Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

镍-酸性铬兰K络合物吸附波

用微分脉冲溶出伏安法研究了镍(11)与酸性铬兰K(ACBK)所生成的络合物在悬汞电极上的电化学特性及电化学反应机理，发现电极反应为镍与酸性铬兰K所生成的络合物吸附在电极表面后发生的不可逆还原。在HCl-硼砂介质中(pH8．67)，络合物在-316mV处有一吸附还原峰，其峰电流与镍浓度在0．001～0．010μ/mL范围内呈现良好的线性关系，其最低检出浓度为0．0005μg／mL。     

稀薄气体二维外部柱体绕流特性研究

本文采用直接模拟蒙特卡罗方法对稀薄气体二维外部柱体绕流问题进行了数值模拟。结果表明:外部绕流问题,在特定情况下会产生激波,激波的产生,不仅与气体的稀薄程度有关,还与来流马赫数有关。而气流与壁面之间的换热,随来流马赫数增加而增加,随气体稀薄程度增加而减小。     

Finite-Dimensional Approximations for Scattering Theory Operators in the Wave-Packet Representation

We consider some types of packet discretization for continuous spectra in quantum scattering problems. As we previously showed, this discretization leads to a convenient finite-dimensional (i.e., matrix) approximation for integral operators in the scattering theory and allows reducing the solution of singular integral equations connected with the scattering theory to some suitable purely algebraic equations on an analytic basis. All singularities are explicitly singled out. Our primary emphasis is on realizing the method practically.     

Laser spectroscopic investigation of a new precursor-type polyparaphenylenevinylene

Optical, structural and morphological properties of thin films of polyparaphenylenevinylene (PPV) formed by an alkyl sulfinyl precursor route have been studied. Thin films were fabricated on an optical glass and on quartz glass either by spin-coating of the precursor solution or by layer-by-layer deposition using Langmuir–Blodgett technique. PPV precursor films were also spin-coated on gold-coated glass in order to study thin-film optical parameters by surface plasmon spectroscopy. We have been successful in forming about 40 precursor mono layers on quartz glass by Langmuir–Blodgett technique using optimized surface pressure and dipping conditions. After thermal conversion of the precursor layers good quality fluorescent PPV films of yellow colour have been obtained. Optical characterization of the films was carried out by linear absorption and emission spectroscopy, ellipsometry, and surface plasmon spectroscopy. Structural and morphological studies on the thin films were carried out by using X-ray scattering and atomic force microscopy. Wave-guided travelling-wave laser action has been achieved in a PPV film on quartz glass. The sample was transversally pumped with picosecond laser pulses (wavelength 347.15 nm, duration 35 ps). Laser emission occurred at 550 nm for pump pulse energy densities above .     

An optical fibre pH sensor based on dye doped mesostructured silica

This paper describes the synthesis and optical pH sensing properties of a pH indicator dye activated mesostructured silica coated optical fibre. The pH-sensitive dye bromothymol blue was incorporated into the mesostructure sol precursor and thin films/coatings were used for pH-sensing applications without prior removal of the surfactant. The pH sensitivity range and operating wavelength were analysed by absorption measurements on layer dip-coated on glass slides. The pH sensing properties of coated optical fibre were tested by evanescent wave method. Experiments were carried out by using a series of solutions of known pH. No leaching was observed (except at very high pH) and an excellent reversibility was obtained between pH=2 and 5.     

双光束相干控制产生多次谐波的实验验证

利用两束相干度可改变的飞秒脉冲光对产生的五次谐波的强度特性进行了研究，发现谐波信号的强度随相干程度的增大而增加，谐波信号的最大值相对于相干零点(双光束相干度最大处)是非对称的，从而证明了合成的激光脉冲波形变化对谐波信号的影响.同时对谐波的受激放大理论进行了初步的实验探索和展望. 关键词： 五次谐波 波形变化 相干 受激放大     

A Note on Cactus Trees: Variational vs. Recursive Approach

In this article we deal with the variational approach to cactus trees (Husimi trees) and the more common recursive approach, that are in principle equivalent for finite systems. We discuss in detail the conditions under which the two methods are equivalent also in the analysis of infinite (self-similar) cactus trees, usually investigated to the purpose of approximating ordinary lattice systems. Such issue is hardly ever considered in the literature. We show (on significant test models) that the phase diagram and the thermodynamic quantities computed by the variational method, when they deviates from the exact bulk properties of the cactus system, generally provide a better approximation to the behavior of a corresponding ordinary system. Generalizing a property proved by Kikuchi, we also show that the numerical algorithm usually employed to perform the free energy minimization in the variational approach is always convergent.     

利用模式的对称性研究光子晶体光纤的色散

由光子晶体光纤的对称性可以得到模式分布的对称性，根据模式的对称性选择适当的展开函数，可以使计算量大大减少。计算了六角结构光子晶体光纤的色散特性，得到了波长在1．55pm处色散为零时，光子晶体光纤的结构参量所满足的方程。     

The Study of MMW and MW Attenuation Considering Multiple Scattering Effect in Sand and Dust Storms at Slant Paths

The influence of sand and dust storms on modern MMW and satellite communication systems reliability have been paid more attention to. The attenuations induced by sand and dust storms are estimated by means of Mie-theory and Rayleigh approximation, in the case of the tenuous distribution of particles. With the particle density increasing, however, these method become inadequate, the multiple scattering effects then become dominant for attenuation estimation. The attenuations considering multiple scattering effects are estimated by Monte-Carlo and four fluxes method at horizontal paths. At slant paths, based on multi-layer media model, the attenuations considering multiple scattering effects are calculated by layered Monte-Carlo method at 100, 37, 24, and 14GHz. It is shown that the multiple scattering effects should be considered at the attenuation prediction in the sand and dust storm, which the visibility is about 0.5km and smaller than 0.5km and frequency is about 20GHz. Above 30GHz, the multiple scattering effects due to sand and dust particles should be considered, as visibility is about 1km and smaller than 1km at slant paths.