Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials

In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.     

Linear Transformation Theory of Quantum Field Operators and Its Applications

We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.     

An Invariance for (2+1)-Extension of Burgers Equation and Formulae to Obtain Solutions of KP Equation

In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Bäcklund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+1)-extension of Burgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can help us find the solutions of KP equation. At last, based on the invariance of Burgers equation, the corresponding recursion formulae for finding solutions of KP equation are digged out. As the application of our theory, some examples have been put forward in this article and some solutions of the (2+1)-extension of Burgers equation, Burgers equation and KP equation are obtained.     

转动相对论系统的Appell方程及其形式不变性

给出转动相对论系统的Appell方程,讨论相对论力学的四个新型基本动力学函数 在无限小群变换下研究转动相对论系统Appell方程的形式不变性,给出定义和判据 研究形式不变性与Noether对称性与Lie对称性的关系,寻求转动相对论系统的守恒量 关键词： 转动相对论 Appell方程 形式不变性 对称性与守恒量     

再谈洛伦兹变换的推导

评论了仅仅依据光速不变假设和相对性原理推导洛伦兹变换公式的方法.     

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.     

完整力学系统的Lie-形式不变性

研究完整力学系统Lie-形式不变性的定义与判据，给出由Lie-形式不变性导出的Noether守恒量，Hojman守恒量和Lutzky守恒量. 举例说明结果的应用. 关键词： 完整系统 Lie-形式不变性 Noether守恒量 Hojman守恒量 Lutzky守恒量     

Correction-to-Scaling Exponents for Two-Dimensional Self-Avoiding Walks

We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ₁=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.     

旋转不变的非局域均值算法在磁共振图像去噪中的应用

磁共振成像（MRI）实验时常采用多次扫描累加平均提高图像信噪比（SNR）,但当扫描过程中运动引起图像变形时,简单地累加平均就无法奏效.为此,本研究组曾提出一种匹配加权平均方法（MWA）提高图像的信噪比.在此基础上,该文提出一种旋转不变的非局域均值算法（RINLM）,即选取圆形邻域区域并将其划分为一系列以中心像素为圆心的等面积圆环,再计算模式的相似性.RINLM算法可以更好地利用图像中旋转的冗余信息、找到更多的相似结构,提高算法的去噪性能.我们把该方法应用于低信噪比图像序列的平均和去噪中,可以更好地处理旋转的局部运动.与非局域均值算法（NLM）相比,RINLM算法可以进一步提高图像的信噪比;与MWA方法相比,其与RINLM算法的结合可以进一步提高磁共振图像序列信噪比,更好的保持图像边缘信息.     

Synthesis of camptothecin-loaded gold nanomaterials

Camptothecin-loaded gold nanomaterials have been synthesized by the sodium borohydride reduction method under a strong basic condition. The obtained gold nanomaterials have been characterized by transmission electron microscopy (TEM), atomic force microscopy (AFM) and UV-vis absorption spectroscopy. The camptothecin-loaded gold colloidal solution was very stable and can be stored for more than two months at room temperature without obvious changes. The color of the colloidal solution can change from wine red to purple and blue during the acidifying process. It was revealed that the release of camptothecin and the aggregation of gold nanoparticles can be controlled by tuning the solution pH. The present study implied that the gold nanomaterials can be used as the potential carrier for CPT delivery.