具耗散项的对称正则长波方程的显式精确解

~~其中 :l =-γv ,m =1 + C1- v2v2 ,n =12 v,C =C2v2 ,而 C1,C2 为积分常数 .假设式 ( 7)有解u(ξ) =∑ni=0AiΦi =∑ni=0Ai(Φ (ξ) ) i,Φξ =a( 1 -Φ2 ) ,a≠ 0 , ( 8)如果函数 1 ,v,… ,vn( n∈ N)线性无关 ,由主导阶分析 ,可选取u(ξ) =A0 + A1Φ + A2 Φ2 , ( 9)将式 ( 9)代入式 ( 7) ,得到 A0 ,A1,A2 ,a的一组代数方程6A2 a2 + n A2 2 =02 A1A2 n + 2 A1a2 - 2 A2 al =0( 2 A0 A2 + A12 ) n + m A2 - la A1- 8A2 a2 =0m A1+ 2 A0 A1n + 2 A2 al - 2 A1a2 =02 A2 a2 + l A1a + m A0 + n A0 2 =C　 . ( 1 0 )为了求得…     

环上线性码的深度谱以及深度分布的一个注记

给出了环R1=Fq[u]/(um)(um=0,m≥2,q为素数的方幂)以及环R2=Fq+uFq+vFq+uvFq上码长为n的线性码C的深度谱以及深度分布计算公式,证明了环Ri(i=1,2)上n维向量的深度值均可取遍0,1,…,n,以及对任意A={l1,l2,…,lk}■{0,1,…,n},均存在Ri(i=1,2)上码长为n的线性码C,其深度谱恰为A.     

用HBSG法对多枝赖草、普那菊苣根尖染色体进行C-分带的研究

利用HBSG法对多枝赖草、普那菊苣的根尖染色体进行了C -分带研究.根据李懋学等(1991年)对C -分带的描述方法,首次确认多枝赖草染色体的C -分带为2n=28=5CT 2CTI 2CT 1CTI 1CTI 1C 1T 1TI,普那菊苣各染色体的C -分带为2n=18=2CT 4CTI 1CT 1CTI 1CT I .另外还对C -分带实验中的一些技术细节做了初步的分析.     

离散形式的加权几何平均不等式

研究离散形式的加权几何平均不等式,证明了对任何非负数列{an},不等式∑ukk√a1…ak≤C1∞∑k=1vkak成立的充分必要条件是对任意n ≥ 1,有1/n n∑k=1 uk/k√v1…vk≤C2,其中un≥0,vn＞0,C1,C2为常数.     

图C~2_n的优美性

给出了图C2n的定义,并对其优美标号进行研究,得到了当n=4k(k≥2)时图C2n是优美图的结论。     

线性流形上一类双结构矩阵反问题的最小二乘解

设 J=[-0In I0n]In是n阶单位辛矩阵,若A∈C2n×2n满足AHA=I2n,AHJA=J,则称A为辛酉矩阵,所有2n阶辛酉阵的全体记为SUC2n×2n.令S={A∈SUC2n×2n|‖AY-Z‖=min,Y, Z∈C2n×p},本文考虑如下问题:问题Ⅰ给定X,B∈C2n×m,求A∈S使f(A)=‖AX-B‖=min.问题Ⅱ给定～A∈C22n×2n,求～A∈SE使得‖～A-～A‖=infA∈SE‖～A-A‖,其中SE是问题Ⅰ的解集合.本文给出了解集SE的通式及逼近解～A的表示式和一些有关的结果,并给出了相应的数值算法.     

非洲菊常见品种的染色体核型与倍性分析

采用常规根尖压片技术对非洲菊3个常见品种的染色体进行核型分析,并用流式细胞仪检测其倍性.结果表明:供试的3个非洲菊品种均为二倍体.深圳5号核型公式为2n=2x=50=2M+34m+16sm,染色体相对长度系数组成为2n=6L+12M2+24M1+8S,按照Stebbins标准核型分类属于2C核型,不对称系数AS.K% =60.09%.香槟核型公式为2n=2x=50+B=36m+12sm+2st+B,染色体相对长度系数组成为2n=8L+10M2+16M1+16S,属于2C核型,不对称系数AS.K% =62.17% .大头粉核型公式为2n=2x=50+B=34m+12sm+4st+B,染色体相对长度系数组成为2n=8L+8M2+28M1+6S,属于2B核型,不对称系数AS.K% =62.21%.综上所述,3个非洲菊品种的染色体长度、着丝点位置、B染色体的有无均不同,核型呈现多态性.     

大麦染色体C带与N带的研究

本文报道了栽培大麦早熟3号的 Giemsa C 带与 Giemsa N 带带型.C 带带型公式为2n=2x=14=2CIT+2CIT+2CIT+2CIT+2CI+T+2CI+TS+2CITS,共显32条带,可识别每一染色体及染色体臂;N 带带型公式为2n=2x=14=2CI+2CI+2CI+2CI+2CT+2CI+S+2CIS.C 带与 N 带有较大的差异.经过 C 带或 N 带分带处理的间期细胞核内有明显的、分散分布的染色中心,经改造的 C 带分带程序能使较多的带显示出来,具有重复性和成功率较高的优点。     

非连通图Gn-1k∪i=0C3i（2n＋1）的优美性

证明了当自然数n≥2时,非连通图Gn-1k∪i=0 C3i（2n＋1）是优美图,其中C3i（2n＋1）是有3i（2n＋1）个顶点的圈（i为自然数）,Gn-1是任意一个有n-1条边的优美图.     

偶圈的Turán数和Wenger图

设G是一个图,G的Turán数记作ex(n;G),是指阶数为n的不含G作为子图的图的最大边数.根据Erds在1965年给出的偶圈C2m的Turán数ex(n;C2m)的上界10mn1 1/m和Wenger在1991年构造的偶图Hm(q),并由这种图得到的ex(n;C2m)(m=2,3,5)的下界cn1 1/m(其中c为一个与n无关的常数),可以知道,当n→ ∞时,ex(n;C2m)=O(n1 1/m)(m=2,3,5).n1 1/m就是ex(n;C2m)的准确阶.给出了Wenger图Hm(q)的一些一般性质,并分别构造了Hm(q)中长为8的圈(m≥4)和Hm(q)中长为12的圈(m≥6),从而证明了不可能由图Hm(q)得到ex(n;C2m)的所有准确阶.     

Formation, structure and properties of GeCn± and Ge2Cn± binary clusters

The binary cluster ions Ge₂C_n⁺/Ge₂C_n^- and GeC_n⁺ have been produced by laser ablation. The parity effect is present in the negative ions Ge₂C_n^-, though it is not very prominent. While the experiments tell that the parity effect is totally not shown in the positive ions Ge₂C_n⁺. An extensive theoretical investigation on GeCn/GeC_n⁺/GeC_n^-(n=1-10) and Ge₂Cn/Ge₂C_n⁺/Ge₂C_n^-(n=1-9) has been carried out by density functional theory at B3LPY level. The calculation shows that the low-lying states of GeC_n/GeC_n⁺/GeC_n^-(n=1-10) and Ge₂C_n/Ge₂C_n⁺/Ge₂C_n^-(n=1-9) are linear structure with germanium atoms locating at terminals respectively. The electronic distributions, ionization potential (IP_ad), elec-tron affinity (EA) and increasing bonding energy reveal that the parity effect of neutral species is much stronger than that of ions, which is attributed to the valence π-electrons. It is explained that the differences between experiments and cal-culations are due to the kinetic factor in the formation of Ge₂C_n^±.     

求解对流扩散方程的一类AGE方法

结合Crank-Nicolson格式和第二类Saul’yev非对称格式,设计求解对流扩散方程的交替分组显式方法.得到求解对流扩散方程的交替分组显式方法为该方法是绝对稳定的,且使用方便,适合并行计算,具有较好的精度.     

最小Q-特征值第二小的给定悬挂点数的非二部单圈图

图的最小Q-特征值常被用来衡量一个图的非二部程度,受到研究者的广泛关注。在路Pn-k-2的一端接出一个圈C3,另一端接出k个悬挂边,所得的n阶图记为Ukn(3)。范益政等人最近证明Ukn(3)是最小Q-特征值达到最小的图。在他们的基础上,证明C13(n-k-1)是最小Q-特征值达到第二小的图,其中C13(n-k-1)是将Ukn(3)的一条悬挂边移至与悬挂邻点相邻的非悬挂点上所得的图。     

关于Smarandache LCM函数的方程S(SL(n~(14,36)))=φ_2(n)的可解性

令S(n)为Smarandache函数,SL(n)为SmarandacheLCM函数,φ_2(n)为广义欧拉函数。讨论方程S(SL(n~(14)))=φ_2(n)和S(SL(n~(36)))=φ_2(n)可解性,利用初等方法并结合函数φ_2(n)与函数S(n)的性质,给出了这两个方程的所有正整数解。     

玻色型反氢原子结构及氘核PB+1nB0和PF+1nF0结构函数的矩

摘要：根据费米型质子PB^ 1、中子nF^0、电子e^-1的超对称性伴子玻色型PB^ 1nB^0、-↑Ue^-,1↑B粒子,讨论反氢原子的结构,计算费米型氘核PF^ 1nF^0和玻色型氘核PB^ 1nB^0结构函数的矩,结果发现反氢原子的结构与目前观测到费米型反氢原子不同,氘核PB^ 1nB^0结构函数的矩的理论值与实验数据较好相符,PB^ 1nB^0结构函数的矩的计算结果比PB^ 1nF^0要大,增大的值是由于费米型中性矢量反轻子-↑l0F,T结构函数的贡献所致。     

On random Taylor series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X _n } with the property: αE ^1/2{|X _n |²}≤E{|X _n |}<∞,E{X _n }=0 (Ån) for some positive constant α. The convergence, growth, and value distribution of the series are investigated. Supported by the National Natural Science Foundation of China (No. 101960433) Ding Xiaoqing: born in Oct. 1958, Doctoral candidate     

Climatic and environmental implications from n-alkanes in glacially eroded lake sediments in Tibetan Plateau: An example from Ximen Co

Gas chromatography-mass spectrometry was used to identify a series of n-alkanes in the sediments of a typical glacially eroded lake in the eastern Tibetan Plateau.By comparing the distribution patterns of n-alkanes in lake sediments,surface soils and cow manure,it was shown that n-C 27-n-C 33 alkanes in the soil ecosystem of Ximen Co are derived from vascular plant species and that the distribution pattern of n-C 27-n-C 33 alkanes remains unchanged during the feeding and digestion processes of herbivores.The relative percentage of C 27,C 29 and C 31 n-alkanes decreased from the bottom to the top of the sediment core showing a trend of degradation of higher plants in the Ximen Co lake region during the formation of the 44 cm core.210 Pb dating,combined with pre-existing AMS 14 C dating results showed that the depositional core reflects climatic and environmental variations since about 900 years before present.The n-alkane indexes (ACL 27-33,P aq,P wax) are comparable with regional temperature variation,especially recording the Little Ice Age event (LIA).This study highlights that n-alkanes are valid proxies for paleo-climate and paleo-environment reconstruction,despite the same distribution patterns in n-alkane molecular fossils derived from a typical glacially eroded lake.     

线性交换子的加权估计

 多线性交换子T_b(f)(x)=∫_Rⁿ∏_i=1^m(b_i(x)-b_i(y))k(x,y)f(y)dy在L^p(Rⁿ)(1K是一个标准的Calderón-Zygmund核.主要研究交换子Mf(x)=sup_x∈Q∫_Q|f(y)|dy,其中f∈L_loc(Rⁿ),x∈Rⁿ,Q是任何包含x的方体,并用Sharp极大估计得到了该多线性交换子在Herz空间的一个加权有界性.     

Superconvergence for L2-projection in finite elements

Two classes of superconvergence points for L 2 projection u\-n in n degree finite elements on uniform grids are shown by element analysis method. Superconvergence points of u n are n+1 order Gauss point G n+1 for odd d≥1 (so the endpoint of each element is of superconvergent), and n+1 order pointset Z n+1 for even n ≥2 (which includes the endpoints and midpoint), respectively. Symmetry point is only an important part of them.     

Calculation method of electronic structure and its application to (I h andI) fullerenes

A new calculation method was discussed to treat the Hückel Hamiltonian of any fullerene with a certain point group symmetry. This method was applied to calculating the electronic energy levels of icosahedral fullerenes C\-n(I\-h: n=60h 2, 0相似文献