多项式偏最小二乘法对非线性体系红外谱图的分析

文章利用了一种非线性模型多项式偏最小二乘法(PPLS),结合傅里叶变换红外光谱遥感技术,对大气中的五组分混合体系进行了同时分析。并与偏最小二乘法(PLS)得到的结果进行了比较,PPLS显示出较好的处理非线性数据的能力。尤其是对混合物中的苯和氯仿的预测,均方根预测误差(RMSEP)分别是0.043和0.087,用PLS预测相应的RMSEP为0.402和0.842。PPLS的这一预测精度,可以满足遥感傅里叶变换红外光谱对大气中有毒气体的实时、在线监测的需要。同时PPLS可以用较少的潜变量对变量进行解释,显示出PPLS模型的稳健性和简单化。     

A high-order finite volume method for systems of conservation laws—Multi-dimensional Optimal Order Detection (MOOD)

In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.     

On a problem of Byrnes concerning polynomials with restricted coefficients, II

As in the earlier paper with this title, we consider a question of Byrnes concerning the minimal length of a polynomial with all coefficients in which has a zero of a given order at . In that paper we showed that for all and showed that the extremal polynomials for were those conjectured by Byrnes, but for that rather than . A polynomial with was exhibited for , but it was not shown there that this extremal was unique. Here we show that the extremal is unique. In the previous paper, we showed that is one of the 7 values or . Here we prove that without determining all extremal polynomials. We also make some progress toward determining . As in the previous paper, we use a combination of number theoretic ideas and combinatorial computation. The main point is that if is a primitive th root of unity where is a prime, then the condition that all coefficients of be in , together with the requirement that be divisible by puts severe restrictions on the possible values for the cyclotomic integer .

     

二元整系数多项式因式分解的一种理论和算法

我们发现可以把二元多项式盾成系数为一元多项式的一元多项式来进行分解，据此，本文建立了二元整系数多项式因式分解的一种理论，提出了一个完整的分解二元整系数多项式的算法。这个算法还能很自然地推广成分解多元整系数多项式的算法。     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

On theorems of Gelfond and Selberg concerning integral-valued entire functions

For each sN define the constant θ_s with the following properties: if an entire function g(z) of type t(g)<θ_s satisfies then g is a polynomial; conversely, for any δ>0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g)<θ_s+δ. The result θ₁=log2 is known due to Hardy and Pólya. We provide the upper bound θ_sπs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941).     

A Color Appearance Model Applicable in Mesopic Vision

We propose a color vision model that can be used to predict color appearance in mesopic vision as well as photopic and scotopic vision. It is based on a two-stage model which consists of the cone and opponent stages and it assumes rod intrusion at the opponent stage. The model has the following features to describe the color appearance in mesopic vision. First, it includes a gradual and nonlinear shift in spectral luminous efficiency from V (LD) to V (LD) to cope with the spectral sensitivity difference between photopic and scotopic vision and the nonlinearity of rod influence on the luminance channel. Second, the model assumes decrease of the chromatic component with decreasing illuminance to explain the reduction of saturation at low illuminance levels. Third, it assumes that red/green and yellow/blue components change with illuminance levels independently, thus explaining hue shifts with decreasing illuminance. We applied the model for color appearance simulation of natural scenes in a mesopic visual environment.     

Polynomial functions and permutation polynomials over some finite commutative rings

We extend some classical results on polynomial functions . We prove all results in algebraic methods avoiding any combinatorial calculation. As applications of our methods, we obtain some interesting new results on permutation polynomials in several variables over some finite commutative rings.