耦合径向基函数与多项式基函数的无网格方法

耦合径向基函数和多项式基函数,形成一种新的近似函数.该近似函数对散乱分布的离散数据点进行逼近时,只需节点信息,不需要划分网格.详细描述了耦合近似函数的建立、属性、插值行为及其形函数和形函数导数的性质.最后引入修正变分原理和单位分解积分技术求解边值问题,并给出了计算实例,表明耦合径向基函数和多项式基函数是一种非常有效的方法.     

The superstability of pair-potentials of positive type

We prove that a pair-potential which is continuous,L ¹, and of positive type satisfies a condition of the superstability kind with best-possible constants. The applications to statistical thermodynamics are mentioned.     

Wei-Norman分解及其在量子系统控制的应用

W e i-Norm an分解对于分析矩阵微分方程的解是比较成熟的理论,含有幺正演化矩阵的薛定谔方程是矩阵微分方程,所以可以利用W e i-Norm an分解来分析求出多能级量子系统的解。由于W e i-Norm an分解适用的范围是小时间变化的邻域,为了求出量子系统在任意时刻的幺正演化矩阵,根据量子系统的特性,提出了对量子系统的控制时间进行分段,利用W e i-Norm an分解来获得每段小时间的幺正演化矩阵。最后通过一个两能级的例子进行仿真,根据实验结果总结出该量子系统的状态与控制场作用之间的关系。     

GG Functions and their Relations to General Hypergeometric Functions

In this Letter, we present a new approach to the notion of hypergeometric functions.     

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state(EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory(PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid.The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact(RDFC) of mixtures.The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.     

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.     

应用径向基函数去除数字图像中的椒盐噪声

去除图像中的椒盐噪声可转化为二维曲面的重建问题。选用Multi-Quadric函数对图像中损失的信息构造插值格式,自动选择待插值点和插值参考点并求解插值方程组得到处理后的图像。实验证明,本方法可以在很少破坏图像细节的情况下去除大部分甚至全部噪声,并且在噪声密度非常大的情况下仍然可以还原相当多的图像信息。对噪声密度为50％和90％的单色Lena图像进行处理,该方法得到的信噪比比自适应中值滤波高6dB以上。     

Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized q-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.     

Quantum Mechanical Image of Matrices＇ LDU Decomposition

For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.     

Interacting Quantum and Classical Continuous Systems II. Asymptotic Behavior of the Quantum Subsystem

In the framework of event-enhanced quantum theory the dynamical equation for the reduced density matrix of a quantum system interacting with a continuous classical system is derived. The asymptotic behavior of the corresponding dynamical semigroup is discussed. The example of a quantum–classical coupling on Lobatchevski space is presented.     

Quantum Correlations and Speed Limit of Central Spin Systems

In this article, single, and two-qubit central spin systems interacting with spin baths are considered and their dynamical properties are discussed. The cases of interacting and non-interacting spin baths are considered and the quantum speed limit (QSL) time of evolution is investigated. The impact of the size of the spin bath on the quantum speed limit for a single qubit central spin model is analyzed. The quantum correlations for (non-)interacting two central spin qubits are estimated and their dynamical behavior with that of QSL time under various conditions are compared. How QSL time could be availed to analyze the dynamics of quantum correlations is shown.     

铝吸附氢同位素的热力学数据的量子力学计算

用原子分子反应静力学与群论的方法,推导了ＡｌＨ、ＡｌＤ及ＡｌＴ的基电子状态为１Σ＋。在ＱＣＩＳＤ／６－３１１Ｇ水平上对氢化铝进行了计算,导出了其ＭｕｒｒｅｌＳｏｒｂｉｅ势能函数,并计算了氢同位素分子及其铝化物的能量Ｅ和熵Ｓ。设用总能量中的电子和振动能量近似代表ＡｌＨ、ＡｌＤ和ＡｌＴ分子处于固态时的能量,用总熵中的电子和振动熵近似代表这些分子处于固态时的熵,进而计算了铝吸附Ｈ２,Ｄ２和Ｔ２分子过程的ΔＨ°,ΔＳ°,ΔＧ°和平衡压力,并导出它们与温度的函数关系,计算指出了同位素分子效应,结果合理。     

Harnessing Quantumness of States using Discrete Wigner Functions under (non)-Markovian Quantum Channels

The negativity of the discrete Wigner functions (DWFs) is a measure of non-classicality and is often used to quantify the degree of quantum coherence in a system. The study of Wigner negativity and its evolution under different quantum channels can provide insight into the stability and robustness of quantum states under their interaction with the environment, which is essential for developing practical quantum computing systems. The variation of DWF negativity of qubit, qutrit, and two-qubit systems under the action of (non)-Markovian random telegraph noise (RTN) and amplitude damping (AD) quantum channels is investigated. Different negative quantum states that can be used as a resource for quantum computation and quantum teleportation are constructed. The success of quantum computation and teleportation is estimated for these states under (non)-Markovian evolutions.     

单量子双能级系统和双态系统关联函数的研究

以具有简单三能级结构染料分子的单量子系统为研究对象,用带有边界条件的速率方程来反映低功率单色连续激光激励下单分子发射荧光的动力学过程.该方法可以通过时间分辨光子探测获得处理单分子动力学随机过程.研究给出了一种通过求解反映单量子系统动力学过程的物理量——延迟函数计算关联函数的方法,并给出了双能级系统和双态系统延迟函数和关联函数的具体表达式.研究表明,在实际测量中只要获得关联函数曲线,就可以通过数据拟合计算出分子跃迁的动力学参量.     

Quantum Instruments and Related Transformation Valued Functions

The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their ^*-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained.     

Kinetics Study on Thermal Decomposition of Polyepoxyphenylsilsesquioxane/Epoxy Resin Systems

The thermal decomposition kinetics of epoxy resin (EP) containing polyepoxyphenylsilsesquioxane (PEPSQ) was studied by thermogravimetric analysis (TGA) in a nitrogen atmosphere. Kissinger and Flynn–Wall–Ozawa methods were both used to analyze the thermal decomposition process under nonisothermal conditions. The results showed that a slight increase of activation energy was observed in the presence of PEPSQ, which indicated that the addition of PEPSQ retarded the thermal decomposition of EP. The Flynn–Wall–Ozawa method further revealed that PEPSQ significantly increased the activation energy of the whole EP thermal decomposition, especially in the final stage of the thermal decomposition process, which is attributed to the PEPSQ stabilizing the char layer and improving the flame retardancy of EP.     

Algebras of Operators on Holomorphic Functions and Applications

We develop the theory of operators defined on a space of holomorphic functions. First, we characterize such operators by a suitable space of holomorphic functions. Next, we show that every operator is a limit of a sequence of convolution and multiplication operators. Finally, we define the exponential of an operator which permits us to solve some quantum stochastic differential equations.     

General Decomposition of Spin Connection and Topological Structure in Gauss-Bonnet-Chern Density

By means of devices of geometric algebra the general decomposition of spin connection on the sphere bundle of a compact n-dimensional Riemannian manifold has been studied in detail. Using this decomposition theory it is shown that the Gauss-Bonnet-Cherniensity of the Euler-PoincarB characterictic can be expressed in terms of a smooth vector field φ and take the form of the 6 function δ(φ). The topological structure in Gauss-Bonnet-Chern theorem is reviewed.     

Propagation of General Wave Packets in Some Classical and Quantum Systems

In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.     

Quantum Binary and Triplet Distribution Functions of Plasma by using Green's Function

The aim of this paper is to calculate the binary and triplet distribution functions for one and two component Plasmas in terms of Green's function technique. We obtained the triplet distribution function in two form; one of them is based on the Kirkwood Superposition Approximation (KSA) which is consisting of the assumption that the potential in a set of three particles is the sum of the three pair potentials, this is equivalent to assuming that the triplet distribution function is the product of the three binary distribution functions, but the other form is calculated from BBGKY hierarchy. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)