单负材料界面处反射相位特性研究

根据Maxwell电磁场理论,推导出线偏振单色平面波的普适菲涅尔表达式,得到特异材料反射相移计算公式。利用反射相移公式研究了线偏振单色平面波从空气入射到单负材料(ε0或μ0)时分界面处反射相位的特性。结果表明单负材料界面处反射相位连续变化,与传统材料全反射的相位变化特点相似。     

Unordered and ordered sample from dirichlet distribution

Consider the random Dirichlet partition of the interval inton fragments with parameter π>0. Explicit results on the statistical structure of its size-biased permutation are recalled, leading to (unordered) Ewens and (ordered) Donnelly-Tavaré-Griffiths sampling formulae from finite Dirichlet partitions. We use these preliminary statistical results on frequencies distribution to address the following sampling problem: what are the intervals between new sampled categories when sampling is from Dirichlet populations? The results obtained are in accordance with the ones found in sampling theory from random proportions with GEM(γ) distribution. These can be obtained from Dirichlet model when considering the Kingman limitn↑∞, π↓0 whilenπ=γ>0.     

A note on Black–Scholes implied volatility

An approximate formula for the Black–Scholes implied volatility is given by means of an asymptotic representation of the Black–Scholes formula. This representation is based on a variable change that reduces the number of meaningful variables from five to three. It is stated clearly which is the family of functions we are going to work, specially the inverse of the normal accumulative function. Estimates for the error in the resulting approximate formulas for both the option value and the volatility are obtained as well.     

A combinatorial proof of the reduction formula for Littlewood-Richardson coefficients

There are well-known reduction formulas for the universal Schubert coefficients defined on Grassmannians. These coefficients are also known as the Littlewood-Richardson coefficients in the theory of symmetric functions. We restate the reduction formulas combinatorially and provide a combinatorial proof for them.     

Intrinsic geometry of curves and the Bonnor’s equation

The exact form of the paths of charged particles moving according to Bonnor’s equation, for the case of constant electromagnetic field, is found. The method employed is fully relativistic and is based on systematic use of the Frenet-Serret equations which determine the world line geometry in Minkowskian space.     

A Definiteness Theory for Cubature Formulae of Order Two

Let Ω ⊂ ℝ^d be a compact convex set of positive measure. A cubature formula will be called positive definite (or a pd-formula, for short) if it approximates the integral ∫_Ω f(x) dx of every convex function f from below. The pd-formulae yield a simple sharp error bound for twice continuously differentiable functions. In the univariate case (d = 1), they are the quadrature formulae with a positive semidefinite Peano kernel of order two. As one of the main results, we show that there is a correspondence between pd-formulae and partitions of unity on Ω. This is a key for an investigation of pd-formulae without employing the complicated multivariate analogue of Peano kernels. After introducing a preorder, we establish criteria for maximal pd-formulae. We also find a lower bound for the error constant of an optimal pd-formula. Finally, we describe a phenomenon which resembles a property of Gaussian formulae.     

含Hilbert核的奇异积分带重结点的求积公式

本文讨论了Ｈｅｒｍｉｔｅ三角插值问题利用Ｈｅｒｍｉｔｅ三角插值建立２π周期函数正常积分带重结点的求积公式，用分离奇异点的方法建立了含Ｈｉｌｌｂｅｒｔ核的奇积分带重结点的求积公式。     

Asymptotic enumeration of some RNA secondary structures

In this paper, we derive recursions of some RNA secondary structures with certain properties under two new representations. Furthermore, by making use of methods of asymptotic analysis and generating functions we present asymptotic enumeration of these RNA secondary structures.