On the two methods of kinetic theory of ECRM

The kinetic theory based on the expansion of local field in the guiding center coordinate system, presented by paper[1]–[3], has successfully developed into a theoretical system. The mathematical background and physical explanation of setting up the guiding center coordinate system is expounded in the paper. By using the methods of the guiding center and waveguide coordinate systems respectively, the same dispersion equations for interaction of an axially symmetrical single momentum electron beam with TE_mn field in the circular waveguide are rigorously derived. A number of mistakes in paper[4] are indicated as well.     

Realization of a unique time evolution unitary operator in Klein Gordon theory

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL ²(R ³) and the Einstein’s relativistic equation in the spaceL ²(R ³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL ²(R ³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL ²(R ³).     

Bone-ablation mechanism using CO2 lasers of different pulse duration and wavelength

Bone ablation using different pulse parameters and four emission lines of 9.3, 9.6, 10.3, and 10.6 m of the CO₂ laser exhibits effects which are caused by the thermal properties and the absorption spectrum of bone material. The ablation mechanism was investigated with light- and electron-microscopy at short laser-pulse durations of 0.9 and 1.8 s and a long pulse of 250 s. It is shown that different processes are responsible for the ablation mechanism either using the short or the long pulse durations. In the case of short pulse durations it is shown that, although the mineral components are the main absorber for CO₂ radiation, water is the driving force for the ablation process. The destruction of material is based on explosive evaporation of water with an ablation energy of 1.3 kJ/cm³. Histological examination revealed a minimal zone of 10–15 m of thermally altered material at the bottom of the laser drilled hole. Within the investigated spectral range we found that the ablation threshold at 9.3 and 9.6 m is lower than at 10.3 and 10.6 m. In comparison the ablation with a long pulse duration is determined by two processes. On the one side, the heat lost by heat conduction leads to carbonization of a surface layer, and the absorption of the CO₂ radiation in this carbonized layer is the driving force of the ablation process. On the other side, it is shown that up to 60% of the pulse energy is absorbed in the ablation plume. Therefore, a long pulse duration results in an eight-times higher specific ablation energy of 10 kJ/cm³.     

解析对冲基金经理人的收费最大化问题

由于近年来对冲基金发展迅速,对冲基金经理人收费最大化问题也成为学者关注的焦点。文中将研究对冲基金经理人价值最大化的2篇文章作对比,其次考虑在只收取激励费和高水位线有增长率的情况下,分析对冲基金经理人的价值最大化问题。     

非保守动力学系统的Noether定理的一个证明

本文直接从动力学系统的Lagrange函数在无穷小变换下的变换性质出发,得到了完整非保守和非完整非保守的Noether定理。本文的方法具有优越性。     

一类多维的非线性Schrdinger方程组的初边值问题

本文考虑一类具有耗散与磁场效应的多维非线性Schrdinger型方程组的初边值问题。使用积分估计(包括L~p—L~q估计)证明了整体解的存在性。     

广义集值强非线性拟变分不等式

本文引入并研究一类新的广义集值强非线性拟变分不等式,讨论这类广义集值强非线性拟变分不等式解的存在性以及由算法所构造的迭代序列的收敛性.我们的结果改进和发展了Noor,Siddiqi和Ansari等人近期的一些主要结果.     

Bernoulli泛函空间中广义计数算子的表示

得到离散时间正规鞅平方可积泛函空间L^{\mathrm{2}}(M)中广义计数算子N_h的5种表示：（1）量子Bernoulli噪声（quantum Bernoulli noises,QBN）\{{?}_k,{?}_k^{\mathrm{*}};k\ge \mathrm{0}\}的加权表示;（2）N_h的谱表示,广义计数算子N_h以h-计数测度{\#}_h的值域为其点谱;（3）N_h的“对角化”表示,N_h可表示为L^{\mathrm{2}}(M)的标准正交基\{Z_{\sigma };\sigma \in \mathrm{\Gamma }\}所生成的一维对角化正交投影算子的加权极限;（4）广义Skorohod积分-广义随机梯度表示,N_h可表示为互共轭算子{\delta }_h和{?}_h的复合算子;（5）对\mathbf{N}上的任意非负函数h,可构造一列有界广义计数算子,N_h恰为该有界广义计数算子的强极限,当h可和时,N_h为该有界广义计数算子的一致极限。     

Spinor Green’s functions via spherical means on products of space forms

We explicitly compute the Green’s function of the spinor Klein–Gordon equation on the Riemannian and Lorentzian manifolds of the form _M0×?×_MN$M_0\times ?\times M_N$, with each factor being a space of constant sectional curvature. Our approach is based on an extension of the method of spherical means to the case of spinor fields and on the use of Riesz distributions.