CONSERVATION LAWS FOR THE SCHRÖDINGER–NEWTON EQUATIONS

In this Letter a first-order Lagrangian for the Schrödinger–Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 4844–4877]. Then Noether's theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the Schrödinger–Newton equations, Nonlinearity 19(7) (2006) 1507–1514] in order to find conservation laws of the Schrödinger–Newton equations.     

HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

A conformal invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimension is proposed. Many new Painlevé integrable models with the same dimension can be obtained at the same time. Taking the (2+1)-dimensional KdV-Burgers (KdVB) equation, (3+1)-dimensional Zabolotskaya-Khokhlov and Kudomtsev-Petviashvili (ZKKP) equation as concrete examples, we obtain some new higher dimensional conformal invariant models with Painlevé property and the approximate solutions of these models. In certain special cases, some of the approximate solutions become exact.     

ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS

In this paper, we analyse the commutation relations of the infinitesimal generatorsof all simple classical Lie groups and establish a new basis for these generators, calledthe tensor basis. In tensor basis, the infinitesimal, generators can be written as somescalar operators, some sets of angular momentum operators and some sets of irreducibletensor operators. The commutation relations, of these operators are very simple andhave many regularities. By means of the method that has been used in the earlier papers, "On the irre-ducible representations of the compact simple Lie groups of rank 2, I,II,III" and thetensor basis, all the irreducible representations of the classical simple Lie groups canbe calculated systematically.     

THE FLUID THEORY OF SELF-SUSTAINING MAGNETICALLY CONFINED ELECTRON CLOUDS (Ⅰ) FLUID EQUATIONS

In this paper the axisymmetrical self-sustaining magnetically confined electron clouds are studied by means of the fluid theory.In the electron clouds which supported by the Penning discharge the property of motion of electrons can be described by the fluid equations:continuity equation,momentum equation,energy equation,Poisson equation and heat transfer equation.The problems of the diffusion and escape of electrons and the energy transport in the electron clouds are discussed.     

THE IMPACT OF SDI ON THE ARMS RACE——A SOLUTION OF GAME THEORY

The impact of SDT on arms race has been discussed in a model which includes intercontinental ballistic missiles, anti-FCBM satellites and anti-satellite weapons for U.S. and former Soviet Union. It is assumed that each side of U. S. and former Soviet Union wants to reach the biggest retaliatory capability for given expenditure. This problem is considered as a two-person game and the optimal configurations of the three kinds of weapons for both sides is calculated under different conditions. The results show that the SDI can not lead to the transition from an offensive mode to a defensive mode and can not also offer an effective protection against the threat of ICBMs.     

REALIZATION OF THE WAVE-PACKET-COLLAPSE —A VIEWPOINT TO THE QUANTUM MEASUREMENT THEORY

An interpretion of the wave-packet-collapse (WPC) in the system of quantum mechanics is given. We find a connection between the WPC and the limitation to the measurement precision determined by the quantum fluctuation. A simple and explicit relation about them is obtained.     

ON THE BOUNDARY CONDITION AND CANONICAL S-WAVE HAMILTIONIAN FOR THE DYON-FERMION SYSTEM——THE SURFACE LAGRANGIAN AND GAUGE INVARIANT CHARGE CURRENT

By means of the surface Lagrangian and gauge invariant charge current, we make a detailed discussion to the physical meaning of each quantity in the boundary condition of the dyon-fermion dynamics; It is shown that adding the surface Lagrangian to the system is equivalent to selecting suitable boundary condition; By gauge trans-forming the Lagrangian by a charge generator, We get a corresponding U(1) charge current density which is both gauge invariant and spherosymmetrical. Ause of the canonical method and a careful treatment of surface terms show that the S-wave Hamiltonian given by Yamagishi requires amendment by a surface energy term.     

REALIZATION OF THE WAVE-PACKET-COLLAPSE —A VIEWPOINT TO THE QUANTUM MEASUREMENT THEORY

An interpretion of the wave-packet-collapse (WPC) in the system of quantum mechanics is given. We find a connection between the WPC and the limitation to the measurement precision determined by the quantum fluctuation. A simple and explicit relation about them is obtained.     

THE 4—3—N MATRIX MULTI-CHANNEL SOUND SYSTEM

In this paper,it is proved that,although there are only three independent signals in a pano-ramic sound system,there can be different forms of each of the three channel signals to be selected.The general method of N(≥3)channel reproduction using the three independent signals and itsapplication as an example of N=8 are to be discussed.It may improve the reproduction effectof the conventional quadraphony. The use of this system in radio broadcasting and its compatibility with conventional systemare also discussed.     

THE INTERACTION OF A HIGH ENERGETIC PROTON WITH A NUCLEUS—THE RELATION OF THE PRODUCED PARTICLES WITH THE NUCLEAR MASS NUMBER A

Suppose that a high energetic proton interacts with a cluster of m particles in anucleus the mean multiplicity of this interaction and that of PP interaction followthe same law: n=CS^k. Using the Glauber theory we get R(A)≡n_PA/n_PP1.26A ^1/3(A ^1/3+1) ^-2/3 This formula explains the current experimental result quite well.     

THE ENERGY SPECTRUM AND WAVEFUNCTION OF NUCLEUS 31Si——A TEST ON THE COMPOSITE PARTICLE REPRESENTATION THEORY

The nuclecus ³¹Si₁₇ is studied by the composite particle representation theory and compared with the shell model calculations. It is shown that the entire energy spectrum agrees with the shell model results very well, and the wave function is equivalent to the shell model wavefunction exactly. Therefore it strongly supports the composite particle representation theory.     

PARTIAL ANALISIS FOR THE ELECTRON EXCITATION OF HYDROGENIC IONS IN THE COULOMB—EIKONAL APPROXIMATION

A method is developed for the evaluation of the Coulomb-Eikonal crosssections for the electron impact excitation of H-like ions employing Partialwave analysis firstly.In the Coulomb-Eikonal Approximation(CEA),thetransition matrix element is given byWhere r_o and r_1 denote the coordinates of the incident and boundelectrons respectively,and r_(o1)=|r_o-r_1|.The Eq.(2)represents the eikonal     

THE ACOUSTICAL QUALITY OF HALLS——A COMPARISON OF SIMULATION TO EXPERIMENT

The acoustical quality of an ordinary hall,namely the reverberation time and the spatial nonuni-formity of sound pressure level in audience area,was simulated on a microcomputer.Comparisonbetween calculation,measurement and simulation of reverberation time shows that the reverberationtime from simulation is closer to measurement than from calculation,if the absorption of the audience isproperly chosen,in the frequency range from l25 to 4000 Hz;the average deviation is less than 10%.For the spatial nonuniformity of sound pressure level,there is a good correspondency botween thesimulation and the measurement.In addition,some details in simulation were discussed.     

THREE—BODY SCATTERING CROSS SECTION AND SINGULARITIES OF THE T—MATRIX

Cross section is a fundamental concept in collision theory. This concept hasbeen formulated for binary collisions,i.e.,collisions between two incidentparticles.As far as binary collisions are concerned,one can describe withdifferential and integrated cross sections any elementary processes includingdissociation and rearrangement as well as elastic and inelastic scattering.It isbelieved,however that besides binary collisions there are three-body colli-sions,i.e.,collisions among three incident particles.Thus it is of general     

DESIGN OF THE AIR—CORE TRANSFORMER IN SPHERICAL TOKAMAK

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THE AB INITIO CALCULATION FOR THE BONDING STATE OF THE Hn CTUSTERS

The equilibrium geometries of several Hn（n=4,5,6,7,9,13) clsters with certain symmetry have been optimized by the ab inito Murtaug-Sargent(MS) method.We find that the stability of a centered cluster depends on the structure,the spin symmetry and the coordinate number,and the latter plays a more important role.     

STATICAL SPHEROSYMMETRICAL SOURCELESS SOLUTION OF SU(2) GAUGE FIELD——THE SELFDUALITY,UNIQUENESS AND THE SELF INDUCED CHARGE CURRENT

It is shown that the statical spherosymmetrical sourceless solutions of SU(2) guagefield,which satisfy a physical boundary condition,must be selfdual.Then from theselfdual condition,we solve the equation explicitily,hence show the uniqueness analy-tically.By gauge transforming the Lagrangian by a local generator of synchrono-symmetry,we get a corresponding local charge current density,which is both gaugeinvariant and conserved.The total values of either electric or magnetic charge arequantized,but the charge distributions in space are continuous and not restrictedby quantization.Finally we discuss a mechanism of spontaneous symmetry break-down.Contrary to ordinary magnetic flux string,now the ordered phase is surround-ed by the normal phase,the ordered phase repels electric fields,and electric fieldsdestory the ordered phase.     

THE MACQM CALCULATION OF THE TOTAL ENERGY CURVE OF THE BODY-CENTERED CUBIC STRUCTURE OF THE H_9~- CLUSTER

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SEMI-MICROSCOPIC OPTICAL POTENTIAL CALCULATION BY THE NUCLEAR MATTER APPROACH——I. SYMMETRIC NUCLEAR MATTER

In this paper semi-microscopic nuclear matter approach is introduced to calculatethe microscopic optical potential. The first and second order mass operator in sym-metric nuclear matter is derived with Skyrme effective interactions and the real andimaginary part of the optical potential for finite nuclei is obtained by applying alocal density approximation. The five kinds of the different parameters of Skyrmeinteractions Ⅱ-Ⅵ are used and compared with the experimental data to study how wellthese Skyrme interactions can work for our purposes. Our results obtained in such asimple way seem to be to some extent comparable with those obtained with "nuclearmatter approach" and "nuclear structure approach" without adjusting the parame-ters of the Skyrme interactions so far.