左对称超代数上的超S-方程

主要研究左对称超代数上奇型的超O-算子,研究了左对称超代数上的超S-方程的解与超O-算子之间的关系,进一步找到在左对称超代数上奇型的超O-算子与左对称超代数和表示空间的对偶空间的直和空间上的超S-方程的解的关系.给出了左对称超代数上超2-上循环的定义,研究了左对称超代数上超S-方程的解与超2-上循环之间的关系.

Pre-Lie超代数的超θ-算子和超S-方程

介绍了Pre-Lie超代数的超θ-算子以及其与超S-方程解的关系,并引出了超θ-算子背后的代数结构,即L-dendriform超代数.研究了L-dendriform超代数、dendriform超代数和Pre-Lie超代数之间的关系.

关于Schinzel-Sierpinski方程组的推广

本文给出Schinzel-Sierpinski方程组的若干推广,并给出了解。得到的结果包含了Mordell的书[2]中总结的Williams,Szymiczek等人的结果。

Localization of s-Wave and Quantum Effective Potential of a Quasi-free Particle with Position-Dependent Mass

The properties of the 8-wave for a quasl-free partide with position-dependent mass （PDM） have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in D dimensions except D = 1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction, which may be attractive in some cases. The analytical expressions of the eigenfunctions and the corresponding probability densities for the 8-waves of the two- and three-dimensional systems with a special PDM are given, and the existences of localization around the origin for these systems are shown.

L^s- norm Estimates of Solutions for theImhomogeneous Cauchy- Riemann Equation

In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.

Entropy and Entanglement in Master Equation of Effective Hamiltonian for Jaynes-Cummings Model

In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.

从一个四维左对称代数构造一些八维相空间

相空间是一类特殊的辛李代数,与辛几何有密切的关系。左对称代数与李代数有密切的关系,通过左对称代数上的S-方程(类似于李代数上的Yang-Baxter方程)的一个对称解可以构造出其邻接李代数上的一个辛李代数结构。本文通过计算结构常数的方法,得到了一个特殊的四维交换左对称代数(域的直和)上S-方程的对称解,并且通过这些解构造出一些非平凡的八维的相空间。

Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations

Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.

N-S EQUATION CALCULATIONS ON MULTI-ELEMENT AIRFOILS WITH ZONAL PATCHED GRIDS

For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.

FLOW CHARACTERISTIC AND HEAT TRANSFER FOR SINGLE PHASE GASEOUS IN SLIP REGIME OF MICROCHANNEL FLOW

Based on analyzing some simulation models of single phase gaseous flow in microchannels （0. 001〈 Kn〈0. 1 ）, a numerical simulation of N-S equations with the slip model is presented. In the simulation, the collocated grid and the SIMPLE scheme are used. Results show that the pressure in the inlet is changed with Knudsen number. The slip speed and the temperature creep are increased with the augment of Knudsen number. The drag force decreases and the resistance of the heat trensfer has a little increase.

Heisenberg代数上左对称代数对应的6维左对称双代数

主要研究Heisenberg代数上的左对称代数对应的6维左对称双代数.首先利用左对称代数的分类计算了这些左对称代数上S-方程的对称解,从而找到S-方程的对称解对应的上边界左对称双代数中的代数运算.

Numerical Modeling of Floating Oil Boom Motions in Wave-Current Coupling Conditions

Containment booms are commonly used in collecting and containing spilled oil on the sea surface and in protecting specific sea areas against oil slick spreading.In the present study,a numerical model is proposed based on the N-S equations in a mesh frame.The proposed model tracks the outline of the floating boom in motion by using the fractional area/volume obstacle representation technique.The boom motion is then simulated by the technique of general moving object.The simulated results of the rigid oil boom motions are validated against the experimental results.Then,the failure mechanism of the boom is investigated through numerical experiments.Based on the numerical results,the effects of boom parameters and dynamic factors on the oil containment performance are also assessed.

Spectra of Free Diquark in the Bethe-Salpeter Approach

In this work, we employ the Bethe-Salpeter （B-S） equation to investigate the spectra of free diquarks and their B-S wave functions. We find that the B-S approach can be consistently applied to study the diqaurks with two heavy quarks or one heavy and one light quarks, but for two light-quark systems, the results are not reliable. There are a few free parameters in the whole scenario which can only be fixed phenomenologically. Thus, to determine them, one has to study baryons which are composed of quarks and diquarks.

Low Dissipation Simulation for Vortex Flowfield of Rotor in Hover Based upon Discontinuous Galerkin Method

The discontinuous Galerkin(DG) method is established and innovatively conducted on accurately simulating the evolution of blade-tip vortex and the aerodynamic characteristics of helicopter rotor. Firstly,the Reynolds-Averaged Navier-Stokes(RANS)equations in rotating reference frame are employed,and the embedded grid system is developed with the finite volume method(FVM)and the DG method conducted on the blade grid and background grid respectively. Besides,the Harten-Lax-Van Leer contact(HLLC)scheme with high-resolution and low-dissipation is employed for spatial discretization,and the explicit third-order Runge-Kutta scheme is used to accomplish the temporal discretization. Secondly,the aerodynamic characteristics and the evolution of blade-tip vortex for Caradonna-Tung rotor are simulated by the established CFD method,and the numerical results are in good agreement with experimental data,which well validates the accuracy of the DG method and shows the advantages of DG method on capturing the detailed blade-tip vortex compared with the FVM method. Finally,the evolution of tip vortex at different blade tip Mach numbers and collective pitches is discussed.

Numerical simulation of the influence of ground effect on the performance of multi section wings

the establishment of multi-element airfoil in steady and unsteady ground effect N-S equation turbulence model, the S-A model of multi element airfoils during takeoff and landing high attack angle change numerical simulation analysis, the calculation results show that the lower altitude, lift and drag wing angle decreased; the greater the ground the effect is more obvious, the greater the loss of lift. The simulation results show that the lift coefficient is slightly less than that of unsteady numerical simulation, and the drag coefficient is slightly less than that of unsteady numerical simulation. The ground disturbance to the wing not only affects the steady state flow field, but also is closely related to the unsteady aerodynamic performance. The results of this study can provide a reference for the design and flight control of large aircraft wings.

Generalized Dirac Equation with Vector Structural Coefficient and Its Generalized Solutions in Biquaternions Algebra

On the base of differential biquatemions algebra and theories of generalized functions the biquaternionic wave equation of general type is considered under vector representation of its structural coefficient. Its generalized decisions in the space of tempered generalized functions are constructed. The elementary twistors and twistor fields are built and their properties are investigated. Introduction. The proposed by V.P. Hamilton quatemions algebra [1] and its complex extension - biquaternions algebra are very convenient mathematical tool for the description of many physical processes. At presence these algebras have been actively used in in the work of various authors to solve a number of problems in electrodynamics, quantum mechanics, solid mechanics and field theory. The properties of these algebras are actively studied in the framework of the theory of Clifford algebras. In the papers [2, 3] the differential algebra of biquatemions has been elaborated for construction of generalized solutions of the biquaternionic wave （biwave） equations. The particular types of biwave equations were considered, which are equivalent to the systems of Maxwell and Dirac equations and their generalizations, their biquaternionic decisions also were constructed. Here the biwave equation is considered with vector structural coefficient which is biquaternionic generalization of Dirac equations. Their generalized solutions in the space of tempered distributions are defined and their properties are researched.

Jacobian matrix for the inversion of P-and S-wave velocities and its accurate computation method

The optimization inversion method based on derivatives is an important inversion technique in seismic data processing,where the key problem is how to compute the Jacobian matrix.The computation precision of the Jacobian matrix directly influences the success of the optimization inversion method.Currently,all AVO(Amplitude Versus Offset) inversion techniques are based on approximate expressions of Zoeppritz equations to obtain derivatives.As a result,the computation precision and application range of these AVO inversions are restricted undesirably.In order to improve the computation precision and to extend the application range of AVO inversions,the partial derivative equation(Jacobian matrix equation(JME) for the P-and S-wave velocities inversion) is established with Zoeppritz equations,and the derivatives of each matrix entry with respect to Pand S-wave velocities are derived.By solving the JME,we obtain the partial derivatives of the seismic wave reflection coefficients(RCs) with respect to P-and S-wave velocities,respectively,which are then used to invert for P-and S-wave velocities.To better understand the behavior of the new method,we plot partial derivatives of the seismic wave reflection coefficients,analyze the characteristics of these curves,and present new understandings for the derivatives acquired from in-depth analysis.Because only a linear system of equations is solved in our method,the computation of Jacobian matrix is not only of high precision but also is fast and efficient.Finally,the theoretical foundation is established so that we can further study inversion problems involving layered structures(including those with large incident angle) and can further improve computational speed and precision.

On S-Shaped Bifurcation Curves for a Class of Perturbed Semilinear Equations

By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.

在源作用下的n体不可逆聚集过程集团尺寸分布

把在源作用下两体作用的Ｓｍｏｌｕｃｈｏｖｓｋｉ方程推广到ｎ体相互作用的广义Ｓｍｏｌｕｃｈｏｖｓｋｉ方程，讨论了系统在源作用下，核为Ｋ（ｉ１，ｉ２，…，ｉｎ）＝（ｉ１·ｉ２…ｉｎ）ω（０≤ω≤１），源项为Ｉ（ｔ）＝Ｉδｍ，１的非凝胶系统广义Ｓｍｏｌｕｃｈｏｖｓｋｉ方程的定态解，得到了不可逆聚集过程的集团尺寸分布．同时。

相对论热力学向量理论对Schwarzschild场中物质系统特性的研究

应用相对论热力学向量理论，讨论了Ｓｃｈｗａｒｚｓｃｈｉｌｄ场中球对称静态理想流体恒星结构，得到了ＴｏｌｍａｎＯｐｐｅｎｈｅｉｍｅｒＶｏｌｋｏｆ方程，并且就该引力场中粒子系统的不同运动状况做了讨论，由此得到了与经典极限相符合的结果．