最大k次方部分,bk(n)表示不小于n的最小k次方部分,并给出了关于这两个数列的有趣的均值渐近公式。     

Multivariate Bernoulli Functions and Polyharmonically Exact Cubature Formula of Euler–Maclaurin

In the present paper we provide a multivariate generalization of the Euler–Maclaurin formula which is based on an appropriate multivariate extension of the Bernoulli functions.     

Littlewood–Paley Theory and Function Spaces with Alocp Weights

Characterizations via convolutions with smooth compactly supported kernels and other distinguished properties of the weighted Besov–Lipschitz and Triebel–Lizorkin spaces on ℝⁿ with weights that are locally in A_p but may grow or decrease exponentially at infinity are investigated. Square–function characterizations of the weighted L^p and Hardy spaces with the above class of weights are also obtained. A certain local variant of the Calderón reproducing formula is constructed and widely used in the proofs.     

Monotone Proofs of the Pigeon Hole Principle

We study the complexity of proving the Pigeon Hole Principle (PHP)in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We prove a size‐depth trade‐off upper bound for monotone proofs of the standard encoding of the PHP as a monotone sequent. At one extreme of the trade‐off we get quasipolynomia ‐size monotone proofs, and at the other extreme we get subexponential‐size bounded‐depth monotone proofs. This result is a consequence of deriving the basic properties of certain monotone formulas computing the Boolean threshold functions. We also consider the monotone sequent expressing the Clique‐Coclique Principle (CLIQUE) defined by Bonet, Pitassi and Raz [9]. We show that monotone proofs for this sequent can be easily reduced to monotone proofs of the one‐to‐one and onto PHP, and so CLIQUE also has quasipolynomia ‐size monotone proofs. As a consequence of our results, Resolution, Cutting Planes with polynomially bounded coefficients, and Bounded‐Depth Frege are exponentially separated from the monotone Gentzen Calculus. Finally, a simple simulation argument implies that these results extend to the Intuitionistic Gentzen Calculus. Our results partially answer some questions left open by P. Pudlák.