In this paper we report the multisoliton solutions of Landau-Lifshitz's equation for a classical ferromagnetic chain and their asymptotic behaviors as well as the formulas of shifts of their phases and centers of mass.They include the single-and double soliton solutions as particular cases.

This paper is a generalization of an article on the twodimensional system, in which the kink and phase transition were treated at a unified level. As in the two-dimensional case,there are two sorts of kink which correspond to domain walls with 90° and 180° transition angle. But unlike the two-dimensional case, there are two types of phase transition, one of which is displacive and the other is of order-disorder.

Based on the composite particle representation presented in the last paper(I),a method of solving the many-body problem knpwn as the compqsite particle approximation is proposed.It is shown that a many-body system can be simplified to a composite particle system (plus one or more uncorrelated basic particles if any existed) if the following conditions are satisfied:1) the binding energies of the composite particles are much larger than the excitation energies of the system; 2)there is domination of the collective mode for the composite particles.The interac-tions between the composite particles,,as well as the interactions between composite particles and the basic particles can be evaluated from the original particle-particle interactions. Applications of this theory are indicated.

In this paper the concept of the clusterizations of partons of two kinds is proposed. In terms of the model of quark recom bination and the perturbative QCD a set of distribution functions describing the clusterization of the second kind are separated from the quark fragmentation function, and so some quantitative phenomenological information about the QC3 soft processes is obtained.

A recombination model of subquarks for superhigh energy collision is proposed.The new phenomena observed in experiments of superhigh energy cosmic ray can be explained naturally via the cascade decay of superfireballs of subquark stratum from this model.The mean multiplicity,the average transverse momentum,the distributions of both transverse and longitudinal momenta and the inclusive spectrum for the superhigh energy collision are obtained based on this model.It is shown that if the mean multiplicity of secondary particles increases as S increases according to the power law,the scaling violation should take place.Espe-cially,when the behavior of mean multiplicity changes from s⁺ to S⁺ there will be a significant jump of violation coofficient and the scaling violation.wil1 become more significant as S in-creases.It is also pointed out that the characteristic behavior of the existence of subquark stratum for the inclusive distribu-tion is almost model-independent and can be treated as a decided experimental verification of the appearance of subquark stratum,in particular,for the experiments with accelerator in the near future.

A-unified model based on the mechanisms of scattering and recombination for quarks and subquarks is proposed. The implications of this model for different energy regions are discussed. For the low energy regions, the predictions of this model are consistent with the well-known picture given experimentally. For the superhigh energy region it can be used to explain naturally almost all the new phenomena observed in the cosmic ray experi-ments. The predictions of this model for the experiments made on the colliding beam acce1erators are discussed in detail.These predictions can be verified and used as significant evidence of the existence of these mechanisms.

In this paper we construct the lattice formulation of the pure gauge fields in a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a fourdimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the quark system by calculating latt-ice current-current propagztor when the coset pure gauge fields are retained manifest1y.

We investigate the lattice gauge theory with a gauge group UxV(1) where U is a non-Abelian group and V(1) is a chiral Abelian group.In the strong coupling approximation for the U gauge field we find that the V(1) chiral symmetry is realized through parity doublets of composite fermions for strong V(1) coupling and that it is spontaneousely broken through a techni color-like mechanism for weak V(1) coupling.

We will briefly review the prolongation structure theory for nonlinear systems, such as nonlinear evolution equations and soli-ton equations, and its applications to the solutlon generating techniques for the gravitational fields with two commuting Killing vectors.

The averase effect of the non-resonance harmonics on slow extraction from synchrotrons does not vanish in a long perlod, in some cases it becomes so important that it cannot be neglected. A method based on the theory of average is emplosyed for studying the problem. The asymmetric shape of the seperatrices in the phase-plane of the third-integer resonance extractlon is expldilied. The effect of sextupole fields on the half-integer resonance extraction is analyzed in detail. It is shown that the extraction efficiency would be improved if some sextupoles are introduced properly into a half-integer resonance extraction system.

Two scaling relations between the thermodynamic critical amplitudes and exponents are obtained.

The catastrophe theory is applied to investigating the number of permissible phase for homogeneous-isotropic and homogeneous anisotropic Ising lattices.

The problem of symmetry breaking of Su(n) is discussed more completely with Higgs scalar fields belonging to an adjoint representation or an adjoint together with a fundamental one.

The N-fold Kerr family and charged Kerr family solutions have been given in this paper by means of the inductive method to solve the principal homogeneous Hilbert problems associated with the principal inverse scattering equations, i.e., the W-equations, for both vacuum and electrovac cases with stationary axial symmetry in general relativity.

The experimentally observed quantized Hall plateau of P_xy=3h/e² in two-dimensional electron gas, when the lowest Landau level is 1/3 filled, is discussed. The consistency of the cxtremal condition for the Hartree-Fock potential in the possible charge-density-wave state with, opening an energy gap at the Fermi level is indicated. The exactness of Such 1/3 "fractional" quantization might be justified by a modified version of Laughlin's argument based on gauge invariance.

In this paper, the Bethe-Salpeter equation for a Coulombic bound system consisting of a fermion (mass m_l and spin 1/2) and an anti-fermion (mass m₂ and spin 1/2) is solved. The approximate B-S wave functions for (∑U) atom are given. Utilizing the perturbative expansion of the quantum field theory of composite particles, the decay rate and branching ratio for E°→(∑⁺μ^-)+ν_μ are calculated with accuracy up to order O(α).

The departure of electronic distribution from local electrical neutrality and the additional energy due to such a departure in compositionally modulated structures are calculated using a simplified Thomas-Fermi equation. with the energy, we have derived the variation of the biaxial modulus with the modulation period. The result agrees at least qualitatively with the exprimental finding of a supermodulus effect in such structures.

The Scalapino-Huberman equation is studied by the Fourier analysis method. The multiple-gap states, its bifurcation points and the corresponding spatial structures are found. The solution of the first-order transition which cannot be obtained by singular-perturbation method is obtained. Our results show that the conclusion of the μ^* model about the sequence of first order transition and second-order transition with the rising of the temperature is contrary to experimental results.

Using the inverse Mellin transformation method, we get the analytic expression for non-singlet nucleon structure function from its moment to the. next order effects. The comparison betweent heoretical prediction and experimental data is also made.

A dual transformation is found for a class of nonlinear σ-model defined on a multidimensional curved space with cylindrical symmetry. The system is invariant under a proper combination of the dual transformation and the general coordinate transformation. An infinite number of nonlocal conservation laws as well as the Kac-Moody algebra follow directly from the dual transformation. A Backlund transformation that qenerates new solutions from a given. one can also be constructed.

A scheme for obtaining masses of gluons from the spontaneons breaking of the local colour gauge symmetry with possible preserved asymptotic freedom is chosen. In this scheme we have cal-culated the rates of processes l⁺⁺→2G and l^--→γL⁺⁺. It is shown that it is possible to ascertain if the gluons have masses by observing if the decay l⁺⁺→2 jets for the heavy axial vector meson exist.

Phase diagram for 3-dimensional lattice Z₄ gauge-Z₂ Hiygs coupling system is constructed using Monte Carlo method (heat-bath method). The resulb are in agreement with the features predicted by Fradkin and shenker_[1]. To find accurate positions of the transition points we proposed a method of thermal cycles recooling near the transition points.

In this paper the lattice current-current propagator is calcdlated and the influence of coset pure gauge fields of an abelian chiral group G=U₁×U₁⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion in lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current current propagator which has no influence on confinement properties of the system. When subgroup H is U_s, the coset puregauge fields have no influence on wnfinement properties of the system either.

The generating functional approach to Green functions in the thermal equilibrium is used to explore the geometrical origin of the temperatures of the quantum fields in the Rindler space-time and black hole spacetimes. It is shown that under the transformation from Minkowski space to the Rindler space the path integral representation for the Euclidean generating functionals of Green functions at zero temperature would transform into the corresponding ones of the quantum fields at a certain finite temperature, and the Minkowski vacuum state would have the same properties as that of the quantum mixed state at the same temperatfire. All thermal Green functions for the mixed state are given. Similar results would be obtained for the Schwarzschild, the Reissner-NordstrOm and the Kerr black holes and whereupon the Hawking temperature for the black holes would have geometrical origin as well as that in the Rindler spacetime. The various density operators of the mixed states at the Hawking temperature for the black hole sacetimes are specified.

In the lecture notes^[1] one of us (LU) has studied the relations between the theory of connections and Gauge theory. But the formulation of the connection theory or Gauge theory in the lecture notes is linear in nature,i.e., we mainly studied the covariant derivative of a vector, tensor or spinor fields.

We present a simple and crude model of galaxies consisting of baryons and neutrinos with spherical symmetry. The baryon matter is rotatinq. in the central region of the galaxy as a nucleus. If the rotational curve of the heavy matter is known from the observational data, then the gravitational potential, and therefore the density distribution in this region, can also be obtained. This enables us to estimate the mass and the radius of the neutrino halo. Furthermore, the condition on the interface of the nucleus-halo will set an upper bound on neutrino mass. If the corresponding parameters duoted in Ref.[10] are adopted, then a value of ≤20eV. for the neutrino mass is obtained. By choosing m_v=15eV and a parameter in the rotational curve n=4, one can deduce that neutrino halo radius is about four times the heavy matter radius, and the total mass of neutrinos is about 14 times that of baryons. It seems, that these results are not in contradiction with the observations on the missing mass of the galaxies^[6].

A fireball theory in the quark level with supersymmetry between quark and antidiquark is suggested. A preliminary study of this model indicates that it can well describe all characteristic phenomena of multiproduction. In particular, the appearance of diquarks will enhance the baryon yield in multiproduction.

The hadronic decay widths of P-wave quarkonium states are calculated in the broken QCD with massive gluons. The comparison with prelfiminary data is also discussed.

The periodicity in the distribution of quasar redshifts is interprete dassuminq that the cosmological space is a topologi-cally compactified manifold like three-dimensional torus.The present size of such compact space is estimated at the order of 600Mpc.

The principle of maximum overlap is applied to the derivation of optimal single particle (sp) wave functions for a many-fermion system under the proposition that the ground state correlation should be taken into account rigorously. If the sp potential U_αβ is defined in terms of the mass operator M_αβ^(u) by u_αβ=M_αβ(εβ), it is shown that the eigenfunctions of the sp Hamiltonian h_αβ=t_αβ+u_αβ automatically fulfill the requirements of the above principle.

In the present paper the cluster model and charge self-consistent method are used to study the chemisorpti on Si(lll1), Ge(111), and GaAs(110) surfaces. The parameters in the calculations are selected to fit the respective bulk energy bands of Si, Ge, and GaAs. Some general rules of chemisorpti on Si(ll1) and Ge(ll1) are investigated and speculated. The three-fold hollow site geometry is favorable for group iii metals on Si(lll), whereas the one-fold top site is more stable for group vii elements, the reason being probably one of the favorable charge distribution. However, the situation for chemisorpti on Ge(ll1) is somewhat different. The adsorptions of group iii and v elements on GaAs(110) are also considered. The possible chemisorption geometries and the related electronic states for these systems are calculated and discussed.

We show numerical evidence of exact U-sequences in the periodically forced trimolecular model (the forced Brusselator). Interspersed among period-doubling bifurcation sequences star-ting with RLⁿ type periods, there are chaotic regions bounded on one side by period-doubling bifurcation sequences and on the other side by intermittent transitions. Along certain directions in the parameter space the most clearly seen periods appear in the same order as that in the logistic map, but along other directions the U-sequences may fold and give rise to deviations from the standard patterns. Our results show the coexistence of different "routes to chaos" in one and the same matheatical model and the necessity to enlarge the parameter space in both real and computer experiments on chaotic transitions.

The second guantization in furry picture is carried out, the perturbation theory is built up and a new method for investigating the electromagnetic phenomena in a constant magnetic field is proposed in this paper. Since the treatment of this method is exact, it is especially suitable for very high magnetic fields.

The multi-fold commutaror representation of hidden symmetry algebra in principal chiral model and the self-dual Yang-Mills field is explicitly shown. All the variations are taken with respect to the potential A_ξ other than field quantity g for principal chiral model in defining the usual operator Q(ξ,η) to give the G⊗c(t) algebra.

In this paper we have analyzed the γ^*π°→γ, γγ→ππ and γγ→ρρ processes by using the sum rules of the distribution amplitude ФM(xi,Q²), which are obtained from the π°→γγ and the π→μν decay processes. Since the angular distributions of the γγ→π°π° and γγ→ρ_⊥ρ_⊥ amplitudes are sensitive to the shape of the distribution amplitude ФM(xi,Q²), there is a possibility to investigate the effect of the quark mass from the angular distributions of γγ→MM exclusive processes.

We calculate the interaction energy between heavy quark pair in the Hamiltonian formulation of lattice gauge theories. Mean field-variational calculations show that the upper limit of the string tension is zero in the weak coupling region if we use approximate vacuum state of the mean field type. The mean field vacuum is unstable against forming closed flux loops.

The high statistics differential cross section, polarisa-tion and density matrix data on K^-P→ΦΛ obtained by the AmsterdamCERN-Nijmegen-Oxford collaboration at 4.2GeV/C is analysed using a Regge pole model with evasive Regge contribu-tions. The exchanges invoked are the K*, K**, K,KA and K_Z The K*-K** exchanges are taken to be non-degenerate and a simplifying assumption on their couplings in O+ζ→O+ζ reactions, advocated recently by Saleem and collaborators, is generalised to the present case. We do not find any need for the K_B in fitting data.

The problems of both El and M1 transitions of charmonium are discussed in the nonrelativistic potential model. It is found that these problems could be resolved by assuming larger constituent quark masses. With m_c=2.50GeV, m_b=5.84GeV in the typical linear plus Coulomb potential model we get satisfactory results for the mass spectra, the El and M1 transition rates, and the relative values of leptonic widths for the ψ and T families. The implication of the large constituent quark masses is also discussed.

In gauge supersymmetry and supersymmetry of nuclei we often meet the superal gebra osp(m/2n). Only the irreducible representations of osp(l/2) B(0,l) have been constructed so far^[1]. Here we construct all the finite-dimensional irreducible representations of osp(3/2)=B(l,l) and osp(l/4)=B(0,2), The conditions of grade star representations are discussed. Only a part of finitedimensional irreducible representations of B(1,1) and B(0,2) are grade star representations. These are different from those of B(0,l).

We discuss in this paper a stellar model of degenerate massive neutrinos with a core made of heavy matter. Dimension of the core is much smaller than the scale of neutrino star. The Oppenheimer-Volkoff equation is solved for such a system. Our calculation shows that under certain conditions, this neutrino halo will resemble a pure neutrino star. We have further obtained insides the neutrino star (or halo) the rdtation curve and the gravitational red shifts. It is interesting to note that the relative rotation velocity v(r)EV(r)/V(R) (R is the radius of the neutrino star) depends only on the relative coordinate ξ=r/R in the nonrelativistic cases. Therefore, all nonrelativistically degenerate neutrino systems will have a universa1 relative rotation curve(v versus ξ). Within the accuracy of numeri calcalculation, we have also obtained a useful relation connecting the maximum velocity V_m and the corresponding coordinate R_m as V_mR_m2=0.231. By comparing this relation with the observed rotation data at large distances for some galaxies, we have obtained an upper bound for neutrino mass of about 6-9eV.