四元数的归域公式及其应用

给出四元数的归域公式,用它可以求得四元数体上左（右）一元多项式的四元数零点及四元数二阶方阵的LL（RR）特征值。     

关于Smarandache素数列及其它的行列式

对任意正整数n≥2,Smarandache下素数列{pp(n))定义为小于或等于n的最大素数;而Smarandache上素数列{Pp(n))表示大于或等于n的最小素数.本文的主要目的是利用初等方法研究Smarandache素数列的性质,并得到由Smarandache素数列组成的行列式的一些性质.     

Modern automated microextraction procedures for bioanalytical,environmental, and food analyses

Sample preparation frequently is considered the most critical stage of the analytical workflow. It affects the analytical throughput and costs; moreover, it is the primary source of error and possible sample contamination. To increase efficiency, productivity, and reliability, while minimizing costs and environmental impacts, miniaturization and automation of sample preparation are necessary. Nowadays, several types of liquid-phase and solid-phase microextractions are available, as well as different automatization strategies. Thus, this review summarizes recent developments in automated microextractions coupled with liquid chromatography, from 2016 to 2022. Therefore, outstanding technologies and their main outcomes, as well as miniaturization and automation of sample preparation, are critically analyzed. Focus is given to main microextraction automation strategies, such as flow techniques, robotic systems, and column-switching approaches, reviewing their applications to the determination of small organic molecules in biological, environmental, and food/beverage samples.     

关于Fibonacci多项式通项的证明

Fibonacci多项式是以递推方式定义:F0(x)=1,F1(x)=x,F n+2(x)=x F n+1(x)+F n(x).利用代数知识,给出Fibonacci多项式通项的行列式形式和矩阵、向量乘积形式的通项公式证明.     

辐射剂量分布对低能电子束分层固化复合材料层间剪切强度的影响

为了进一步降低电子束固化复合材料制造成本,研究了预浸带双面辐射分层固化复合材料的最小电子束能量值,以及双面辐射剂量分布对复合材料层间剪切强度的影响。试验验结果表明,125keV低能电子束双面辐射可以获得较好的穿透性,并且辐射固化比较均匀,是能够实现复合材料分层制造的最小电子束能量值。相对于双面等剂量辐射固化复合材料层合板的层间剪切强度(ILSS)的61.7MPa,双面不等剂量辐射固化复合材料层合板的ILSS达到66.3MPa,提高幅度为7.5%。光学显微镜及SEM分析与DSC测试结果表明,辐射剂量分布导致的层间键合树脂基体活性官能团数量,是造成双面等剂量与双面不等剂量辐射复合材料层合板ILSS产生较大差异的主要原因。     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's and Dougall's summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

函数y=ex在[0,1]上有理插值样条的存在性及递推算法

在原有研究的基础上,讨论函数y=ex在[0,1]上的有理插值样条的存在性和惟一性,并利用Sylvester恒等式得到P[L,M]和Q[L,M]的(* * *)、(* * *)型递推关系,建立相应的C[L,M]表、P[L,M]表和Q[L,M]表,提供S[L,M]的一种递推算法.     

有理样条不可约解的行列式表示

１引言在文［１］中,对于剖分ａ＝ｘ０＜ｘ１＜…＜ｍｎ＝ｂ及给定的ｙ０,ｙ１,…,　…,Ｌ＋Ｍ－１,我们构造了有理样条Ｓ［Ｌ,Ｍ（ｘ）Ｑ［Ｌ,Ｍ］为次数不超过ｍ的多项式全体．在［１］中,已经讨论了Ｓ［Ｌ,Ｍ］（ｘ）的存在性,并指出：若问题（１）（２）（３）可解,则解唯一这里总假设问题（１）（２）（３）可解．２有理样条解不可约的充要条件由Ｓ［Ｌ,Ｍ］（ｘ）的依区间递推算法（见［１］）,我们只需讨论［ｘ０,ｘ１］上的情形．当［Ｘ０,ｘ１］时,将Ｓ［Ｌ,Ｍ］　（ｘ）,Ｐ［Ｌ,Ｍ］　（ｘ）和Ｑ［Ｌ,Ｍ］（…     

四元数体上Minkowski不等式与Bergstrom不等式

我们对四元数体上自共轭半正定矩阵按广义Ｓｃｈｕｒ补给出了Ｂｅｒｇｓｔｒｏｍ不等式的推广。然后应用自共轭半正定矩阵的Ｂｅｒｇｓｔｒｏｍ不等式得到了Ｍｉｎｋｏｗｓｋｉ不等式,我们的结果修正了重行列不等式的一些错误。     

{Omega}-Admissible Theory

Arakelov and Faltings developed an admissible theory on regulararithmetic surfaces by using Arakelov canonical volume formson the associated Riemann surfaces. Such volume forms are inducedfrom the associated Kähler forms of the flat metric onthe corresponding Jacobians. So this admissible theory is inthe nature of Euclidean geometry, and hence is not quite compatiblewith the moduli theory of Riemann surfaces. In this paper, wedevelop a general admissible theory for arithmetic surfaces(associated with stable curves) with respect to any volume form.In particular, we have a theory of arithmetic surfaces in thenature of hyperbolic geometry by using hyperbolic volume formson the associated Riemann surfaces. Our theory is proved tobe useful as well: we have a very natural Weil function on themoduli space of Riemann surfaces, and show that in order tosolve the arithmetic Bogomolov-Miyaoka-Yau inequality, it issufficient to give an estimation for Petersson norms of somemodular forms. 1991 Mathematics Subject Classification: 11G30,11G99, 14H15, 53C07, 58A99.