BC型量子GIM代数及其Lusztig对称

对$\ell$阶BC型Cartan矩阵的2-仿射矩阵$\tilde{A}_{\ell+2}\times\ell+2}$,定义了相应的量子广义相交矩阵(GIM)代数$U_{q}$,对每个$1\leq i\leq\ell+2$,证明了$U_{q}$有自同构$T_{i}$,讨论了它们的基本性质. 所得到的结果推广了经典量子群和ADE型量子广义相交代数的Lusztig对称理论.     

赋Luxemburg范数的广义Orlicz函数空间中的$\lambda$点和$\lambda$性质

为了研究在更一般情形下的Orlicz空间的$\lambda$性质, 借鉴经典Orlicz空间中的方法并发展了广义情形下的新方法, 给出了赋Luxemburg范数的广义Orlicz空间单位球中的点是$\lambda$点的充分必要条件. 这些结果表明, 在某些广义Orlicz空间中, 并不是所有单位球中的点都是$\lambda$点, 这与在经典Orlicz空间中, 单位球中的点都是$\lambda$点的结果是不同的. 最后, 给出了具有$\lambda$性质和一致$\lambda$性质的赋Luxemburg范数广义Orlicz空间的充要条件.     

关于一类四阶偏微分方程解的一个 Bernstein 性质

设$x:M\rightarrow A^{n+1}$ 是由定义在凸域 $\Omega\subset A^n$ 上的某局部严格凸函数 $x_{n+1}=f(x_1,\dots,x_n)$ 给出的超曲面. 我们记 $\rho(x)=\left(\det\left(\frac{\partial^2f}{\partial x_i\partial x_j}(x)\right)\right)^{-\frac{1}{n+2}} $. 假设 $(M, g)$ 是一完备的Hessian流形且具有非负的李奇曲率,如果 $\rho$ 满足 $\Delta_{g}\rho=\beta\frac{\parallel\nabla\rho \parallel_g^2}{\rho}(\beta\neq 1)$ , 则 $M$ 一定是椭圆抛物面.     

矩阵广义逆偏序的新定义

从矩阵的偏序定义出发,提出了在集合意义下新的矩阵广义逆偏序的定义.$\boldsymbol{A}\leqslant^{\{1\}}\boldsymbol{B}\Leftrightarrow\boldsymbol{A}\boldsymbol{A}\{1\}=\boldsymbol{B}\boldsymbol{A}\{1\},\boldsymbol{A}\{1\}\boldsymbol{A}=\boldsymbol{A}\{1\}\boldsymbol{B}$以及$\boldsymbol{A}\leqslant^{\{1,2\}}\boldsymbol{B}\Leftrightarrow\boldsymbol{A}\boldsymbol{A}\{1,2\}=\boldsymbol{B}\boldsymbol{A}\{1,2\},\boldsymbol{A}\{1,2\}\boldsymbol{A}=\boldsymbol{A}\{1,2\}\boldsymbol{B} $.并分别讨论了四种情况下, 矩阵$\boldsymbol{A},\boldsymbol{B}$的形式.最后得到了相应的广义逆偏序的充要条件.     

四阶两点边值问题3个对称正解的存在性

应用广义的Leggett-Williams不动点定理,研究了四阶两点边值问题 $ {{u}^{\left( 4 \right)}}\left( t \right)=f\left( u\left( t \right) \right)\ \ \ \ \ \left( t\in \left[ 0, 1 \right] \right), u\left( 0 \right)=u\left( 1 \right)=0, {u}'\left( 0 \right)={u}'\left( 1 \right)=0 $ 正解的存在性, 其中$f:\mathbb{R}\to \left[ 0, +\infty \right)$连续. 在f满足适当的增长条件下, 得到该问题至少存在3个对称正解.     

协方差矩阵的乘积及其迹的估计

对于两个不同总体的协方差矩阵$\Sigma_1$和$\Sigma_2$,估计其乘积$\Sigma_1 \Sigma_2$及乘积的迹$\trace(\Sigma_1 \Sigma_2)$是统计推断问题的关键步骤. 首先,构造$\Sigma_1 \Sigma_2$的几个等价估计,同时对于任意的正整数$m,n$建立了$\Sigma_1^m \Sigma_2^n$ 和 $(\Sigma_1 \Sigma_2)^m$的无偏估计。其次,利用$\Sigma_1 \Sigma_2$ 的等价估计,发现了$\trace(\Sigma_1 \Sigma_2)$的多个常用估计量是相等的. 最后,基于上述发现,证明了两个常用的检验统计量(被用于检验两个协方差矩阵是否相等)是渐近等价的.     

关于第二类 Stirling 数的 p-adic 赋值的一些新结果

设 $n$ 和 $k$ 为任意正整数. 第二类\ Stirling 数, 记作\ $S(n,k)$, 表示将\ $n$ 个元素划分为恰好\ $k$ 个非空集合的个数. 设\ $p$ 为奇素数, 令\ $v_p(n)$ 表示 \ $n$ 的\ $p$-adic 赋值, 即\ $v_p(n)$ 是能整除\ $n$ 的最大的\ $p$ 的方幂. 一般来说, 计算\ $S(n, k)$ 的\ $p$-adic 赋值是很困难的. 有许多作者研究了第二类\ Stirling 数 $S(n,k)$的算术性质, 包括\ Davis, Lengyel 以及\ Hong 等. 在本文中, 我们研究第二类\ Stirling 数的\ $p$-adic 赋值的一些性质. 事实上, 我们通过对\ $S(n, k)$ 进行\ $p$-adic 分析证明了\ $S(p, 2)\ge 1$, 其中等号成立当且仅当\ $p$ 为一个 Wieferich 素数. 当\ $n\ge 2$ 时, 我们还证明了\ $v_p(S(p^n, 2p))\ge n$, 以及\ $v_p(S(p^n, 4p))\ge n-2\ (p\ge 5)$, 这改进了\ Adelberg 不久前的结果.     

一类二阶非线性矩阵微分方程的振动性定理 (英)

建立了二阶非线性矩阵微分系统 $ (a(t)\X’(t))’+b(t)\X’(t)+\Q(t)f(\X(t))= 0,t\geqslant t_ 0 >0$ 的振动性标准, 这里 $\Q(t),$ $f’(\X(t))$ 是 $n \times n$ 矩阵， $f’(\X(t))$ 正定, $a(t)$ 和 $b(t)$ 实值函数. 引进了一个特殊函数 $\phi(t,s,r)=(t-s)^ \alpha (s-r)^ \beta , \alpha,\ \beta > \frac 1 2 $\ 是常数，$ \ r \geqslant t_0,$ 得到了形式为 $\lim \sup\lambda_ 1 [.] > $ const 的振动性标准, 改进了一些已知的结果.     

$\bf\Lambda _{\bf c} \textbf{(2880)}^{\bf +} \textbf{2}$D波激发态的强衰变

在$^3P_0 $模型框架下, 计算$\Lambda _{c} (2880)^+$作为2D波激发态的衰变宽度和分支比, 确定其量子态并探究内部激发模式. 计算结果表明: $\Lambda _{c} (2880)^+$有可能是2D激发态$\Lambda _{{c}2} \big(\frac{3}{2}^+\big)$, $J^P=\frac{3}{2}^+$, 且$n_\rho =1$、$l_\lambda =2$, 为径向$\rho $激发、轨道$\lambda $激发的激发模式, 总衰变宽度${\it\Gamma}_{total} =18.53$ MeV, 分支比比值$R={\it\Gamma}(\Lambda _{c}(2880)^+\to \Sigma _{c}(2520)\pi)$/${\it\Gamma}(\Lambda _{c} (2880)^+\to \Sigma _{c} (2455)\pi)=0.16$; 也可能是2D激发态$\Lambda _{{c}2}^{'}\big(\frac{3}{2}^+\big)$, $J^P=\frac{3}{2}^+$, 且$n_\lambda =1$、$l_\lambda =2$, 为径向$\lambda $激发、轨道$\lambda $激发的激发模式, 总衰变宽度${\it\Gamma} _{total} =1.69$ MeV, 分支比比值$R={\it\Gamma}(\Lambda _{c} (2880)^+\to \Sigma_{c}(2520)\pi )$/${\it\Gamma} (\Lambda_{c} (2880)^+\to \Sigma_{c}(2455)\pi )=0.10$.     

图的能量的几个可达下界（英）

图\ $G$ 的能量\ $\mathcal{E}(G)$ 定义为它的邻接矩阵的所有特征值的绝对值之和, 在化学中, 它用来近似分子的\ $\pi$ 电子总能量. 本文给出了关于图的能量\ $\mathcal{E}(G)$ 的几个下界, 同时刻画了达到这些下界的极图.     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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