函数的H-导数和分形动力学

 给出了函数的Hausdorff测度与H-导数。从而，为开展自给的分形动力学提供了解析的数学工具。同时，给出了分形动力学的演化方程组并做了初步讨论与分析。     

从布朗运动的发现到RR方法

对朗之万方程研究的历史和现状进行了全面的综合评述。     

THE REGGE TRAJECTORY OF MESONS AND THE SU(4) MASS RELATIONS

A relativistic equation of motion of a two particle system under the constraints p_i²-m_i²-U(x²)=0.(i=1,2), where U(x²) is an infinite spherical square well poten-tial, is applied to the SU(4) quark model of mesons. A set of linear mass relations areobtained. Instead of the linear relation between J and M², the Regge trajectory ob-tained is a relation between p_nl² and M², where ζ_nlπ are zeros of the spherical Besselfunctions. The new trajectory seems more satisfactory than the former one.     

定义在分形集上函数的H-导数

 分形的生成含有降维与升维两种形式,采用适当的方式总可以对分形集加以定向化,分形的内禀测度是Hausdorff测度。因此,定义在分形集上的函数可以看作是在Hausdorff测度下定义在区间[0, h]。在函数图像也是分形的前提下,依函数的Hausdorff测度的定义,给出了定义在分形集上的函数f(p)关于Hausdorff测度p的导数以及一些性质。     

BROWNIAN MOTION MODEL OF THE FISSION PROCESS

Fission process is considered as a multidimensional Brownian motion. The Planck-Fokker equation is solved and the fission probability in the steady state approximationis calculated. The results is compared with the Bohr-Wheeler theory. Numerical cal-culations are performed for the fission of ²³⁶U and the results are discussed.     

THE DEPENDENCE OF OVERLAP INTEGRAL ON QUARK MASS IN BETHE-SALPETER THEORY

In the literature, the overlap integral of a transition (e.g. 1^-→0^-+γ) is usuallywritten asI = ∫d³xe^iσx/2φ_f^*(x')φ_i(x) Using Bethe-Salpeter equation with instantaneous approximation, we arrive at adifferent result which depends obviously on the mass of the quarks. Our result willapproximate the above expression only when the binding energy can be neglected.     

CHARGE DISTRIBUTION IN THE FISSION OF 232Th BY 14MeV NEUTRON

Independent yields of ⁸²Br, ⁹⁶Nb, ¹¹²Ag, ¹³⁰I,¹³²I, ¹³⁴I, ^134mCs, ^135mCs, ¹³⁶Cs and upper limitof independent yield for ¹⁴⁰La in the fission of ²³²Th induced by neutrons of 14 MeVwere determined with nuclear chemistry techniques. The correlation of the fractionalindependent yields in the high yield mass chains with a Gaussian curve of charge dis-tribution has been investigated using various mass formulae and charge distributionhypotheses. The results indicate that the hrpothesis of minimum potential energy witha shell-effected mass equation gives the best fit to the data. The width parameter Cof the charge distribution is found to be 0.80. The large deviations of ³²Br and ¹¹²Ag from the Gaussian curve seem to show that the low yield in very asymmetric fissioncan be attributed to a narrower width of charge distribution, whereas the high yield insymmetric fission may correlate with a wider width. The trends have been explainedqualitatively in terms of a liquid drop model. There is no evidence for 40-proton subshell effect on the fission yield.     

THE INFRARED STRUCTURE AND THE ELECTROMAGNETIC FORM FACTORS OF QUANTUM CHROMODYNAMICS IN TWO DIMENSIONS

We discuss a model of quantum chromodynamics in 1+1 dimension.Using't Hooft's 1/N expansion and considering the effects of the infrared structure in non-Abelian gauge theories by assuming that the coupling g²（t）～1/t^κ-1,the Straton's Pro-pagator and the Bethe-Salpeter equation of mesons are obtained;the propertiesof the meson wave functions and their characteristics are also discussed.From thebehaviour of the electromagnetic form factors and the deep inelastic scattering struc-ture functions obtained,it follows that κ≤2.     

THE SPECTRA OF THE NEW PARTICLES

Considering ψ (4030) as a semi stable bound state of D^*D* instead of exitedstate of J/ψ, the spectra of the J/ψ family can de described by the wave equation of har-monic oscillator with mass squared eigen values. The case is similar with that of the or-dinary mesons. The only difference is that the gap of energy level squared for J/ψfamily is as twice large as the ordinary hadrons. The similar conclusion is also valid tothe γ family with energy level gap 5.6 times larger than the ordinary hadrons. In edition, the mixing of S and D wave induced by tensor force is calculated and the energylevel of ψ(3770) with D wave dominance is obtained.     

ANGULAR DISTRIBUTIONS OF FISSION FRAGMENTS AND THE SHAPES OF THE SADDLE POINT OF COMPOUND NUCLEI

We have measured the angular distributions of fission fragments for a series of compound nuclei formed in the bombardment of ¹⁶⁹Tm, ¹⁷⁵Lu, ¹⁸¹Ta, ¹⁹⁷Au, ²⁰⁹Bi, ²³²Th and ²³⁸U by 78 MeV ¹²C ions and in the bombardment of natural lead by 96.6, 92.2, 88.1, 79.0 and 75.6 MeV ¹⁴N ions with mica track detectors. All the measured angular distributions can be fitted by the theoretical formula given by Halpern and Strutinski. The effective moments of inertia of the fissioning nuclei at the saddle point are derived from the angular distribution anisotropies. A comparison is made for the shapes of experimental saddle point with the theoretical predictions by the liquid drop model.     

DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS

Physical processes of the propagation of the solar cosmic rays in the interplanetary space include the diffusion in interplanetary disordered magnetic fields and the convection in solar winds. Dimensional method can be applied to solve those equations convertible into Bessel equation, the results obtained are identical with those solved by the commonly used separate variable method. In order to derive an analytic solution to the diffusion convection equation in an unbounded, uniform medium, two dimensionless parameters reflecting the diffusion and convection characteristics of the particles are introduced. In the diffusion dominated case, the solution is similar in form to the diffusion of a source moving with the convection velocity and is modified by another convection term, which can be expanded into a power series of the convection parameter with coefficients composed of the generalized hypergeometric function series of the diffusion parameter. This solution has a clear physical meaning, and can suitably be used in the discussion of the rise phase characteristics of the solar cosmic rays from medium to high energies （E_p≥10¹ MeV）.     

APPLICATION OF THE EIKONAL WAVE FUNCTION TO QUASIFREE SCATTERING

In this paper. we have used the Eikonal wave functionφ_E(r)=(2π)^-3/2 exp(ik.r)X(r)whereexp{-i/hv∫_-∞^zV(x,y,z,')dz'}and V=nk/m to investigate the quasifree scattering ⁶Li (p, pd)α with E_p=156 MeV,590MeV and 670 MeV. In V(x, y, z), the nuclear interaction and the Coulomb inte-raction are included. For the case of 156 MeV, the nuclear potential is taken to be the Woods-Saxon type.The result is shown in fig. 1. This result is compared with those obtained by themethod of partial waves. For the cases of 590MeV and 670MeV, a new method is used to describe thenuclear potential, and the results are showh in fig. 3 and fig. 4, respectively.     

THE SPECTROSCOPY OF FOUR-BARYON SYSTEM

In this paper, using SU(6) symmetry theory four-baryon system is discussed and a method of analyzing experimental spectra is provided. Because of the gound states of _ΛΛ⁴H, _ΛΛ⁴He_{, Λ}⁴He and ⁴He are in the same I. R. of SU(6), on can derives masses for _ΛΛ⁴H, _ΛΛ⁴He from the experimental data of _Λ⁴H, _Λ⁴He, and ⁴He. Calculation shows that these J^π=0⁺ double Λ hypernuclei _ΛΛ⁴H, _ΛΛ⁴He are not likely bound states.     

THE MEASUREMENT OF THE EXCITATION FUNCTIONS OF ISOTOPES OF Fr AND At,PRODUCED IN THE BOMBARDMENT OF 12C ON 209Bi

Excitation functions for Fr and At isotopes produced in ¹²C on ²⁰⁹Bi had been measured in the energy range 60—72 MeV. It was quite obvious that ²¹³Fr and ²¹⁴Fr were formed by the reactions ²⁰⁹Bi (¹²C,4n) ²¹⁷Ac and ²⁰⁹Bi (¹²C,3n) ²¹⁸Ac following the a decay of the Ac isotopes respectively, and ^214mFr was produced probably by compound nucleus evaporation of neutrons and an α particle, i.e. (¹²C, α 3n). ²¹¹At was mainly contributed by a multi-nucleon transfer reaction （e.g. ⁸Be transfer）. The experimental data for neutron evaporation reaction were fitted by the Jackson formula.     

Augmented Langevin approach to fluctuations in nonlinear irreversible processes

A Fokker-Planck equation derived from statistical mechanics by M. S. Green [J. Chem. Phys. 20:1281 (1952)] has been used by Grabertet al. [Phys. Rev. A 21:2136 (1980)] to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker-Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker-Planck equation as that of Grabertet al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker-Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.     

FURTHER DISCUSSION ON THE EQUATION AND ITS SOLUTIONS FOR THE BOUND STATES OF MESONS

We continue the investigation of the equation and its solutions for the bound states of mesons discussed previously, emphasizing on large values of v, a parameter characterizing the shape of the potential. The results show that the dependence of the eigenvalues λ and some related physical quantities upon the potential parameters v and E is approximately the same as in our previous work. But the average radii of the bound mesons cease increasing as v increases. For each value of v, there exists a maximum average radius√<R²>_max, and all these √<R²>_max are approximately equal to 12.6 M^-1 （M being the mass of the straton）, which is much smaller than the experimental value of the radius of the π meson. However, if we assume, in addition to the attractive potential, there exists, for the straton-anti-straton superstrong interactions, also a repulsive potential, and, in particular, if we introduce a differencetype potential V_D（r） corresponding to the potential V_v（r） in our previous work, the calculated radii of the bound mesons do approach the experimental value.     

ON THE PROBLEM OF MIXING OF NEUTRAL MESONS

After simplifying the two types of Morpurgo's quark-antiquark interaction poten-tial, in the framework of SU(4) the three neutral mesons of 0^-+, 1^--, 1^+-,2⁺⁺, whose charges, strangeness and isospins are all null, are mixed. The mass spectrum for the quark-antiquark consitituents of the mixing mesonsare calculated and compared with experiments.     

晶面结构非均匀性对金刚石晶形的影响

 不仅考虑表面能，同时也引入表面结构非均匀性自由焓G_stⁱ，通过热力学分析，解释了随着晶体的逐渐长大而{110}面常在金刚石的外形中消失的机理，并用逆推法计算了有关数值。     

THE POSSIBILITY OF EXITENCE OF NEW ISOTOPE 65Se

A new beta-delayed proton precussor ⁶⁵Se has was probably produced via the reaction ⁴⁰Ca (²⁸Si,3n)⁶⁵Se and identified from its beta-delayed proton emission.A single proton group at 3.75±0.05MeV with half-life of 10.8±4.1/3.7ms was observed,corresponding to superallowed beta decay of ⁶⁵Se to the isobaric analog state of ⁶⁵As (the lowest T=3/2 state in ⁶⁵As) then proton emitting to the ground state of ⁶⁴Ge.Because of poor statistics further experimental effort is required to confirm this discovery.     

凝聚炸药中超压爆轰的实验研究

 采用飞片碰撞技术，在TNT/RDX（40/60）炸药中获得了2.5倍于正常爆轰的最大超压值，得到了超压爆轰下爆轰产物物态方程p=Aρ^{k+A₁(p-p_J)}（p－爆压，单位GPa，ρ－密度，单位kg/m³，A=ρ_J/ρ^k_J，p_J=27.06 GPa，ρ_J=2.3×10³ kg/m³，k=2.77，A₁=2.7×10^-3 GPa^-1，下表J代表正常爆轰状态）。该方程还可以较好地描述超压爆轰产物的二次冲击状态。