Bergman kernels on generalized Hua domains

The Bergman kernel functions with explicit formulas of the generalized Hua domains are obtained. And the holomorphic automorphism group for each generalized Hua domain is also given.     

Busemann functions on RI( m, n ) and IV(n)

The Busemann function plays a very important role in studying topology and geometry of a complete Riemannian manifold. In this paper, the Busemann functions on the real classical domain of the first type and the Cartan domain of the fourth type in the explicit formulas are obtained.     

Explicit analytical solutions of transport equations considering non-Fourier and non-Fick effects in porous media

Based on the method of separation variables with addition developed in recent years, new methods of separation variables are proposed, and two algebraically explicit analytical solutions to the general partial differential equation set of non-Fourier and non-Fick heat and mass transfer in porous media drying are derived. The physical meaning of these solutions is simple and clear, and they are valuable for computational heat and mass transfer as benchmark solutions.     

Thermoequilibrium statistics for a finite system with energy nonextensivity

A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.     

Explicit solvent model for spectral shift of acrolein and simulation with molecular dynamics

By introducing the concept of spring energy of permanent dipole and taking the conforma-tions of solvent molecules into account,the formulas of electrostatic solvation energy in equilibrium and nonequilibrium are derived from the explicit solvent scheme,with the spatial distribution of the discrete permanent charges and induced dipoles of the sol-vent molecules involved. The energy change of sol-ute due to the variation of wave function from the case of vacuum to that in solution is estimated by treating the solvent effect as external field in the it-eration cycles of the self-consistent field. The ex-pression for spectral shift is deduced and applied to the processes of light absorption and emission in solution. According to the new formulations,the av-eraged solvent electrostatic potential/molecular dy-namics program is modified and adopted to investi-gate the equilibrium solvation energy of water mole-cule and spectral shift of acrolein.     

Density-functional formula for strongly correlated systems

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.     

Estimating the Shareholder's Terminal Payoff in Insurer's Solvency Ratio Model under Fractional Market

The insurer's solvency ratio model in a class of fractional Black-Scholes markets is studied. In this market,the price of assets follows a Wick-It stochastic differential equation,which is driven by the fractional Brownian motion. The market coefficients of market model are deterministic functions. By the stochastic calculus of the fractional Brownian motion and the pricing formula of European call option for the fractional Brownian motion,the explicit formula for the expected present value of shareholder's terminal payoff is given. The model extends the existing results.     

Extremal problems on the generalized Hua domain of the first type

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.     

Localization of calmodulin and calmodulin-like protein and their functions in biomineralization in P. fucata

Calmodulin （CAM） and calmodulin-like protein （CaLP） are two proteins involved in biomineralization. Their localizations in Pinctada fucata mantle epithelia were studied by Western blot （WB） analysis of the nuclear/cytosol fraction of primary cultured P. fucata mantle cells and immunogold electron microscopy. The results showed a completely different distribution of these two proteins at the subcellular level. CaM was distributed throughout both the nucleus and cytoplasm of the mantle epithelium but CaLP was distributed only in the cytoplasm. The functions of these two proteins in biomineralization were investigated by shell regeneration. During this pro- cess, the expressions of CaM and CaLP were greatly enhanced in different organelles of the mantle epithelium. Overexpression of these two proteins and a mutant of calmodulin-like protein （M-CaLP） that lacks an extra C-terminal tail in MC3T3-E1 promoted the mRNA expression of osteopontin, a biomineralization marker for osteoblasts. All of the results indicated that CaM and CaLP have completely different distributions in the mantle epithelium and affect the biomineralization process at different levels. The extra C-terminal tail of CaLP is important for its functions in biomineralization in P. fucata.     

量子隧道效应的数值计算

采用量子流体动力学方法(QHD)研究电子穿过隧道结的概率. 将复数形式的波函数表示为指数形式,给出Lagrange框架下C和S的时间演化方程,并给出采用时间的二阶差分方法的数值计算过程. 由于Lagrange框架下格点是随着时间的演化其分布也是变化的,计算过程中涉及到C和S的导数时,直接结合数值计算方法中的求函数近似的有理近似方法. 以初始波包为高斯波包为例进行了数值计算和分析,所得到的图像明显地显示了量子效应.     

Construction vectors for visual cryptographic schemes

The concept of group construction vector and independent construction vector for visual cryptography is proposed, and the method based on construction vector is presented for con-structing basis matrices. The general solutions to construction vectors and the general solutions to k out of n visual cryptographic schemes are obtained. Using the construction vectors, everyone can construct visual cryptographic schemes simply and efficaciously according to the formulas. The concept and the general solutions to construction vector present a good idea for researches on visual cryptographic schemes, including structural properties, the bound of pixel expansion and contrast, and optimal construction.     

桩-承台竖向强迫振动试验和分析

采用横观各向同性 (TI)层状弹性模型来模拟半空间上的层状场地 ,计算中忽略土体水平位移对竖向位移的影响 .用常系数阻尼器代替半空间 ,以吸收上部场地传至下边界的振动能量 .利用薄层元素法和子结构法建立运动方程 .在推导过程中 ,先利用格林公式算得自由场地刚度矩阵 ,再与桩单元刚度矩阵拼装得到桩的竖向总刚度矩阵 ,在此基础上推出单桩 -承台及双桩 -承台体系在垂直简谐荷载作用下的阻抗函数 ,其中双桩的阻抗函数考虑了桩 -土 -桩的动力相互作用的影响 .利用牛顿第二定律推导出这 2种体系在竖向强迫振动下的响应公式 .利用某次桩基动力试验所得的土参数和激振器数据 ,分别计算出这 2种体系的第一共振频率及频响曲线 ,并将计算结果与试验结果进行比较 .     

某些华罗庚域的Bergman核函数的显式表达

通过构造超几何函数和球型积分变换方法,给出了更多变量的新域$E(k,q_{2},\cdots,q_{m}, \Omega,p_{2},\cdots,p_{m}$上的Bergman核函数的显示表达式,其中$\Omega$是指任意不可约有界圆型齐性域,$k,m,q_{2},\cdots,q_{m}$都是正整数, $p_{2},\cdots,p_{m}$都是正实数,$N(Z,Z)$是$\Omega$的一般范数.而且,当$\Omega$是4大类的不可约的对称典型域时,上述域就是华罗庚域.同时可以得出相应华罗庚域上的Bergman核函数的显示表达式.     

Riemann Zeta函数的求和问题

使用Fourier级数理论得到了RiemannZeta函数的一些新的求和公式,同时也得到了其它无穷级数的一些递推公式,这些公式的递推关系鲜明而且便于使用,在理论和实际中都有一定的意义.     

非线性方程和一维搜索的反函数解法

用Ｎｅｗｔｏｎ法，无论是解非线性方程，还是进行一维搜索，都只是对函数或导函数进行Ｔａｙｌｏｒ展开取一阶近似．为了提高求解效率欲进行高阶展开则遇到了困难：首先，二阶、三阶展开相应地要解二次、三次代数方程，计算较　麻烦；其次．更高阶展开则不可能求解．本文基于反函数的表达，首次提出了任意阶展开的解法，得到显式表达的解．Ｎｅｗｔｏｎ法成为该方法的一个特例．算例表明反函数解法克服了Ｎｅｗｔｏｎ法有时振荡不收敛的弱点．     

(2，2)-可视密存的最小象素方案

在Naor和Shamir提出的可视密存的基础上,给出了一种较简单的方案来解决(2,2)-可视分存中的象素膨胀问题.利用可视分存矩阵实现(2,2)-可视密存并证明了此方案的有效性,进而得到了实现此方案的象素膨胀的最小上界.同时给出了一个黑白象素分存时的一个选择原则,用它可增强分存图的对照度.其结果是新的.针对不同的象素膨胀值,编码密图“DES”.在附录中给出(2,2)-可视分存的结果,它们看起来象随机图.事实上,单一分存图,不能得到任何有关密图的信息,无论用什么方法和采用何种工具.其密图的恢复只要重叠两张分存图的透明片,它不需要加密知识也不需要密码计算.     

用一个2维DFT计算实矩阵的二维DFT和另一个实矩阵的2维DFT的IDFT的新公式及其应用

熟知,两个N维实向量的DFT,可以用一个N维复向量的DFT计算．最近,S．Moshe和D．Hertz提出一个方法用一个N维复向量的DFT计算一个N维实向量的DFT和另一个N维实向量的DFT的IDFT．这是一个优美的结果,具有理论意义和应用价值．如何把上面的结果推广到二维的情形,是一个值得研究的问题．一个矩阵的2-D(2维)DFT通常用行列法化为1-DDFT来计算．但是,用行列法把上述一维的结果推广到二维是困难的．作者得到了计算二维情形的一些新的直接公式,其证明是简明的,它们分别推广了已有的结果．同时还指出,在数字信号处理中当处理实信号时,这些公式非常有用．特别地,作者改进了小波分析中的Mallat分解算法     

CIE L*a*b*色空间色调角对比敏感度函数研究

为获取人眼视觉在均匀颜色空间下的空间频率响应特性并构建其模型,在CIE 1976 L* a* b*色度系统下,对色调角对比敏感度函数(S_H)进行了测试研究. 采用校准的彩色显示系统,对色调角正弦波变化的图像序列进行显示,经大量视觉观察实验,获取了人眼在12种色调角中心下的对比敏感度函数曲线. 结果表明,在不同色调角中心下,色调角对比敏感度函数存在差异,这种差异与人眼对不同色调的辨别能力紧密相关. 基于测试数据,构建了色调角对比敏感度的数学函数模型.