COMPLETENESS OF THE JOST SOLUTIONS IN THE CASE OF THE NLS+ EQUATION WITH NONVANISHING BOUNDARY CONDITION

In the case of the NLS⁺ equation with nonvanishing boundary condition, a complete set of the Jost solutions is chosen, and its completeness is shown by means of the Marchenko inverse scattering equation.     

NLS+方程的平方Jost解的完备性

对于NLS⁺方程相应的平方Jost函数的完备性,通过求得的广义Marchenko方程给出了证明,从而建立了含修正项的直接微扰理论． 关键词：     

GENERAL SOLITON SOLUTIONS OF THE NLS+ EQUATION UNDER NON-VANISHING BOUNDARY CONDITION

For the NLS⁺ equation under nonvanishing boundary condition, to avoid complexity due to Riemann surface, required for double-valued function of the usual spectral parameter, starting from a particular auxiliary spectral parameter, a special inverse scattering method is systematically developed, and explicit expressions of the general multi-soliton solutions are successfully obtained. Asymptotic behaviors of the muiti-soliton solutions, additional displacement of center and additional phase shift of the peak are derived. When the boundary value approaches zero, all the formulas become the known ones naturally.     

FOCUSING mKdV BREATHER SOLUTIONS WITH NONVANISHING BOUNDARY CONDITION BY THE INVERSE SCATTERING METHOD

Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain an explicit breather solution with nonzero vacuum parameter b of the focusing modified Korteweg–de Vries (mKdV) equation. Moreover, taking the limiting case of zero frequency, we obtain a generalization of the double pole solution introduced by M. Wadati et al.     

GENERAL SOLITON SOLUTIONS OF THE NLS+ EQUATION UNDER NON-VANISHING BOUNDARY CONDITION

For the NLS⁺ equation under nonvanishing boundary condition, to avoid complexity due to Riemann surface, required for double-valued function of the usual spectral parameter, starting from a particular auxiliary spectral parameter, a special inverse scattering method is systematically developed, and explicit expressions of the general multi-soliton solutions are successfully obtained. Asymptotic behaviors of the muiti-soliton solutions, additional displacement of center and additional phase shift of the peak are derived. When the boundary value approaches zero, all the formulas become the known ones naturally.     

氢、氘和氚离子在固体表面上的反射

本文应用最近发展的离子输运双群模型计算了氢,氘和氚离子在固体表面的反射系数。与有关的实验资料和Monte-Carlo计算比较表明,双群模型所取得的结果是合理的、可用的。同时也表明了双群模型有可能成为研究离子在固体表面反射的有效的理论方法。 关键词：     

Burgers方程初边值条件的控制

为将优化控制技巧用于复杂的地球物理环流模型及其它领域,以Burgers方程为模型,描述了初边值条件的优化控制.在一般化的意义上,给出了连续问题及其相应的离散形式.引入伴随变量,并由此导出伴随方程.比较初始控制中不同频率误差对优化控制的影响,分析了用有限观测数据作空间插值后的数据、方法的优化控制能力及效果,并进行了数值实验.     

电气石中离子对(Fe2+—Fe3+跃迁

本文在晶体场理论的基础上,采用Fe²⁺的自洽场解析近似3d轨道,考虑到电气石中b,c两位置的实际对称性(C_s,C₁),计算了属于3d⁶组态的Fe²⁺在该两位置的自旋允许能谱:用离子对跃迁的观点,从理论上探讨了前人尚未处理过的离子对的(Fe²⁺(g)-Fe³⁺)→(Fe²⁺(e)-Fe²⁺)跃迁;并对偏振依赖性很大的三条谱:9000cm^-1,13800cm^-1,15000cm^-1作了强度估计,较为满意地解释了电气石的近红外光谱。 关键词：     

THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS

Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.     

Sb5+和Sb3+在新的高温相形成中的作用

本文通过比较Sb⁵⁺和Sb³⁺样品的R-T曲线及X射线衍射谱,讨论了Sb⁵⁺和Sb³⁺在新的高温相中的作用。发现Sb³⁺替代Bi时形成了2223结构,而Sb⁵⁺替代Bi时却形成了一种新的高温相。 关键词：     

红宝石Cr3+:Al2O3的电子云延伸效应及压力对电子云延伸效应影响(英文)

本文以Cr³⁺自由离子的3d电子径向波函数为基础,对Cr³⁺:Al₂O₃中的电子云延伸效应进行了理论研究,引入了电子云延伸效应系数κ,得到了Cr³⁺:Al₂O₃中Cr³⁺离子的最优化3d电子径向波函数.并研究了压力对电子云延伸效应系数κ的影响.     

RADIAL SOLUTIONS OF THE DIRAC EQUATION IN A LEMAITRE METRIC

In this paper the radial solutions of the Dirac equation in a metric with spheroidal symmetry are given.It is shown that there exists no quantum bound states of Fermions about the Schwarzschild black hole.Some cases are discussed,one is a soliton wave of the temporal state,which provides a new insight for checking the existence of a black hole,the other is a solution of the stationary state which describes the accretion and vaporization of the black hole.     

变格距网格中平流和扩散方程的求解

根据非均匀网格中一阶和二阶中心差分的精度,讨论了线性平流方程和扩散方程的解。非均匀网格的主要影响有二:一是造成同一波长的谐波在各点的视在波长不同;二是与均匀网格相比,一阶中心差分产生附加的实部,二阶中心差分出现附加的虚部。这种空间差分的误差使平流方程的解成为一调幅移行波,而使扩散方程的解带有平流误差。克服的方法可在平流方程中附加一人工粘性项,在扩散方程中附加一平流项。     

等离子体噻吩聚合膜的研究及I+注入的掺杂效应

以噻吩为单体,在等离子体环境中聚合成致密的有机膜。利用Rutherford背散射(RB2S)和质子弹性反冲(ERD)、傅里叶红外谱(FTIR)测定了膜的成分和结构;从近红外-可见-紫外光的反射和透射谱,运用传递矩阵方法研究了膜的光学性质;此外,还探讨了24keV的I⁺离子束的注入对等离子体噻吩聚合膜的掺杂效应。结果表明,注入层内电荷载流子的输运机理可用Mott的可变自由程跳跃(VRH)理论给以解释。 关键词：     

Ne+离子与Li原子碰撞过程中激发态的研究

本文通过观测Ne⁺离子与Li原子碰撞中的发射谱,对碰撞中的电子俘获和靶激发过程进行了研究。在可见光范围给出了所观察到的各条谱线的发射截面及相应上能级的激发截面。对电子俘获过程与能量亏损和靶原了电离势的关系进行了讨论。Ne⁺离子能量范围为20—150keV 关键词：     

H1+,H2+,H3+和He,Ne,Ar碰撞过程中的巴耳末系Hα,Hβ,Hγ发射

实验利用TN-1710光学多道分析系统(OMA),对H₁⁺,H₂⁺,H₃⁺和He,Ne,Ar碰撞过程中产生的巴耳末系H_α,H_β,H_γ发射进行了测量,入射离子H₁⁺,H₂⁺,H₃⁺的 关键词：     

Co2+-Ti4+和Cu2+-Nb5+离子取代BaFe12O19单晶体中Fe3+离子的研究

本文对用Co²⁺-Ti⁴⁺和Cu²⁺-Nb⁵⁺离子取代BaFe₁₂O₁₉单晶体中Fe³⁺离子进行了研究,以Bi₂O₃作为助熔剂生长出了BaFe_12-2xCo_x²⁺Ti_x⁴⁺O₁₉(x=0;0.04;0.09;0.13;0.27和0.68)以及BaFe_12-x[Nb_1/3⁵⁺Cu_2/3²⁺]_xO₁₉(x=0;0.28;0.44和0.60)这两系列的单晶体,测定了100—300K温度范围内样品的磁化强度σ与单轴各向异性常数K₁,我们发现,对Co²⁺-Ti⁴⁺取代的样品,当x≤0.09时,其σ与K₁随x的增加而缓慢增加;当x>0.09时,其σ与K₁随x的增加而迅速降低,至x=1.1时,K₁变为零,对Nb⁵⁺-Cu²⁺取代的样品,其σ值在整个成份范围内基本保持不变,且有缓慢增加趋势;而K₁值则随x增加而单调下降,提出了取代离子在M型六角铁氧体中可能的分布模型来解释我们的结果。 关键词：     

场流关系和π+→e++ν+γ的衰变过程

本文应用由复合场场论或场代数导出的轴矢流的场流恒等式计算了π介子的辐射衰变π⁺→e⁺+ν+γ过程。计算结果与目前的实验大致相合。     

2.5MeV的He+离子辐照316L不锈钢中氦泡的形核与生长研究

利用透射电子显微镜分析了0.3—0.5T_m温区（T_m为材料溶点）316L奥氏体不锈钢经高剂量氦离子辐照后辐照损伤峰区氦泡的形成行为.实验结果支持氦泡的双原子形核模型，并证实氦泡的形成主要受制于自间隙子/氦置换机制扩散.材料中高密度位错的存在显著增强氦泡形核并抑制氦泡生长.与前人低剂量辐照实验结果的比较表明0.3—0.5T_m温区氦泡形核机制不随辐照剂量或剂量率发生显著变化． 关键词：