Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

Summary The thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant K_o which can be derived from solubility data. At 25°C, this constant amounts to 80 cm³/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.     

Convexlike and concavelike conditions in alternative,minimax, and minimization theorems

Convexlike and concavelike conditions are of interest for extensions of the Von Neumann minimax theorem. Since the beginning of the 80's, these conditions also play a certain role in deriving generalized alternative theorems of the Gordan, Motzkin, and Farkas type and Lagrange multiplier results for constrained minimization problems.In this paper, we study various known convexlike conditions for vector-valued functions on a set and investigate convexlike and concavelike conditions for real-valued functions on a product setC×D, where we are mainly interested in the relationships between these conditions. At the end of the paper, we point out several conclusions from our results for the above-mentioned mathematical fields.The author is indebted to Dr. R. Reemtsen and Dr. V. Jeyakumar for their helpful comments during the preparations of this paper.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

高频聚焦超声声场和温度场的仿真研究*

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

Phase Transitions Induced by Top-Priority of Randomization

We study the characteristics of phase transition to take the top-priority of randomization in the rules of NaSch model (i.e.noise-first model) into account via computing the relaxation time and the order parameter.The scaling exponents of the relaxation time and the scaling relation of order parameter,respectively,axe obtained.     

高效液相色谱法和硫氰酸钾滴定法检测煤中氯的比较研究

比较了测定煤中氯的高效液相色谱(HPLC)法和硫氰酸钾滴定法。以密闭氧弹燃烧或艾氏卡剂熔融分解样品，分别以高效液相色谱法和硫氰酸钾滴定法测定煤中氯，通过对国家标准物质GBW11118、GBW11119、GBW11120分析结果的比较及t检验，表明两方法无显著性差异。     

Functional neuroimaging of inner fields-of-view with 2D-selective RF excitations

Echo-planar imaging is widely used in functional neuroimaging but suffers from its pronounced sensitivity to field inhomogeneities that cause geometric distortions and image blurring which both limit the effective in-plane resolution achievable. In this work, it is shown how inner-field-of-view techniques based on 2D-selective RF excitations (2DRF) can be applied to reduce the field-of-view in the phase-encoding direction without aliasing and increase the in-plane resolution accordingly. Free-induction-decay (FID) EPI and echo-train-shifted (T2*-weighted) and standard (T2-weighted) spin-echo (SE) EPI with in-plane resolutions of up to 0.5×1.0 mm² (slice thickness 5 mm) were acquired at 3 T. Unwanted signal contributions of 2DRF side excitations were shifted out of the object (FID-EPI) or of the refocusing plane by tilting the excitation plane (SE-EPI). Brain activation in healthy volunteers was investigated with checkerboard and finger-tapping block-design paradigms. Brain activation could be detected with all sequences and contrasts, most reliably with FID-EPI due to its higher signal amplitude and the longer 2DRF excitation that are more sensitive to magnetic field inhomogeneities. In conclusion, inner-FOV EPI based on 2DRF excitations could help to improve the spatial resolution of fMRI of focal target regions, e.g. for applications in the spinal cord.     

无穷积分余项与其被积函数比值的收敛阶

对一类函数的无穷积分余项与该函数的比值得到当x趋于无穷大时的收敛阶,这类函数是幂函数与指数函数的乘积函数,并将其应用到Mittag-Leffler函数.同时考虑了对应的级数情形.     

Effects of laser irradiation on optical properties of a-Se100−x Te x thin films

The effect of laser irradiation on the optical properties of thermally evaporated Se_100?x Te _x (x=8, 12, 16) chalcogenide thin films has been studied. The result shows that the irradiation causes a shift in the optical gap. The results have been analyzed on the basis of laser irradiation-induced defects in the film. The width of the tail of localized state in the band gap has been evaluated using the Urbach edge method. As the irradiation time increases, the values of the optical energy gap for all compositions decrease, while tail energy width increases. It is also observed that the optical energy gap decreases with increasing Te content in the alloy. These changes are a consequence of an increment in disorder produced by laser irradiation in the amorphous structure of thin film.