A Remark on Polynomial Mappings from Cn to Cn-1 and an Application of the Software Maple in Research

In [1], we construct singular varieties associated to a polynomial mapping where such that if G is a local submersion but is not a fibration, then the 2-dimensional homology and intersection homology (with total perversity) of the variety are not trivial. In [2], the authors prove that if there exists a so-called very good projection with respect to the regular value of a polynomial mapping , then this value is an atypical value of G if and only if the Euler characteristic of the fibers is not constant. This paper provides relations of the results obtained in the articles [1] and [2]. Moreover, we provide some examples to illustrate these relations, using the software Maple to complete the calculations of the examples. We provide some discussions on these relations. This paper is an example for graduate students to apply a software that they study in the graduate program in advanced researches.

A Remark on the Topology at Infinity of a Polynomial Mapping F: Cn→Cn via Intersection Homology

In [1], Guillaume and Anna Valette associate singular varieties VF to a polynomial mapping . In the case , if the set K0(F) of critical values of F is empty, then F is not proper if and only if the 2-dimensional homology or intersection homology (with any perversity) of VF is not trivial. In [2], the results of [1] are generalized in the case where n≥3, with an additional condition. In this paper, we prove that for a class of non-proper generic dominant polynomial mappings, the results in [1] and [2] hold also for the case that the set K0(F) is not empty.

An Algorithm to Classify the Asymptotic Set Associated to a Polynomial Mapping

We provide an algorithm to classify the asymptotic sets of the dominant polynomial mappingsof degree 2, using the definition of the so-called “fa?ons” in [2]. We obtain a classification theorem for the asymptotic sets of dominant polynomial mappingsof degree 2. This algorithm can be generalized for the dominant polynomial mappingsof degree d, with any (n,d)∈(N*)2.

Uniform Convergence of Extremal Polynomials When Domains Have Corners and Special Cusps on the Boundary

We study the approximation properties of the extremal polynomials in Ap?norm and C?norm. We prove estimates for the rate of such convergence of the sequence of the extremal polynomials on domains with corners and special cusps.

Numerical solution to the Falkner-Skan equation:a novel numerical approach through the new rational α-polynomials

The new rationalα-polynomials are used to solve the Falkner-Skan equation.These polynomials are equipped with an auxiliary parameter.The approximated solution to the Falkner-Skan equation is obtained by the new rational a-polynomials with unknown coefficients.To find the unknown coefficients and the auxiliary parameter contained in the polynomials,the collocation method with Chebyshev-Gauss points is used.The numerical examples show the efficiency of this method.

MODIFIED ROPER-SUFFRIDGE OPERATOR FOR SOME SUBCLASSES OF STARLIKE MAPPINGS ON REINHARDT DOMAINS

In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.

DICHROMATIC SUM EQUATIONS FOR OUTERPLANAR MAPS

This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. By the equation, the dichromatic sum function can be found explicitly.

Results About Parabolic-Like Mappings

In this paper we present the most important definitions and results of the theory of parabolic-like mappings, and we will give an example. The proofs of the results can be found in [2,4] and [3].

融合T-分布小波变异的混沌鲸鱼优化算法

针对鲸鱼优化算法难以跳出局部最优导致收敛精度不足的问题,提出一种融合了T-分布小波变异和多项式差分学习策略的鲸鱼优化算法.该算法首先引入Circle混沌扩大搜索范围,提高收敛速度;然后采用T-分布小波变异策略平衡全局和局部搜索能力;最后采用多项式差分学习策略改进算法的优化精度.对3种改进策略作单一引入的仿真对比分析,并将改进的鲸鱼优化算法在12个可变维度的基准测试函数上进行仿真,对本文改进的鲸鱼优化算法与其他改进策略的鲸鱼优化算法以及其他几种智能算法进行比较.结果表明,基于T-分布小波变异和多项式差分学习策略的改进鲸鱼优化算法具有较好的稳定性,收敛速度和精度更好.

多项式变异和自适应权重优化的阿奎拉鹰算法

针对基本阿奎拉鹰算法存在收敛精度低、易陷入局部最优的问题,通过在全局搜索阶段引入多项式变异扰动策略,在局部开发阶段引入自适应权重优化策略,改进了阿奎拉鹰算法的局部探索能力,并且引入了Tent混沌映射初始化种群,增加种群多样性,引入动态转换概率策略来平衡全局探索和局部开发的比重,故提出多项式变异和自适应权重优化的阿奎拉鹰算法。采用基本阿奎拉鹰算法、哈里斯鹰算法、灰狼算法、鲸鱼算法、海鸥算法做对比,9个基准测试函数和2个工程优化问题对改进后的算法进行寻优性能验证,结果表明:改进后的算法在多数测试函数上取得较好的寻优效果,在工程优化问题中,效果优于多数对比算法。证明了改进后的算法具有更快的收敛速度和精度,并在工程应用中取得较好效果。

基于陆态网和IGS站联合数据的中国区域电离层建模方法

为了提高中国区域电离层垂直总电子含量(vertical total electron content,VTEC)建模的精度,减少区域建模边缘误差,利用中国地壳运动观测网络(Crustal Movement Observation Network of China,CMONOC)和国际GNSS服务组织(International GNSS Service,IGS)GPS数据联合进行电离层建模,并对中国区域电离层建模策略进行定量考察,对比给出各类建模策略对中国区域电离层建模精度的影响,从而给出更符合中国区域的电离层建模方式。将建模后的结果同IGS中心的全球电离层格网产品进行比对,结果显示:基于本文方法对中国区域电离层建模的结果精度更高,与IGS数据中心发布的电离层格网产品相比误差平均值为1.2109 TECU,与卫星实测电离层TEC的内符合精度误差为1.050 TECU。说明利用联合数据建模能一定程度上提高中国区域建模的精度,同时减少区域建模边缘的误差。

基于改进蜣螂优化算法的机械臂轨迹规划方法研究

本文以ABB-IRB 120为研究对象,建立了机械臂连杆坐标系以及DH参数表,并在给定运动学基础上,将改进蜣螂优化算法应用于4-3-4分段多项式轨迹优化中;最后将改进蜣螂优化算法和粒子群优化算法进行对比,得到了机械臂关节适应度变化曲线。仿真实验结果表明,相较粒子群算法,改进蜣螂算法能有效提高解的寻优精度和收敛速度,大幅度缩短机械臂运行时间,降低了机械臂在运行过程中的冲击与振动。

二阶奇异摄动问题的新的谱元方法

由于二阶奇异摄动问题的解具有边界层,用传统的数值方法很难得到理想的逼近效果.为了高效地求解此类问题,对区间做剖分,分别使用移位的映射Legendre多项式和传统Legendre多项式作为基函数,提出新型混合谱元法.该方法能够更好地模拟解在边界层附近的奇异行为.数值结果验证了所提方法的高效性.

Some Polynomial Maps with Jacobian Rank Two or Three

We classify all polynomial maps of the form H=(u(x,y,z),v(x,y,z),h(x,y))in the case when the Jacobian matrix of H is nilpotent and the highest degree of z in v is no more than 1.In addition,we generalize the structure of polynomial maps H to H=(H_(1)(x_(1),x_(2),…,x_(n)),b_(3)x_(3)+…+b_(n)x_(n)+H^((0))_(2)(x_(2)),H_(3)(x_(1),x_(2)),…,H_(n)(x_(1),x_(2))).

Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form

This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field F_(q), which are functions F_(q)→F_(q) that agree with a suitable monomial function x↦axr on each coset of the index d subgroup of F_(q)^(*). We discuss two important rewriting procedures in the context of generalized cyclotomic mappings and present applications thereof that concern index d generalized cyclotomic permutations of F_(q) and pertain to cycle structures, the classification of (q−1)-cycles and involutions, as well as inversion.

三线阵CCD卫星影像的模拟研究

在讨论从给定的DEM和相应的正射影像模拟三线阵CCD卫星影像的原理和方法的基础上 ,通过模拟影像考察两种卫星影像近似核线的适应能力和地球自转效应对同轨立体成像能力的影响 ,并讨论了从DEM和正射影像确定投影中心轨迹、姿态模拟、共线方程和影像生成等细节。通过试验验证了模拟影像的正确性 。

多项式插值法绘制发动机万有特性曲线

发动机万有特性可直观的反映发动机在其运行范围内的各项性能参数的变化情况。该文利用多项式插值法绘制发动机万有特性曲线。推导了三次多项式插值公式和三次多项式插值余项,绘制了发动机万有特性曲线。结果表明三次多项式插值法能精确地反映发动机特性,并可用该方法绘制发动机等油耗、等排放等特性曲线。为绘制发动机特性曲线、研究发动机性能提供较好的方法。

时间序列InSAR技术中的形变模型研究

对时间序列InSAR的形变模型问题展开研究。首先从干涉相位模型解算的方法入手,针对线性形变模型当干涉点目标的密度不够并且真实形变的非线性较强时,干涉相位方程的解将会发散的不足,根据魏尔斯特拉斯(Weier-strass)逼近定理,提出以高阶多项式取代线性形变模型,并给出了基于多项式形变模型的干涉相位方程解算方法。以太原市地面沉降监测为例,分别采用线性形变模型和三次多项式形变模型进行形变反演。结果表明,多项式形变模型不仅能取得更高的形变测量精度,而且能提高点目标的密度。

室内移动机器人路径规划研究

路径规划是自主移动机器人的研究重点。针对传统的A*算法搜索出的路径存在途径危险区域,未考虑机器人外形尺寸、路径不平滑等问题,提出了一种改进A*算法的路径规划方法。在新的栅格化环境地图中,通过改进的搜索策略进行路径搜索;并对路径点删减和优化,通过分段多项式曲线平滑路径。实验仿真结果表明,新方法生成的路径满足移动机器人的动力学和运动学特性,且更符合室内移动机器人的轨迹跟踪和运动控制,该方法简单有效。

基于GPS定位的导航地图的转换与纠正方法

介绍了利用GPS定位技术对低精度的地图进行转换和变形纠正的算法 ,结合实例分析了GPS数据采集、坐标转换和利用拟合算法进行地图纠正的步骤 ,对一次多项式、二次多项式和三次多项式的拟合结果进行了比较 ,结果表明采用二次或三次多项式拟合精度最好 ,获得了与GPS定位结果相匹配的精度 ,坐标分量X和Y的拟合精度分别为 8m和 17m ,纠正后的地图适合于一般车载导航和监控 .