On bipartite graphs with minimal energy

The energy of a graph is the sum of the absolute values of the eigenvalues of the graph. In a paper [G. Caporossi, D. Cvetkovi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs with external energy, J. Chem. Inf. Comput. Sci. 39 (1999) 984-996] Caporossi et al. conjectured that among all connected graphs G with n≥6 vertices and n−1≤m≤2(n−2) edges, the graphs with minimum energy are the star S_n with m−n+1 additional edges all connected to the same vertices for m≤n+⌊(n−7)/2⌋, and the bipartite graph with two vertices on one side, one of which is connected to all vertices on the other side, otherwise. The conjecture is proved to be true for m=n−1,2(n−2) in the same paper by Caporossi et al. themselves, and for m=n by Hou in [Y. Hou, Unicyclic graphs with minimal energy, J. Math. Chem. 29 (2001) 163-168]. In this paper, we give a complete solution for the second part of the conjecture on bipartite graphs. Moreover, we determine the graph with the second-minimal energy in all connected bipartite graphs with n vertices and edges.     

A bound for orders in differential Nullstellensatz

We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed in [A. Seidenberg, An elimination theory for differential algebra, Univ. of California Publ. in Math. III (2) (1956) 31–66] but no complete solution was given. Our result is a complement to the corresponding result in algebraic geometry, which gives a bound on degrees of polynomial coefficients in effective Nullstellensatz [G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1) (1926) 736–788; E.W. Mayr, A.W. Meyer, The complexity of the word problems for commutative semigroups and polynomial ideals, Adv. Math. 46 (3) (1982) 305–329; W.D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. 126 (3) (1987) 577–591; J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (4) (1988) 963–975; L. Caniglia, A. Galligo, J. Heintz, Some new effectivity bounds in computational geometry, in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Rome, 1988, in: Lecture Notes in Comput. Sci., vol. 357, Springer, Berlin, 1989, pp. 131–151; N. Fitchas, A. Galligo, Nullstellensatz effectif et conjecture de Serre (théorème de Quillen–Suslin) pour le calcul formel, Math. Nachr. 149 (1990) 231–253; T. Krick, L.M. Pardo, M. Sombra, Sharp estimates for the arithmetic Nullstellensatz, Duke Math. J. 109 (3) (2001) 521–598; Z. Jelonek, On the effective Nullstellensatz, Invent. Math. 162 (1) (2005) 1–17; T. Dubé, A combinatorial proof of the effective Nullstellensatz, J. Symbolic Comput. 15 (3) (1993) 277–296].This paper is dedicated to the memory of Eugeny Pankratiev, who was the advisor of the first three authors at Moscow State University.     

α螺旋蛋白质螺旋链模型的精确解组

文章运用Maple语言程序,在没有假设的条件下,得到了α螺旋蛋白质螺旋链运动模型方程组的行波精确解组,它涵盖了所有的耦合解组与非耦合解组,具有任意性.耦合解组的算例函数及其特性分析,解释了α螺旋蛋白质螺旋链运动模型的行波孤立子解的耦合效应,揭示了增加、稳定和控制蛋白质活性和功能的方向,文章的研究方法,为求解生物大分子螺旋链运动模型的行波精确解组探索了溪径.     

LS-SVM的梨可溶性固形物近红外光谱检测的特征波长筛选

为提高梨可溶性固形物含量(soluble solids content,SSC)的近红外光谱模型的精度和稳定性,以160个梨样品为实验对象,分别对原始光谱、多元散射校正(MSC)和标准正态变量变换(SNV)处理后的光谱,经无信息变量消除算法(UVE)挑选后,再结合遗传算法(GA)和连续投影算法(SPA),筛选梨可溶性固形物的近红外光谱特征波长。将筛选后的波长作为输入变量建立梨可溶性固形物的最小二乘支持向量机(LS-SVM)模型。结果表明经过SNV-UVE-GA-SPA从全波段3112个波长中筛选出的30个特征波长建立的梨可溶性固形物LS-SVM模型效果最好,该模型的预测集相关系数(R_p)和预测均方根误差(RMSEP)分别为0.956和0.271。该模型简单可靠,预测效果好,能满足梨的可溶性固形物含量的快速检测,为在线检测和便携式设备开发提供了理论基础。     

微型X射线管靶材厚度理论计算与出射光谱模拟研究

根据端窗透射微型X射线管阳极靶的结构,建立了数理模型,讨论了电子束打靶的平均厚度与光管高压的关系,得到了X光管出射特征光谱强度的角度分布特征。同时利用Monte Carlo方法,对出射光谱在2π方向上的强度分布特征开展模拟研究。结果表明,微型X射线管阳极靶材平均厚度在2 μm左右,在与入射电子束垂直方向几度的范围内获得的出射光谱其单色性较好。这些结论对于微型X射线管的结构设计和出射光谱单色化应用具有一定的理论指导意义。     

一种改进型多组分气体的Tikhonov正则化特征光谱提取方法

针对FTIR光谱分析数据计算量大,具有相同基团的多组分混合气体交叉灵敏度过高,以及在线分析过程中基线漂移等问题,提出了一种改进的TR2-1(Tikhonov 2norm-1norm)正则化特征变量提取法。该方法借鉴TR1和TR2模型的基本思想,引入谱线距离和谱线系数绝对值最小化两个约束项来保证所提取特征量的准确度,消除基线漂移所带来的影响,并结合上述两种模型建立了不适定问题的最优化求解通式。该通式有效地克服了经验法和实验法确定正则矩阵和参数所带来的误差。实验以浓度为0.01%~20%的甲烷、乙烷、丙烷、正丁烷、异丁烷、正戊烷和异戊烷气体为例进行了特征光谱选取。结果表明,对于浓度为0.2%的甲烷气体,其预测误差平方和仅为2.6×10-4,可决系数达到0.959 2,分析准确度高,有效增强了TR正则法的实用性。     

高光谱信息的农林植被种类区分

为了能够更加快速、准确对粮食主产区的作物与树木进行种类区分,以黄淮海地区三种主要植被(玉米、小麦和杨树)为研究对象,获取该三种植被原始反射率光谱,并对原始光谱进行特征点提取、一阶微分变换、二阶微分变换以及植被指数计算四种方法的分析处理,提取三种植被各自的光谱特征点、特征波段、蓝黄红边微分值和、位置、振幅以及面积四个特征指标以及植被指数的数值区间。基于特征值在不同植被种类间数值重叠范围越小区分精度越高的原理,比较分析植被光谱在不同处理方法下的植被区分精度,并且最终选取重叠范围最小的特征指标作为区分不同植被的识别指标。结果显示：相较于原始光谱特征点提取、二阶微分变换以及植被指数计算,一阶微分变换对于玉米、小麦和杨树的识别分类具有较高的精度,其中黄边振幅、黄边面积以及黄边微分值和具有较高的识别精度,黄边振幅的识别精度达到97.5%,黄边面积以及黄边微分值识别精度达98.1%,用另外167组数据对该结果进行验证,显示黄边振幅的识别精度达96.4%,黄边面积以及黄边微分值和的识别精度达97.6%。该结果与用平均光谱曲线区分单种植被不同生长状态选取的特征值结果不同,这种方法能有效的保留个体光谱反射曲线的差异,从结果可见通过一阶微分变换提取黄边参数的方法能有效的用于树木和粮食作物共同种植区域的植被区分, 并且黄边面积以及黄边微分值和的识别精度最高。     

Motion generation of RCCC mechanism using numerical atlas

This article presents a synthesis method for the motion generation of RCCC mechanism using the numerical atlas. Based on the Fourier series theory, the geometrical model of the rigid body rotation angle of RCCC mechanism is established. Through harmonic analysis, the rotation angle output characteristics were observed to be dependent on the rigid body rotation angle operator. Subsequently, two numerical atlas databases are constructed. The theoretical formulas to calculate the real size and installing dimensions were proposed. On the basis of the theoretical formulas and two numerical atlas databases, the problem of rigid body guided synthesis of RCCC is solved.     

西范坪矿区土壤铜元素的高光谱响应与反演模型研究

为解决传统的土壤地球化学测量方法成本高、效率低等问题,研究了利用可见-近红外光谱技术检测土壤重金属含量的简易方法。研究对西范坪矿区土壤反射光谱进行微分、连续统去除等六种变换,利用逐步回归法和皮尔逊相关系数选出对土壤铜含量敏感的特征波段,组成综合特征变量集,再应用不同的特征变量选取方法和参数建立估算模型并检验。结果表明：不同的光谱变换方法对土壤铜含量信息提取能力不同,每种光谱变换都对应特定的敏感波谱区间;基于综合光谱变换信息建立的土壤铜含量反演模型精度优于基于单种光谱变换信息建立的模型;利用综合光谱变换信息建立土壤铜含量反演模型,后向剔除法优于前向引入法和逐步回归法,当Removal取0.20时得到最优回归模型,其模型决定系数R2和预测模型决定系数R2_pre分别达到了0.851和0.830,建模均方根误差RMSEC和预测均方根误差RMSEP分别为0.349和0.468 mg·kg-1,能较好地检测土壤铜含量,同时为其他土壤重金属元素的光谱检测提供了思路。     

Effect of gas pressure on ionization of ambient gas

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