Positive solutions of nonlinear beam equations with time and space singularities

We consider the existence and multiplicity of positive solutions to a nonlinear fourth-order two-point boundary value problem. The nonlinear term may be singular with respect to both the time and space variables. In mechanics, the problem describes the deformation of an elastic beam fixed at the left and supported at the right by sliding clamps. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, several local existence theorems are obtained.     

EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role.     

System size dependence in backward relativistic hadron production in pA and AA collisions

Abstract： In this comprehensive study the multiplicity characteristics of the backward emitted relativistic hadron （shower particle） through hadron-nucleus and nucleus-nucleus are overviewed in three dimensions. These dimensions are the projectile size, target size, and energy. To confirm the universality in this production system, wide ranges of system size and energy （Elab～2.1 A up to 200 A GeV） are used. The multiplicity characteristics of this hadron imply a limiting behavior with respect to the projectile size and energy. The target size is the main effective parameter in this production system. The exponential decay shapes is a characteristic feature of the backward shower particle multiplicity distributions. The decay constant changes with the target size to be nearly 2.02, 1.41, and 1.12 for the interactions with CNO, Era, and AgBr nuclei, respectively, irrespective of the projectile size and energy. While the backward production probability and average multiplicity are constants at different projectile sizes and energies, they can be correlated with the target size in power law relations.     

重核存活几率的N/Z效应

用Langevin方程计算了重核 194Pb, 200Pb和206Pb的蒸发残余形成几率。结果表明系统中质比(N/Z）影响了该几率大小,并且高的N/Z增加了重核存活几率。这是由于裂变位垒和鞍点前粒子发射依赖于系统N/Z的缘故。     

CoAlN(N=2-11)团簇基态结构的稳定性和磁性

采用密度泛函理论中的广义梯度近似(GGA),对CoAlN(N=2-11)团簇进行构型优化和磁性计算.在考虑自旋多重度的情况下得到了团簇的平衡构型及基态结构,并重点讨论了Co原子的sp-d杂化效应对体系稳定性和磁性的影响.结果表明:N为偶数时,团簇的基态为自旋双重态,Co原子磁矩随N增加整体上呈减小趋势;N为奇数时(除N=5为自旋三重态外),团簇的基态为自旋单重态,Co原子磁矩为零.N≥8时,Co原子陷入主团簇内部,体系的对称性降低,稳定性增强;轨道杂化增强了体系的稳定性,但减小了双重态和三重态体系中Co原子的磁矩;N=3,8,10是团簇CoAlN(N=2.11)的幻数.     

Research on the prompt neutron multiplicity of fission fragments for 235U（n,f）

According to some experimental and evaluated data,the total excitation energy partitioning way between both of the fission fragments was given with a semi-empirical method. With the calculated energy partitioning way,the prompt neutron multiplicity as a function of fragment mass,（A） ,for neutron-induced fission of 235U at En=0.0253 eV,3 MeV,and 5 MeV was calculated. The results are checked with the total average prompt neutron multiplicities  and compared with the experimental and evaluated data.     

400 AMeV 12C诱发乳胶核反应重电离粒子前后关联研究

对400 AMeV 12C诱发乳胶核反应重电离粒子的前后关联进行了研究。重电离粒子来源于靶核碎片,分为灰径迹粒子和黑径迹粒子两种。实验结果很好地验证了核-核碰撞几何模型。灰径迹粒子的发射在前、后半球是各向异性的,而黑径迹粒子的发射基本是一致的。向前、向后发射的灰径迹粒子、黑径迹粒子平均多重数对重电离粒子数n_h呈线性依赖,黑径迹粒子、灰径迹粒子的向前发射随n_h的增加而增加的幅度分别大于其向后发射随n_h的增加而增加的幅度,但核内级联效应受靶核大小的影响,向后半球内发射的灰径迹粒子平均多重数随n_h的增加有饱和现象,这些多重数关联特性基本上可以利用基于碰撞几何的旁观体-反应体模型及级联蒸发模型来解释。The forward-backward multiplicity correlation of heavily ionized particles produced in 12C-emulsion interactions at 400 AMeV is investigated. The heavy ionized particles, come from the target fragments, are divided into grey track particle and black track particle. The experimental results can be well explained by the geometry model of the nucleus-nucleus collisions. The emission of grey track particles in forward and backward hemisphere is not isotropic, but the emission of black track particle is almost isotropic. The averaged multiplicity of grey track particles and black track particles in forward and backward hemisphere linearly depend on the number of heavily ionized particle n_h, the correlation strength in forward hemisphere is greater than that in backward hemisphere, but the dependence of grey track particle in backward hemisphere on the number of heavily ionized particle n_h shows the saturation because of the intranuclar cascade effect is influenced by target size. The characteristics of multiplicity correlations can be well explained by the participant-spectator model based on the colliding geometrical picture and the cascade evaporation model of high energy nucleus-nucleus collisions.     

曲率能对热力学驱动力的影响

为了研究曲率能对核裂变热力学驱动力（TDF）的影响,首先利用包含曲率能的截断版小液滴模型计算了200Pb和224Th的位垒和熵垒,对比液滴模型的计算结果表明:曲率能未改变224Th的位垒鞍点,却将200Pb的位垒鞍点向后推移。能级密度参数的形变关系越强则两系统的熵垒鞍点越靠近基态。为了进一步探究曲率能如何通过位势和熵势影响TDF,以断前中子多重性（PNM）为探针,通过两种方案进行了模拟,结果表明:曲率能降低了两系统的位势驱动力,而增强了其熵势驱动力。结合PNM的计算表明,前一种效应要比后一种效应明显,因此曲率能总体减弱了200Pb和224Th的TDF,进而延缓了两系统的核裂变进程。In order to study the effect of curvature energy on the thermodynamic driving force (TDF) of nuclear fission, the potential and entropy barrier of 200Pb and 224Th systems are calculated by using the truncated droplet model including curvature energy, respectively. Compared with the liquid drop model, the results show that curvature energy does not affect the saddle point of 224Th, but pushes the saddle point of 200Pb backwards the ground state. The stronger the deformation dependence of the level density parameter is, the closer the saddle point of entropy barrier for these systems is to the ground state. In order to further investigate how curvature energy affects TDF through nuclear potential and entropy, respectively, the prescission neutron multiplicity (PNM) is selected as the probe, some simulations based on two schemes are carried out. The results show that curvature energy reduces the potential driving force of 200Pb and 224Th, and enhances the entropy potential driving force. Combined with the calculations and analyses of PNM, the former effect is more obvious than the latter, so curvature energy weakens TDF of two systems on whole, thus delaying the nuclear fission process of two systems.     

人口算子的谱性质

本文讨论人口算子的谱性质,得到了人口算子本征值除可能有限个外均是代数单的,人口算子本征值新的分布性质,人口算子广义本征函数不构成基序列,Ｌ２［０,ｒ２］上的人口算子根子空间完整等．     

Initial Value Problem for General Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity

The authors consider the global existence and the blow-up phenomenon of classical solutions with small amplitude to the Cauchy problem for general quasilinear hyperbolic systems with characteristics with constant multiplicity and given some applications.