相对论性量子场反常维度与动量空间维度——纪念爱因斯坦《相对论》诞生百周年

 量子场中的奇异性(发散困难)被量子场反常维度C_B(g_R,e_R)与D=D₀-ε(D₀=4)中ε参数所控制,C_B(g_R,e_R)与ε可以相互替换.C_B(g_R)(QCD)的渐进自由被实验√S=30~1 800 GeV所证实.强相互作用的电荷依赖为C_B(g_R,±)=C_B(g_R,0)[1+be_R/g_R]²(b≤1).非线性相互作用改变了量子场的维度与量子场的拓扑不变性.     

广义逆在最小二乘问题求解中的应用

文中应用矩阵的广义逆讨论了相容线性方程组Ax=b的解,并用Penrose广义逆给出了矛盾方程组Ax=b的最小二乘解及极小范数最小二乘解的Moore-Penrose逆表示。     

亏秩线性方程组PSD迭代法的最优参数

利用数形结合的方法得到了亏秩线性方程组Ax=b的PSD迭代法在一般情形下的最优参数及最优谱半径,其中A∈Cmr×n且r     

Theoretical calculation of the finishing rolling elongation in alloying non-quenched and tempered steel

The finishing rolling elongation δ of the alloying non-quenched and tempered steel is calculated with the covalent electron number n_A of the strongest bond of the alloying phases and the interface electron density difference Δ_ρ of the phase interfaces. The calculations show that the elongation δ^α-Fe of the matrix α-Fe decreases with rolling refinement, the elongation δ^α-Fe-C-M of solid solution phases (M denotes alloying element) is inversely proportional to the covalent electron number n^α-Fe-C-M_A of the strongest bond, the elongation decrement Δ^{δα-Fe/α-Fe-C-M} caused by interface strengthening is directly proportional to the interface electron density difference Δρ^{α-Fe/α-Fe-C-M}, but the elongation decrements Δδ^α-Fe/MC^C₁ and Δδ^α-Fe/MC^C₂ caused by dispersion strengthening and precipitation strengthening respectively are directly proportional to the ratio of the electron density difference Δρ^α-Fe/MC^C₁ and Δρ^α-Fe/MC^C₂ of the strengthening interfaces to Δρ^{α-Fe/α-Fe-C} of the basic interface α-Fe/α-Fe-C. Therefore, the finishing rolling elongation of the alloying non-quenched and tempered steel is considered to be subtracting all the elongation decrements of solution strengthening, interface strengthening, dispersion strengthening and precipitation strengthening from the elongation of the refined α-Fe matrix. The calculation formulas in this paper are integrated with the proposed ones of σ_S, σ_b and of α_K delivered in another paper, the finishing rolling mechanical properties can be achieved and the calculated results agree well with the measured ones.     

PSD迭代法收敛的一个充分必要条件

在线性方程组Ax=b的系数矩阵A为相容次序矩阵及A的Jacobi迭代矩阵的特征值μj均为纯虚数且｜μj｜〈1的条件下得到了PSD收敛的一个充分必要条件,并给出数值例子．     

一个单核三价铬配合物的晶体结构、发光性质及热稳定性

我们重新合成了曾经报道过的反式K[Cr(C₂O₄)_2·(H₂O)₂]_2·3H₂O三价铬配合物, 并借助先进的单晶衍射仪和更先进的解析手段得到了该配合物更加精确的结构模型,该配合物属于单斜晶系,P2/n（No. 13）空间群,晶胞相关参数为：a = 7.8827 (4) Å,b = 5.7296(3) Å,c = 13.6447(7) Å,β= 103.506(5)°,Z = 2,Dc =1.980 Mg/m³,V = 599.22(5) ų。热重测试结果显示该配合物在357 K以前是稳定的,在410 nm最有效的紫外光光源的激发下,配合物在610 nm处有一个尖锐的发射峰。     

关于Pollaczek多项式零点的两点性质

 主要讨论Pollaczek多项式P^λ_n(x;a,b) 的零点关于参数λ的单调性, 及其与P^λ_n(x;a,b), P ^λ+1_n－1(x;a,b) and P ^λ+1_n(x;a,b)三者之间零点的交叉性。     

一类三圈图关于Merrifield-Simmons指标和Hosoya指标的排序

研究了一类三圈图T^m,k,r_n,p,q的Merrifield-Simmons指标和Hosoya指标，根据C_p上两接点u和v之间的距离，给出了该类三圈图关于这两种指标的排序     

关于线性方程组Ax=b的解的注记

考虑了当b固定时，怎样的矩阵G，使x=Gb是相容或不相容线性方程组Ax=b的极小范数解，最小二乘解，从而得到许多有益的结论。     

基于QR分解的线性方程组Ax=b解的结构

基于QR分解，运用列正交矩阵的定义和最小二乘广义逆的定义，得到线性方程组Ax=b解的几个性质．     

RP-HPLC-DAD法测定陈皮中3种多甲氧基黄酮的质量分数

利用高效液相色谱法（RP-HPLC-DAD）, 建立同时测定陈皮中3,5,6,7,8,3′,4′-七甲氧基黄酮、 8-羟基 3,5,6,7,3′,4′-六甲氧基黄酮和5-羟-3,6,7,8,3′,4′-六甲氧基黄酮质量分数的定量分析法, 并采用Cosmosil C18-Ar-Ⅱ（4.6 mm×250 mm, 5 μm）色谱柱, V（乙腈）∶V（ρ（醋酸）=0.2%）为流动相进行梯度洗脱, 流速为1.0 mL/min, 检测波长为258 nm, 柱温25 ℃. 结果表明： 3,5,6,7,8,3′,4′ 七甲氧基黄酮的线性范围为0.01~10.0 μg（r²=0.999 2）, 平均回收率为99.7%, 相对标准偏差（RSD）为0.50%; 8-羟基-3,5,6,7,3′,4′-六甲氧基黄酮的线性范围为0.05~10.0 μg（r²=0.999 4）, 平均回收率为1018%, RSD为2.0%; 5-羟基-3,6,7,8,3′,4′-六甲氧基黄酮的线性范围为0.025~5.0 μg（r²=0.999 8）, 平均回收率为100.2%, RSD为1.7%.     

由强混合序列生成的线性过程重对数律的精确渐近性质

设{ε_t,t∈Z}为定义在同一概率空间(Ω,F,P )上的严平稳随机变量序列, 满足Eε₀=0, E|ε₀|^p<∞, 对某个p>2, 且满足强混合条件. {a_j, j∈Z}为一实数序列, 利用由强混合序列生成的线性过程的弱收敛定理及矩不等式讨论了在b_n=O(1/log log n)的条件下的一类加权级数的收敛性质.     

降能片对12C6+束流影响的Geant4模拟

利用Geant4模拟每核子能量在80~360 MeV内碳离子束（¹²C⁶⁺）穿过靶质量厚度为0.5~4.0 g/cm2的有机玻璃、 铝、 铜和铅后的角度歧离值和能量歧离值, 并对比单能碳离子束直接进入水中和经降能片后再进入水中的Bragg峰. 模拟结果表明: 碳离子束的能量越高、 降能片的质量厚度和原子序数越小, 碳离子束经过降能片后的角度歧离和能量歧离值越小, 其Bragg峰所受影响也越小. 即若仅考虑角度歧离和能量歧离, 则低原子序数的材料更适合做降能片.     

β-Ｄ-吡喃葡萄糖叠氮化物的合成及晶体结构

合成了β-Ｄ-O四乙酰基糖基叠氮化合物， 并得到单晶， 经X射线衍射方法解析， 其晶系属于单斜晶系，P2₁空间群， 其中a=0.759　6(6) nm,b=1.518　4(13) nm，c=1.641　2(14) nm，V=1.893　0(3) nm³，α=90.00°，β=90.045(1)°，γ=90.00° ，Z=2. 在晶体结构中， 六元糖环采取经典⁴C₁椅式构象， 糖环上所有 的取代基均以平伏键存在， 其中叠氮基不是以直线型结构存在， 呈现一定的弯曲现象.     

集值Pramart的Riesz逼近

设（X,‖·‖）为可分的Banach空间, X^*为其对偶空间, X^*可分, (Ω,B,P)为完备的概率空间, {B_n,n≥1}为B的上升子σ域族, 且B=∨B_n. 在X^*可分的条件下给出了集值Pramart的鞅逼近, 并在此基础上证明了集值Subpramart在弱收敛意义下的收敛定理及Pramart在Kuratowski Mosco收敛意义下的收敛定理.     

有限集合上封闭集族的计数

设集合X={a1,a2,a3,…,an},f(n,m)表示X的含m个元素的不同封闭集族的数目。证明了f(n,m)={3n-2n,m=2;4n-2.3n+2n,m=3;5n-25.4n+2.3n-2n-1,m=4;6n-3.5n+3.4n-3n,m=5其中n=1,2,3,…。     

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^±.     

关于任意同分布随机变量序列最大值不等式及应用

设{X,Xn,n≥1}是同分布的随机变量序列(不必独立),记部分和Sn=∑ni=1Xi,n≥1。获得了max1≤k≤n︱Sk︱/n1/p的尾概率的一个上界,其中0p1。作为一个应用,给出了正则和极大值函数sup n≥1︱Sk︱/n1/p的r(r0)阶矩存在的充分条件,推广了独立情形相应的结果。     

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   

Synthesis and assembly with mesoporous silica of platinum(II) porphyrin complexes bearing carbazyl groups:Luminescent and oxygen sensing properties

Determination of oxygen is very important in vari- ous fields such as analytical chemistry, medical chem- istry and environmental and industrial applications[1]. The optical oxygen sensors are based upon the princi- ple that oxygen is a powerful quencher …