On Generalization of a Question of Entrance Test for MA Candidates

2004年漳州师范学院硕士研究生入学考试中有一道高等代数试题,是关于实对称阵的所有正特征根之和与其迹所确定的不等式。证明了这个不等式可推广到实矩阵上去,即实矩阵的所有实部为正的特征根之和与其迹也有类似不等式,同时给出了其等号成立的充要条件。In Entrance Test of Higher Algebra of Zhangzhou Terachers Colleage for MA/MS Candidates in 2004,there is a question on inequality,which is determined by the summation of all positive eigenvalues of real symmetric matrix and its trace.This paper proves that this inequality can be generalized in real matrix,i.e.,there is a similar inequality for the summation of all positive real part of eigenvalues of real matrix and its trace,and we also give the necessary and sufficient conditions for the equality.福建省自然科学基金项目(Z0511051);; 福建省2006年本科精品课程——高等代数;; 莆田学院数学研究项目(JG200521

矩阵与其方幂相似的进一步讨论及应用

证明了如果矩阵A的所有特征值都是1,则对任意非零整数k,A~k与A相似,并给出了A与A~k(k∈Z~+)相似的一些充分必要条件.作为应用,证明了一类非线性矩阵方程解的存在性

Matrix Pair with the Sum and Product Being Equal and Its Polynomial Denotation

用矩阵JOrdAn标准形理论,证明了和与积相等的矩阵对的JOrdAn标准形具有互为确定的性质,进而得到由和与积相等的矩阵对的最小多项式及交换子空间确定的多项式表示的新结果.Applying the theory of Jordan canonical form,we proved the properties of Jordan canonical forms of the matrix pair with the sum and product being equal are determined mutually,obtaining the new results of polynomial denotation determined by minimal polynomial and commutative subspaces.福建省自然科学基金(批准号:2010J01018); 福建省教育厅科研项目基金(批准号:JA12286;JA08196); 福建省高校服务海西建设重点项目(批准号:2008HX03

Investigations on the expression of protein markers in Sertoli cells

目的:探寻小鼠睾丸支持细胞不同发育阶段和功能状态下的特异性标志蛋白。方法:通过对小鼠睾丸组织进行免疫组织化学染色和实时定量(rEAl-TIME)rT-PCr,观察受精后16 d胚胎(E16)到出生后6周的雄性小鼠睾丸组织蛋白和M rnA表达。结果:雄激素受体(Ar)在出生后1周、2周、6周小鼠的睾丸支持细胞、外周小管肌样细胞、间质细胞细胞核内都有表达,且表达量逐渐增强,但在E16不表达;WIlMS肿瘤基因(WT1)在E16、出生后1周、2周、6周的睾丸支持细胞细胞核内表达,但不表达于其它细胞;苗勒氏管抑制素(AMH)在E16、出生后2周的睾丸支持细胞胞质中表达,而在出生后6周不表达;β-链蛋白(β-CATEnIn)和胞质紧密粘连蛋白-1(zO-1)是血睾屏障特异性蛋白,出生后2周时它们分布于整个曲细精管,而出生后4周时规则地分布于靠近外壁的一圈,此时它们的血睾屏障已经完全建立。rEAl-TIME PCr分析睾丸组织M rnA表达,佐证了这些结果。结论:WT1可以作为支持细胞的特异性标志,而AMH则标记不成熟的睾丸支持细胞;Ar单独不适合作为睾丸支持细胞的标志物,但与其他标志物结合,可能可区分睾丸支持细胞的成熟与否。而通过β-CATEnIn和zO-1染色,可以判断血睾屏障是否完全形成,为支持细胞是否成熟提供判断标记。Objective: To examine whether some markers are regarded as accuracy label of Sertoli cells at different development stages, function status of Sertoli cells.Methods: By immunohistochemical staining and real-time PCR methods, the expression of Sertoli cell marker in testis were examined from embryo period 16 d(E16) to 6 weeks after birth.Results: Protein expression of androgen receptor(AR) was observed in nucleus of Sertoli cells, peritubular myoid cells and Leydig cells in 1 week, 2-week, 6-week old mice.Protein expression of Wilms tumour gene 1(WT1) was observed in Sertoli cells' nucleus in E16 and 1 week, 2 weeks, 6 weeks after birth.Protein expression of anti-Müllerian hormone(AMH) was observed in Sertoli cells' cytoplasm at E16-2 weeks after birth.Until postnatal 4-week blood testis barrier(BTB) complex protein β-catenin, Zonula occludens-1(Zo-1) only expressed near basement memberane of seminiferous tubule.By analysis of mR NA expression of testis, these results were confirmed.Conclusion: WT1 could be regarded as protein marker of Sertoli cells at all the development stages.AMH could be regarded as an immature protein marker of Sertoli cells.AR could not be regarded as protein marker of Sertoli cells, but could be a mature marker of Sertoli cells if it is co-immunofluorescence stained with another Sertoli cell marker.By stainning β-catenin or Zo-1, we could judge whether or not Sertoli cells create BTB fully and Sertoli cells is mature.国家自然科学基金资助(基金编号31171375

On Characteristics of(m,l)Rank-idempotent Matrix and(m,l)Idempotent Matrix

如果存在自然数M,l(M>l)使r(A--M)=r(A--l),称A为(M,l)秩幂等矩阵;当A--M=A--l时,称A为(M,l)幂等矩阵.依据矩阵的幂等性与秩幂等性不随数域的改变而改变这一基本事实,应用JOrdAn标准形的性质,得到了这两类既有区别又有密切联系的矩阵类的特性刻画.We call the matrix A as(m,l)rank-idempotent matrix if there exist natural numbers m,l(m>l)such that r(A--m)=r(A--l);when A--m=A--l,then A is called(m,l)idempotent matrix.On the basis of the fact that idempotence and rank-idempotence of matrix are not changed with the number filed,applying the properties of the Jordan canonical form,this paper describes the characteristics of these two kinds of matrices which are different as well as close relationships.福建省自然科学基金项目(Z0511051);莆田学院科研基金项目(2004Q002);莆田学院教学研究项目(JG200521

Studies on Character of Essential(m,l) Idempotent Matrix

若有最小正整数M使当M>l时A--M=A--l成立,称A为本质(M,l)幂等矩阵.本文讨论了本质(M,l)幂等矩阵的特征.作为应用,给出了本质M对合、本质M幂等矩阵的等价刻画,讨论了最小多项式与本质(M,l)幂等矩阵的一些关系.We call the matrix A as essential(m.l) idempotent matrix if there exists minimum natural numbers m such that A--m=A--l in which m>l.This paper studies the character of essential(m,l) idempotent matrix.As application,it has given the equivalent characterizations of essential m involutory matrix and essential m idempotent matrix,and discussed the relationships between minimal polynomial and essential(m,l) idempotent matrix.福建省自然科学基金资助项目(2010J01018);福建省教育厅科研基金项目(JA08196);莆田学院教研项目(JG201018);2008年福建省高校服务海西建设重点项目(2008HX03

(m,l)秩幂等矩阵和(m,l)幂等矩阵的特性研究

福建省自然科学基金项目(Z0511051

Energy stochastic optimization scheduling for micro-grid based on photovoltaic forecasting

可再生能源的间歇性和负荷的随机性对微电网能源管理系统(EMS)产生了巨大的挑战。在随机环境下的能源优化调度问题在微电网的研究中具有重要意义。以微电网中光伏发电系统的功率预测为基础,将光伏预测误差当做随机变量,建立了一种基于期望模型的能源随机优化调度模型。用Monte Carlo模拟方法生成了光伏发电预测误差的情景集,应用粒子群优化算法来解决随机优化调度模型。通过与确定性模型产生的调度方案相对比,证明了随机优化调度模型更加有效。</p

First-principles Calculations on the Optical Properties of Monolayer MoS_2

采用基于密度泛函理论的第一性原理方法计算了单层和体材料二硫化钼(MOS2)的电子能带结构及光学性质.在能带结构计算的基础上,计算了单层和体材料MOS2的介电函数虚部及实部,并导出了单层MOS2的能量损失谱、吸收系数、反射率、折射率和消光系数等.同时给出了体材料及单层MOS2介电函数图像中各峰值与对应的能带带间跃迁之间的关系.所得结果与实验结果及现有的理论结果相符合.The first-principles method based on the density functional theory has been used to calculate the electronic band structures and the optical properties of monolayer and bulk MoS2.Based on calculated band structures,imaginary and real parts of the dielectric functions are determined.The energy loss spectrum,the absorption coefficient,the reflectivity,the refractive and the extinction coefficient are then calculated on the basis of complex dielectric functions.The relationship between peaks in the dielectric function pictures and the inter-bands transitions in the calculated band structures are pointed out,for both the monolayer and bulk MoS2.Our calculation results are in good agreements with available experimental data and previous theoretic results.国家自然科学基金(10774124;10702056

谐波齿轮间隙装配下柔轮齿圈的力学特性及轮齿定位研究

现有理论认为变形后柔轮齿圈中性线为整圈贴合凸轮轮廓的等距线，未考虑配合间隙和中面伸长的影响。为揭示配合间隙装配状态下柔轮的力学特性和齿圈变形后的轮齿定位，以椭圆凸轮波发生器为例，考虑柔轮内壁与波发生器外圈间隙和柔性轴承游隙引起的配合间隙及齿圈中面伸长，建立了柔轮齿圈变形的接触力学模型；引入变形后包角为未知参数，依据包角内用椭圆等距线表示的齿圈中线的曲率及力平衡条件确定齿圈内力；根据短轴处的位移条件和包角处的曲率条件及弧长关系，运用能量法迭代计算了包角、非接触区的大小及齿圈的内力和变形。以有限元模型结果为参照，对比验证了理论结果和轮齿定位偏差。理论分析和数值模拟均表明，受中面伸长的影响，零间隙配合的实际包角远小于90°，整圈贴合凸轮并不符合实际；降低配合间隙可有效增大轴承承载区，降低柔性轴承的径向负载和磨损；考虑包角和周向伸长，可以获得更准确的轮齿定位。研究为谐波齿轮的结构设计和啮合分析奠定了更准确的基础