Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

Analytic solutions of the susceptibility for Doppler-broadened two-level atoms

We derive the rigorous analytic solutions for the susceptibility of Doppler-broadened two-level atoms, valid for arbitrary laser intensities. As is usually the case with real atoms, we observe that, when the homogeneous linewidth is much narrower than the Doppler width, the real part of the susceptibility is given by the product of an imaginary error function and a Gaussian, whereas the imaginary part consists simply of a Gaussian function. By employing the analytic results, in particular, we study the effects of optical pumping and saturation on the atomic susceptibility. We also find that the real (imaginary) part of the susceptibility is weakly (strongly) dependent on such parameters as the laser intensity or the optical pumping rate. The availability of analytic solutions for the simple laser-atom interaction may provide convenient tools for its understanding as well as application to more general and realistic situations.     

LaF分子基态X~1Σ~ 分析势能函数计算

用原子分子反应静力学原理导出LaF分子可能的电子状态和离解极限。在相对论有效核芯势RECP(RelativisticEffectiveCorePotential)近似下 ,用密度泛函理论中的B3LYP方法优化了LaF分子单、三重态平衡几何结构 ,计算了基态X1Σ 的振动基频和离解能。在计算出来的一系列单点势能基础上 ,用非线性最小二乘方法拟合出基态Murrell Sorbie势能曲线 ,得到分析势能函数 ,由此计算出相应光谱常数ωe、Be、αe、ωeχe的理论值并和实验测量的振转光谱比较 ,结果非常吻合。另外还比较了用两种不同有效势得到的分析势能函数和光谱参数 ,以能量一致相对论有效势ECEP(EnergyCosistentRelativisticEffectivePotential)得到的结果最好。     

The weak and strong Gaussian probabilistic realization problem

A classification is given of all σ-algebras that make two given σ-algebras conditionally independent in the case that the σ-algebras are generated by finite dimensional Gaussian random variables. In addition a classification is given of all Gaussian measures that have the conditional independence property and such that restricted to a subspace, they coincide with a given measure.     

Closely packed dense frequency selective surface

In order to realize wideband filtering properties of frequency selective surface （FSS）, FSS of closely packed elements is presented. The Y loop elements are chosen as the graphics elements. Based on the spectral domain method, the frequency response is analyzed for different incident angles and polarizations. The result of the numerical analysis shows that the dense FSS has wide passband with better independence of angle and polarization.     

基于AHP权重和灰色服务器负载预测的云计算On-line迁移策略

为了克服云计算环境下由于实时用户任务的不确定性到来和服务器性能差异而导致的云计算环境的负载不均衡问题,提出了一种AHP权重获取和灰度算法预测服务器负载的云计算on-line虚拟机迁移策略。首先,设计了基于AHP和灰色服务器预测的虚拟机on-line迁移模型,提出了采用AHP获取虚拟机各资源需求权重,然后,采用灰色模型预测下一时刻的服务器负载,采用此权值向量与各无需迁移的服务器的空闲资源向量进行加权得到加权和,将具有最小加权和的物理服务器作为迁移的目标宿主机。最后,定义了基于AHP权重和灰色服务器负载预测的云计算on-line迁移算法。在CloudSim环境下进行实验,结果表明文中的迁移策略使得云计算在响应用户任务时,具有任务失败次数少、SLA违约率低和迁移成功率高的优点,同时与其它方法相比,具有负载均衡程度高的优点,具有较强的可行性。     

n × n 上三角算子矩阵的单值扩张性以及应用*

设X_i是无穷维复Banach空间, L(X_j,X_i)是X_j到X_i上的有界线性算子全体.考虑 n × n 上三角算子矩阵T=(T_ij)_1≤j≤n, 其中T_ij L(X_j,X_i),1≤j≤n; T_ij=0, i>j.本文研究了T的单值扩张性, 通过考察集合S(T)={λ∈C}: T在点λ没有SVEP},证明了S(T)在i=1 ? nS(T_i)中退化,进而给出等式S(T)=i=1 ? n S(T_i)成立的条件. 同时, 考察了T的单值扩张性扰动,得到了S(T)保持对角稳定时T_i所需的条件并予以证明, 同时举例说明这些条件的合理性.最后, 给出单值扩张性关于谱σ(T)和局部谱σT (x)的应用, 得到了谱扰动和局部谱扰动不变的新条件.     

Difference Independence of the Euler Gamma Function*

In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma function Г. More precisely,if P is a polynomial of n+1 variables in C[X,Y₀,…,Y_n-1] such that P(s,Г(s+a₀),…,Г(s+a_n-1))≡0 for some(a₀,…,a_n-1) ∈ Cⁿ and a_i-a_j ■ Z for any 0≤i相似文献   

Blood oxygenation monitoring using hyperspectral imaging after flap surgery

In this paper, we present a new method for the assessment of skin flap perfusion based on the non-invasive monitoring of skin blood oxygenation using hyperspectral imaging. This method consists of generation of oxyhemoglobin and deoxyhemoglobin maps in skin flap from hyperspectral image using an analytic model based on Beer–Lambert law. The results obtained on a fasciocutaneous sural flap have revealed that the oxyhemoglobin and deoxyhemoglobin maps facilitate the visualization of some differences between different areas of the flap, an aspect that clinical examination fails to do. In conclusion, the proposed method could provide a new option for a more accurate assessment of flap survival.     

BeF2分子基态势能函数研究

利用密度泛函理论（DFT）B3LYP/aug-cc-PVTZ方法对BeF和BeF2分子进行计算, BeF分子的基态电子态为X2Σ+,平衡核间距Re=0.1367 nm,BeF2分子最稳定构型为D∞h构型,基态电子态为X1Σg+,离解能De=13.4 eV。利用最小二乘法拟合了BeF分子基态的Murrell-Sorbie势能函数,并得到其光谱数据与力常数。结合全局多体项展式方法,导出了基态BeF2分子基态势能函数的解析表达式,该函数准确反映了BeF2分子的结构以及静态反应特征,这些结果为进一步探索BeF2的微观分子反应动力学提供了基础。