Pseudo-Hermitian Approach to Energy-Dependent Klein-Gordon Models

The relativistic Klein-Gordon system is studied as an illustration of Quantum Mechanics using non-Hermitian operators as observables. A version of the model is considered containing a generic coordinate- and energy-dependent phenomenological mass-term m ²(E,x). We show how similar systems may be assigned a pair of the linear, energy-independent left- and right-acting Hamiltonians with quasi-Hermiticity property and, hence, with the standard probabilistic interpretation.     

Systematic and statistical errors in quantitative evaluation in TLC and HPTLC. 4. Linear calibration

Analytical results are often obtained from reflectance or fluorescence measurements in TLC or HPTLC with the aid of calibration lines. Curve fitting may not be done by conventional least squares methods for both the independent and the dependent variables are erroneous; errors occur in the volumes spotted on to the plate and in the reflectance/fluorescence measurements. Therefore the sum of the squares of the distances to the calibration line has to be minimized instead of the squared sum of the errors of the dependent variable. The algorithms used are derived and explained. Implications of error propagation for the analytical result are also given.     

晶体非比例双滑移的一般运动学

本文对非比例双滑移的变形规律和运动学进行了一般的数学分析。提出了双线性双滑移、逐段线性双滑移的变形梯度张量的解析公式。导出了线元切向量的变形方程以及拉伸轴在极射赤面投影图上位置变化计算公式。 对于任意形式的双滑移,本文提出了运动学分析的精确的数值积分方法。 最后结合面心立方和体心立方晶体,计算了几种典型情况下的拉伸轴旋转。     

Stochastic Response of Laminated Composite Shell Panel in Hygrothermal Environment

In this article, the effect of random system properties is accounted to estimate the free vibration of multilayered composite shell panel in hygrothermal environment. The majority of previous investigations assumed that the material properties are independent of temperature and moisture. Establishing margin on material properties for design, analysis, and conceptualizing the material is highly difficult and uncertain. To perturb that, a first-order perturbation technique is adopted to obtain the response statistics of the structure by obtaining the mean and variance of random natural frequencies. The higher-order shear deformation theory with 9 degrees of freedom per node with the von-Karman sense of nonlinear kinematics is employed for generating basic formulation. The analysis is carried out by using quadratic C⁰ eight-noded isoparametric element. The governing equation for free vibration of laminated composite panel is derived using variational principle, which is a generalization of the principle of virtual displacement. The solution methodology is validated with published results. Mean and variance are obtained for different cross-ply of spherical and cylindrical laminates with different stacking sequence and boundary conditions.     

Symbolic generation of the kinematics of multibody systems in EasyDyn: From MuPAD to Xcas/Giac

In the EasyDyn multibody open source project, computer algebra has been used from the beginning to generate the expressions of velocities and accelerations of the bodies, by symbolic differentiation of their position. Originally, the MuPAD computer algebra system had been retained because it was freely available for non commercial purposes and showed very good technical features. Unfortunately, MuPAD is nowadays only available through commercial channels and needs to be replaced to keep EasyDyn publicly available. This paper presents why Xcas/Giac is finally selected, among other long-term promising projects like Axiom, Maxima, Sage or Yacas. Among the choice criteria, the accessibility, the portability, the ease of use, the automatic export to C language, and the similarity with the MuPAD language are all considered. The performances of the MuPAD and Xcas/Giac implementations are also compared on some examples.     

Kinematics and Mechanical Properties Analyses on Vibration Converter of Intelligent Damper for Drill Strings

Taking vibration converter of intelligent damper for drill strings as the study object, this paper analyzes the influential factors of motion state of the ball and conducts an explicit dynamics simulation by establishing a mechanics model of vibration converter. The study basis is Newton's laws of motion, D'Alembert's principle and Hertz contact theory. And we use world coordinate system, rotating coordinate system and Frenet coordinate system to deduce kinematics equations of vibration converter. The ultimate result demonstrates that the axial velocity and maximum contact stress change with the increment of ball diameter and helix angle. It also proves the validity of our derived kinematics and mechanical models and provides a good consultant value for the design and theoretical arithmetic of vibration converter for intelligent damper of drill strings.     

15顶角模型反射方程的常数解

得到了15顶角模型A2(1)模型和超对称t–J模型反射方程的非对角解,结果发现,A2(1)模型具有三种形式的非对角解,超对称t–J模型具有一种形式的非对角解,每种形式的非对角解均含有两个解,每个非对角解中均含有三个任意参数.关于对角解也得到了一些新的形式的解.     

The supersymmetric WKB approximation for Hartmann potential

Using the method of supersymmetric WKB approximation, the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions. We take the Hartmann potential as an important example for its validation, and the result is consistent with that obtained by using the supersymmetric quantum mechanics and shape invariance.