In this papel, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is P_ca=0.69±0.02 for model 1 and P_ca=0.72±0.01 for model 2, critical fractal dimension. D_c= 1.71±0.06 for model 1 and D_c=1.66±0.07 for model 2, which are in good agreement with those of DLA model (D=5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be inilependent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class.

In this paper we introduced a periodic fractal structure (PFS) and studied the critical behavior of the nearest-neighbor-interacting Ising model within Migdal-Kadanoff bond-moving approximation. The critical curve equation and the formulas of the critical exponents were derived approximately in a special parameter region.

A new model of Bknard-Rayleigh convection has been put forward from mantle convection and liquid crystal, where the external force deviates from constant to a lineal function of vertical dimension z. The dimensionless parameter ε is induced to describe the scale of this kind of deviations. Through linear stability analyses, we find that even-odd symmetry broken appears. By numerical calculation under rigid boundary conditions, we find that α_c is almost α constant but R_c decreases nonlinearly as ε increases, so the increase of ε benefits convection. When ε=0, all results reduce to the former works automatically.

Using the free carrier-negative U center interacting model, we have investigated the superconducting transitionr,temperature T_c, the specific heat jump at T_c, the coherence length, the penetration depth, the thermodynamic critical field and the isotope effect for the high-T_c oxide superconductor. The theoretical values of these physical quantities are consistent with the experimental values. Further, the residual electronic specific heat in the superconducting state is explained as the result of the inherent instability in this superconductive mechanism.

The self-consistent semiclassical approach is extended from zero temperature to finite temperatures. The nucleon densities of a hot nucleus at thermal equilibrium are determined. The centroids of isoscalar giant monopole resonances(GMR) are evaluated by making use of these densities with sum rules. The incompressibility of hot nuclei is studied with these centroids. It is found that the incompressibility decrepes as the temperature increases. A non-self-consistent finite temperature semiclassical approach with a Woods-Saxon mean field is also presented and compared with the self-consistent result.

With the aid of a pair aligned model in many-j configurations and the Hamiltonian including monopole, quadrupole-pair forces and the quadrupole deformed field, the intrinsic states of deformed nuclei are determined by a variational method. The quadrupole moment is calculated and the effect of deformation on the intrinsic states is investigated. The results show that angular momentum (J=0,2,4) nucleon-pairs are dominant in the intrinsic states, so that, s, d, g bosons must be used in the study of deformed nuclei.

The scattering of three-cluster system is studied with the quasi-resonating-group method (QRGM), which is an extended resonating-group method (RGM) by omitting the antisymmetrization of the nucleons in the double-magic cluster with other ones, and CGCT. As an example, the phase shifts and differential cross rrections of N+¹⁹F(t+¹⁶O) elastic scattering are evaluated. In the calculation an imaginary optical potential is introduced to take account of the effect of other reaction channels. The results show that the QRGM is a feaaible approximate method for many-nucleon system such as N+¹⁹F and can be used for other systems containing more nucleons.

A set of nucleon-nucleon rank-two separable potentials is constructed directly from the low energy twebody and three-body experimental data. The fitness of the physical quantities is suitable.

Based on the many-body perturbation theory and cloudy bag model, the long range part of the nuclbar force is discussed. The results show that it agrees with one-pion exchange-potential in respect of both the radial dependence and the strength.

By means of Gaussian effective potential method, we investigate two models with coupling in 3+1 dimensions respectively. While the fermion effect through Yukawa coupling makes the autonomous λф⁴ theory more stable, it is shown that there are three different autonomous phases for model. The temperature dependences of these two models are similar to those in pure λф⁴ autonomous theory.

Using the empirical formula on F₂^N(C)/F₂^N(D) found by us and the analytical expression of the overall structure function d nucleon presented by CERNUA1 Collaboration, a simple calculating method on P+C→2jet+X process is presented. Our results will be checked by future experiments.

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility ehows a clear size-dependent behaviorin low temperature region. This means that it should be divergent in this region.

In this paper, a 3-cocycle is realized in a hybrid chiral bag model as quantities at the boundary of the bag. The equivalence between charges of gauged boson currents in Skyrme model and full gauge transformation generators is established both in 3+1 dimensions and 1+1 dimensions.

The thermodynamic properties of superconducting state in BZA mean-field theory of RVB superconducting mechanism are evaluated in this letter.

Darboux transformation method is used to find soliton solutions of the Landau Lifschite equation of a classical Heisenberg spin chain.

By using the formula of RE³⁺ multiphonon nonradiative transition (MPNRT) probability W_po derived on the basis of single-frequency model, the dependence of the W_po for the various RE ions in 10 hosts at the energy gap ΔE is analyzed and calculated systematically. The results agree well with a great deal of experimental data taken from the references and show clearly the characteristic of MPNRT under the condition of weak electron-phonon interaction: W_po decreases rapidly with the increase of order p which is the leading factor to determine W_po; the vahes of K. HUANG-Rhys factor S progressively increase in the order of halide-oxide-fluoride, and the values of S for the various hosts in the same group are close.

The CDW-SDW transition in the half-filled extended Hubbard model is investigated with the broken-symmetry Hartree theory formulated in terms of the Bogoliubov variational approach. The finite temperature phase-diagram in the weak coupling regime is derived analytically with a model density of states. The results show that there exist charge-order and antiferromagnetic order, but no mixed phase exists at any temperatures.

Considering the coupling of the atomic tunneling states with the vibration modes of its nearby atoms, two different kinds of double-well potentials are obtained. At the meantime, the vibration of nearby atoms are softened, and under certain conditions a new double-wel1,potential of higher rank can be induced which makes a hierarchical double-well potential structure possible.

Based on the extended Skyrme force SKa and GS2, the Hartree-Fock and selfconsistent semiclassical calculations are carried out to investigate the static properties of ²⁰⁸Pb. The present results are compared with each other and with the experiments. A good agreement is obtained between two theoretical approaches and between theories and experiments.

A new method-the operator expansion method is used in neutrinoless double beta decay processes. Both the neutrino mass and mixing of right-handed leptonic current are included. It is shown that for nuclear neutrinoless double beta decay in 2n mechanism, there appear some new terms besides the terms given by the conventional treatment based on closure approximation. The ββ with a Majoron emission is also discussed.

In this paper, by using the collective coordinate of A. Bohr and phenomenological deformed optical potential and Coulomb interaction, the scattering amplitude of two composite particle systems can be obtained. The differential cross sections for the 0⁺, 2⁺, 4⁺ and 6⁺, p(0.8 GeV)+¹⁵⁴Sm and p (0.8 Gev)+¹⁷⁶Yb are calculated. The results show that the Coulomb effect is quite important.

The effective Hamiltonian for nonleptonic decays of strange, charm and beauty, involving the QCD corrections at short distances but with possible t-quark mass m_t > mw and a correction of the initial value for the renormalization group equations, is computed in the framework of the operator product expansion (OPE). The numerical results show that our calculation gives corrections in right direction for approaching to the Δ1=1/2 rule and if using the latest experimental measurements on δ and ε'/ε for system as input, the KM parameter ε₂² would be constrained in a reasonable region (2.5～22.5)×10^-3.

By calculating the Dirac matrices in four dimensions and performing the dimensional regularization for loop momentum integration variables, various Ward identities can be obtained straightforwardly and the puzzle for extending γ5 to n dimensions can be solved.

Casimir effect of scalar field on R⁴×S_n-1 manifolds is evaluated. The results show that compactness of manifolds S₁ and S₂ can be held by Casimir force. However, other compact spaces (S_n-1, n > 3 ) are unstable.

In this paper, the completeness relations of the fundamental representations in quantum mechanics, together with the "integration within orderd product" technique are exploited to derive normally ordered and antinormally ordered expansions of some exponential operators in Hilbert space. Applications of the normally ordered exponential operators to evaluating Feynman matrix element in coherent state representation are given, which seems to be a new approach.

Our analyais^[1] has shown that there exist sensitive and insensitive regions to determine the spin (J = 2 or 4) of ξ(2230) in the general helicity formalism. Whereaa it just falls into the insensitive region by using current data of ξ. If the number of events is not sufficient it is difficult to determine the spin of ξ^[2]. In this paper we generalize the moment analysis^[3]. We define the photon angular distribution H_J(θ_τ, LM) for the moment of process e⁺ +R^- → J/ψ → τ + ξ, ξ → p + p and the weighted moment by choosing appropriate weight function. They provide an effective criterion to determine the spin of ξ. We also use the method to discuss LIE puzzle for process e⁺ + e^- → J/ψ → τ + B₁ B → P₁ + P₂ + P₃.

The Chou-Yang model has been used to explain, in the diffraction peak region, the differential cross section and the slope parameter for the pion-deuteron and the pionhelium elastic scattering at high energies.

Balance equations are established for steady-state nonlinear electronic transport in the presence of an electric field both for a single quasi 1D-heterostructure and for a multi-quantum-wire superlattice. The carrier-impurity scatterings and carrierphonon scatterings have been taken into account. The general equations for determining the resistivities are obtained and the Ohmic mobility formula are given. The density-density correlation functions for the wire structures are also studied in some detail.

The analogue between monopole-fermion interaction in the spontaneously broken gauge theory and phonon-electron interaction in the theory of superconductivity is studied. It is shown that both monopole-fermion interaction and phonon-electron interaction are characterized by the existence of the off-diagonal long-range order. Starting from the analogue between monopole-fermion interaction and phononelectron interaction the possible relevance of condensed solitons to superconductivity is also discussed.

The standard variational-cumulant expansion (VC) combined with a scheme for the enumeration of connected diagrams is employed to study the simple Ising model with the second-order phase transition. This model is evaluated to the 5th order approximations. A comparison with the 2-dimensional exact results shows that thermodynamic quantities converge rather slowly to the exact values in the intermediate region. A strict analytical calculation of the critical temperature with the 5th order approxinlation both for J_i and cumulant expansion suggests that VC chn achieve rather high standard accuracy if the variational parameters J_i could be determined up to higher degrees of corrections rather than the first one. Anomalies are found for U, C and M at extremely low temperature. A detailed study of M implies that thermodynamic formulae should be carefully chosen in VC approach so as to avoid these anomalies.

The pre-equilibrium exciton model of the gamma emission is considered in its lowenergy limit. The basic ingredients of the picture are essentially the same as at more advanced energies; however, a straightforward reduction of the equations to simple formulae, what was the case of higher energies, does not take place here. The influence of the Pauli blocking principle is more significant for the low energies than for the standard energies. Anyway, the manifestation of the pre-equilibrium character in the calculated spectra is highly masked by the equilibrium component, so that one cannot clearly distinguish among the models used.

Based on the concep, t of the formation time, the contribution of secondary collisions to the change of the K⁺/π⁺ ratio in ultra-relativistic heavy ion collisions is calculated. The result shows that the effect of secondary collisions in the target nucleus is not enough to explain the observed change of the K⁺/π⁺ ratio.

A definite integral expression of the SU(3) one-link partition function invariant group integral in the weak coupling regions of lattice gauge theories is obtained by the steepest descent meth.od. The integral can be numerically evaluated easily. This method can be extended to evaluation of some related SU(3) group integrals in the lattice gauge theories.

Phase structure of the 3-d lattice Z₄ gauge-Z₂ Higgs theory is investigated by the Monte Carlo simulation. We find a new phase, named Higgs Ⅱ phaae, when λ (scalar self-coupling constant) is small. It is a result of the radial excitation of Higgs field.

By using the technique of determinant calculation, explicit N-soliton solutions of the Korteweg-de Vries equation and the nonlihear Schrödinger equation are obtained for arbitrary N in terms of the inverse scattering method. Therefore, the relations of the inverse scattering method with the direct method of Hirota become easy to be understood.

A double-chain mean-field renormalization group approach for the Ising model is formulated. With the approach, transition temperatures and critical exponents for several numbers of nearest-neighbor chains are obtained.

A model for the high-T_c Copper Oxides is studied. The, localized nature of Cu 3d electrons is described as the RVB quantum spin liquid and the doped O 2p holes are described with an itinerant band. Our analysis shows that the virtual exchange of two spinons induces a pairing interaction between two holes.

It is shown that the wave functions of a contract-reexpanding universe may be constructed in two different ways corresponding to different boundary conditions in superspace and both may offer satisfactory inflationary scenario.

A particle with position-dependent mass moving in a double well potential is investigated. An exact instanton solution is given and tunnelling effect caused by it is considered. We calculate the energy of the ground state of this model by introducing some effective mass and frequency of oscillator.

The algebras of meromorphic vector fields and the bases of meromorphic λ-differentials with multipoles are constructed explicitly on general genus Riemann surfaces. For Riemann sphere the central extension of the algebra is also given.