BH分子X1∑+和B1∑+态的理论研究

本文应用 Gaussian03 程序包中提供的完全活性空间自洽场 (CASSCF) 方法,采用标准基组 6-311++G(3d,2p) 对 BH 分子X1∑+和B1∑+态势能曲线进行了单点能计算.在此基础上,利用相关理论将计算结果拟合到 Murrell-Sorbie函数得到了与各电子态相对应的光谱常数和力常数,并将计算结果与实验和其他理论结果进行了比较.同时,我们还利用光谱常数与力常数以及 Murrell-Sorbie函数之间的关系计算了与实验光谱数据相对应的力常数和 Murrell-Sorbie 函数,并与CASSCF结果进行了比较得出了一些有价值的结论.最后,对于具有双极小值的B1∑+态给出了更精确的定量的信息.     

Full-Wave Analysis of Inside Cylindrical Microstrip Lines by Finite Element Method

In this paper, a full-wave analysis using finite element method is presented to investigate the dispersion characteristics of inside cylindrical microstrip lines, which are essential to the design of some conformal microstrip circuits in millimeter wave bands. Numerical results of frequency-dependent effective dielectric constants are given for different structural dimensions and dielectric constants of substrate. Some useful conclusions are derived for the design of the special conformal microstrip lines.     

On the lattice dynamics of grey tin

The lattice dynamics of grey tin is studied by fitting a Born-von Karman model to the experimental neutron scattering data of Price and Rowe. In agreement with earlier conclusions drawn for Ge, it is found that fifth neighbor interactions are essential for achieving a good fit. New information is obtained concerning the values of the elastic constants and the Σ₂, Σ₄ branches of the dispersion curves. The density of phonon states is calculated employing the analytical integration method of Gilat and Raubenheimer. Calorimetric data for α-Sn agree reasonably with the results of the computation.     

Integrable dispersive chains and their multi-phase solutions

Earlier the theory of finite-gap integration was successfully applied to finite-component systems only. In this paper, we consider a first example of infinitely many component integrable systems. We construct multi-phase solutions for integrable dispersive chains associated with the three-dimensional linearly degenerate Mikhalëv system of the first order. These solutions are parameterised by infinitely many arbitrary constants. As a by-product, we describe multi-phase solutions for finite-component dispersive reductions in these integrable dispersive chains.

     

Photon-added coherent states for the Morse oscillator

In the paper we have constructed and investigated some properties of the Perelomov's “generalized coherent states” and photon-added coherent states for the Morse one-dimensional Hamiltonian (MO-PACSs), using the SU(2) group generators. We have found the integration measure in the resolution of unity and we have calculated some expectation values in the MO-PACSs representation. Using these states, the diagonal P-representation of the density operator is constructed as a new result for Morse potential. In addition, we have calculated some thermal expectation values for the quantum canonical diatomic gas of the Morse oscillators.     

Revisiting Noether's Theorem on constants of motion

In this paper we revisit Noether's theorem on the constants of motion for Lagrangian mechanical systems in the ODE case, with some new perspectives on both the theoretical and the applied side. We make full use of invariance up to a divergence, or, as we call it here, Bessel-Hagen (BH) invariance. By recognizing that the Bessel-Hagen (BH) function need not be a total time derivative, we can easily deduce nonlocal constants of motion. We prove that we can always trivialize either the time change or the BH-function, so that, in particular, BH-invariance turns out not to be more general than Noether's original invariance. We also propose a version of time change that simplifies some key formulas. Applications include Lane-Emden equation, dissipative systems, homogeneous potentials and superintegrable systems. Most notably, we give two derivations of the Laplace-Runge-Lenz vector for Kepler's problem that require space and time change only, without BH invariance, one with and one without use of the Lagrange equation.     

具有六方晶系结构的多晶体材料弹性常数——Y弹性常数

利用最近提出的新的物理参量——Ｙ弹性常数,将其应用于具有六方晶系结构的多晶体材料.推导了六方晶系结构的多晶体材料之Ｙ弹性常数,通过算例与具有六方晶系结构的多晶体材料之X射线弹性常数进行了比较.运用这个Ｙ弹性常数进一步推导出的多晶体材料整体之机械弹性常数的表达式与Kneer的研究结果中的表达式虽然形式不同,但针对具体材料所计算的结果却完全符合. 关键词： Y弹性常数 六方晶系 多晶体材料     

Mass of a body in Brans-Dicke theory

Exploiting exact spherical solutions of the Brans-Dicke equations, we study various definitions of the total mass of a body in this theory. We argue why the vacuum spherical solutions involve—in general—two arbitrary constants of integration. We discuss the dependence of the total mass on these constants.     

A matter-dominated cosmological model with variable G and Λ and its confrontation with observational data

In the framework of renormalization-group improved cosmologies, we analyze both theoretically and observationally the exact and general solution of the matter-dominated cosmological equations, by using the expression of the cosmological term as a function of the Newton parameter already determined by the integration method employed in a previous paper. A rough comparison between such a model and the concordance ΛCDM model from the point of view of the magnitude-redshift relationship has been already considered, without showing any appreciable differences. Here we test our model by using astrophysical data (the Union2 type Ia supernovae (SNIa) dataset, the Hubble diagram constructed from some gamma ray bursts luminosity distance indicator), to constrain its parameters. We also apply a cosmographic approach to our cosmological model. In order to estimate the cosmographic parameters we fit a large dataset, including not only the Hubble diagram, as traced by SNIa and gamma ray bursts, but also the H(z) measurements from passively evolving galaxies, baryon acoustic oscillations and the distance priors from the cosmic microwave background radiation anisotropy spectrum. We show that this matter-dominated cosmological model with variable Newton parameter and variable cosmological term is indeed compatible with the observations above. The cosmographic approach adopted confirms such conclusions. Last, it seems possible to include radiation into the model, since numerical integration of the equations derived by the presence of both radiation and matter shows that, after inflation, the total density parameter is initially dominated by the radiation contribution and later by the matter one.     

Chaos and dynamics of spinning particles in Kerr spacetime

We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincaré sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.     

The interior field of a magnetized Einstein-Maxwell object

Using the harmonic map ansatz, we reduce the axisymmetric, static Einstein-Maxwell equations coupled with a magnetized perfect fluid to a set of Poisson-like equations. We were able to integrate the Poisson equations in terms of an arbitrary function M = M(ϱ, ζ) and some integration constants. The thermodynamic equation restricts the solutions to only some state equations, but in some cases when the solution exists, the interior solution can be matched with the corresponding exterior one.     

Binaural and monaural auditory filter bandwidths and time constants in probe tone detection experiments.

Auditory filter bandwidths and time constants were obtained with five normal-hearing subjects for different masker configurations both in the frequency and time domain for monaural and binaural listening conditions. Specifically, the masking level in the monaural condition and the interaural correlation in the binaural conditions, respectively, was changed in a sinusoidal, stepwise, and rectangular way in the frequency domain. In the corresponding experiments in the time domain, a sinusoidal and stepwise change of the masker was performed. From these results, a comparison was made across conditions to evaluate the influence of the factors "shape of transition," "monaural versus binaural," "frequency domain versus time domain," and "subject." Also, the respective data from the literature were considered using the same model assumptions and fitting strategy as used for the current data. The results indicate that the monaural auditory filter bandwidths and time constants fitted to the data are consistent across conditions both for the data included in this study and the data from the literature. No consistent relation between individual auditory filter bandwidths and time constants were found across subjects. For the binaural conditions, however, considerable differences were found in estimates of the bandwidths and time constants, respectively, across conditions. The reason for this mismatch seems to be the different detection strategies employed for the various tasks that are affected by the consistency of binaural information across frequency and time. While monaural detection performance appears to be modeled quite well with a linear filter or temporal integration window, this does not hold for the binaural conditions where both larger bandwidth and time constant estimates are found.     

Mathematical Model of Relativistic Anisotropic Compact Stellar Model Admitting Linear Equation of State

In present paper, a static, spherically symmetric, anisotropic stellar object has been discussed by assuming a linear relationship between the matter density ρ and radial pressure pr. The interior solution is continuously matched with the exterior Schwarzschild vacuum solution at the junction interface. Various physical features viz. energy conditions, mass-radius relationship, stability are analyzed for our stellar model. By assigning some particular value to the arbitrary constants we have obtained a model of compact star of radius 6.7 km. and mass 1.148 M⊙, which is very close to the observational data of the compact star Her X-1 proposed by Rawls et al.[Rawls, et al., Astrophys. J. 730 (2011) 25]. We have obtained that the model satisfies all the regularity conditions. We have found that our proposed model is stable as well as singularity-free.     

Microscopic integral relations for the curvature dependent surface tension in a two-phase multi-component system

In this paper we discuss the thermodynamics and statistical mechanics of a curved fluid interface, in a system containing several chemical components. We derive microscopic integral relations for the Tolman-length, the spontaneous curvature and rigidity constants in a multi-component system. A thorough discussion is given of the dependence of the various relevant quantities on the choice of the dividing surface. Also some choice invariant characteristics quantities are given. We furthermore discuss the small-curvature correction to the Clausius-Clapeyron condition.     

Semi-Markov regime switching interest rate models and minimal entropy measure

In this paper, we present a discrete time regime switching binomial-like model of the term structure where the regime switches are governed by a discrete time semi-Markov process. We model the evolution of the prices of zero-coupon when given an initial term structure as in the model by Ho and Lee that we aim to extend. We discuss and derive conditions for the model to be arbitrage free and relate this to the notion of martingale measure. We explicitly show that due to the extra source of uncertainty coming from the underlying semi-Markov process, there are an infinite number of equivalent martingale measures. The notion of path independence is also studied in some detail, especially in the presence of regime switches. We deal with the market incompleteness by giving an explicit characterization of the minimal entropy martingale measure. We give an application to the pricing of a European bond option both in a Markov and semi-Markov framework. Finally, we draw some conclusions.     

An additional kind of nonlinear s-polarized surface plasmon polaritons

We have explored the dispersion relations for s-polarized surface plasmon polaritons guided by a metal film sandwiched between a linear substrate and a cladding with an intensity-dependent refractive index. In contrast to a previous paper we found surface plasmon polaritons for this configuration which exhibit a definite power threshold and a limited range for permitted propagation constants as well.     

Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds.     

Generalized Barut-Girardello Coherent States for Mixed States with Arbitrary Distribution

In the paper we examine some properties of the generalized coherent states of the Barut-Girardello kind. These states are defined as eigenstates of a generalized lowering operator and they are strongly dependent on the structure constants. Besides the pure coherent states we focused our attention on the mixed states one, which are characterized by different probability distributions. As some examples we consider the thermal canonical distribution and the Poisson distribution functions. We calculate for these cases the Husimi’s Q and quasi-probability P-distribution functions.     

真空中某些非晶体材料出气的扩散理论

真空中材料出气过程曾有Dayton,Schram,Jaeckel分别给出过理论假设和模型,这些理论仍为当前研究出气过程的基本依据。但是人们早已发现,当测量非晶体材料,例如:塑料、橡胶等的出气过程时,实验与理论之间仍然有矛盾。1964年我们曾提出了“双重叠加扩散”和“非均匀浓度扩散”两个理论模型,能够解释实验结果中的各种现象。在测量出气速率的工作中,我们还对实验方法做了改进。 关键词：     

Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation

This paper is devoted to study the error growth of numerical time integrators for N-phase or N-band quasi-periodic (in time) solutions of the periodic Korteweg–de Vries equation. It is shown that the preservation, through numerical time integration, of conserved quantities of the periodic problem of the equation, may be an element to take into account in the selection of the numerical method. We explain why the inclusion of these properties of conservation provides a better error propagation. In particular, we emphasize how the preservation of invariants makes influence in the simulation of some physical parameters of the waves.