The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space

LetE andF be Hilbert spaces with unit spheresS ₁(E) andS ₁(F). Suppose thatV ₀ S₁(E) →S ₁(F) is a Lipschitz mapping with Lipschitz constantk=1 such that −V ₀[S ₁(E)] ⊂V ₀[S ₁(E)]. Then V₀ can be extended to a real linear isometric mappingV fromE intoF. In particular, every isometric mapping fromS ₁(E) ontoS ₁(F) can be extended to a real linear isometric mapping fromE ontoF.     

MPT－X磁偏滤器位形的数值计算

ＭＰＴ－Ｘ是带４个内导体坏的托卡马克装置。本文用差分法计算了ＭＰＴ－Ｘ磁偏滤器的平衡磁面位形。结果表明，迭加上各种强度的八极场都能形成磁偏滤器位形，形成电流的放电中心区域随八极场的增加而收缩。还模拟了从多极器运行模式向托卡马克的过渡。     

On strictly separating vectors and reflexivity

It is shown that the set of strongly disjoint pairs of strictly separating vectors for an operator space is open, and an operator subspace having a strongly disjoint pair of strictly separating vectors is reflexive. Some applications are discussed.     

与两个更新过程有关的某些联合分布

本文讨论的两个时偶问题涉及来一个泊松过程与一个更新过程穿越时间和更新数的联合分布．利用向量马氏过程方法得到了这些联合分布的变换，给出了一个与分布均值有关量的数值结果．     

Three-dimensional ab initio dipole moment surfaces and stretching vibrational band intensities of the XH3 molecules

Stretching vibrational band intensities of XH₃ (X=N, Sb) molecules are investigated employing three-dimensional dipole moment surfaces combined with the local mode Hamiltonian model.The dipole moment surfaces of NH₃ and SbH₃ are calculated with the density functional theory and at the correlated MP2 level,respectively. The calculated band intensities are in good agreement with the available experimental data. The contribution to the band intensities from the different terms in the polynomial expansion of the dipole moments of four group V hydrides (NH₃, PH₃,AsH₃ and SbH₃) are discussed. It is concluded that the breakdown of the bond dipole approximation must be considered. The intensity “borrowing” effect due to the wave function mixing among the stretching vibrational states is found to be less significant for the molecules that reach the local mode limit.     

甲醇在纳米TiO2作用下进行光催化氧化反应的机理研究

以纳米TiO2 为催化剂 ,以主波长为 36 4nm的汞灯为光源 ,用气相色谱法分别考察了 0 .1mol/L的甲醇、甲醛和甲酸水溶液进行光催化氧化反应的动力学规律 .Langmuir Hinshelwood方程进行核算结果证明 ,该组反应均为零级反应 .用TEM、XRD、SSA和XPS对催化剂进行表征 .根据XPS的检测结果提出了甲醇光催化氧化的反应机理 .TiO2 光激发活化时间约为 30～ 6 0min ,生成物及剩余反应物浓度随时间变化的曲线表明 ,该反应速率为HCH2 OH 相似文献   

类氦离子的KLL双电子复合过程的相对论理论研究

在相对论多组态Dirac-Fock理论基础上，发展了计算双电子复合截面的程序.并以类锂C³⁺，Ar¹⁵⁺，Kr³³⁺和U⁸⁹⁺等离子为例，详细计算了共振双激发态1s2l2l′的辐射衰变率、Auger衰变率及相应的双电子复合截面.对于C⁴⁺，Ar^l6+和Kr³⁴⁺离子的结果与已有的计算和实验结果都能很好地符合；对于U⁹⁰⁺离子，则重点 关键词： 双电子复合 截面 MCDF     

Generalized G-KKM Theorems in Generalized Convex Spaces and Their Applications

Some new generalized G-KKM and generalized S-KKM theorems are proved under the noncompact setting of generalized convex spaces. As applications, some new minimax inequalities, saddle point theorems, a coincidence theorem, and a fixed point theorem are given in generalized convex spaces. These theorems improve and generalize many important known results in recent literature.     

啁啾激光场中HF分子的经典解离

应用经典理论并采用辛算法，计算了HF分子在啁啾激光作用下的经典解离.讨论了激光场中HF分子的解离概率随时间的变化以及考虑振动-转动能级跃迁对分子解离概率的影响.计算结果与理论分析相符，说明运用经典理论并采用辛格式计算双原子分子在激光作用下的经典解离是有效和可行的. 关键词： 啁啾激光场 经典解离 辛算法     

Echolocation click sounds from wild inshore finless porpoise (Neophocaena phocaenoides sunameri) with comparisons to the sonar of riverine N. p. asiaeorientalis

Acoustic signals from wild Neophocaena phocaenoides sunameri were recorded in the waters off Liao-dong-wan Bay located in Bohai Sea, China. Signal analysis shows that N. p. sunameri produced "typical" phocoenid clicks. The peak frequencies f(p) of clicks ranged from 113 to 131 kHz with an average of 121+/-3.78 kHz (n=71). The 3 dB bandwidths delta f ranged from 10.9 to 25.0 kHz with an average of 17.5+/-3.30 kHz. The signal durations delta t ranged from 56 to 109 micros with an average 80+/-11.49 micros. The number of cycles N(c) ranged from 7 to 13 with an average of 9+/-1.48. With increasing peak frequency there was a faint tendency of decrease in bandwidth, which implies a nonconstant value of f(p)/delta f. On occasion there were some click trains with faint click energy presenting below 70 kHz, however, it was possibly introduced by interference effect from multiple pulses structures. The acoustic parameters of the clicks were compared between the investigated population and a riverine population of finless porpoise.