在对称群Sm中解循环方程组

本文研究了在对称群S_m中解循环方程组:x_mX_(m+1)…x_(ω+k-1)σ_m,其中σ_m∈S_m,ω=1,2,…,s,确定了这个循环方程组有解的充分必要条件和解的个数,而且给出了求解过程。     

Fluorescence anisotropy of acridinedione dyes in glycerol: Prolate model of ellipsoid

Time-dependent reorientations of resorcinol-based acridinidione (ADR) dyes in glycerol were studied using steady-state and time-resolved fluorescence studies. The difference between fluorescence anisotropy decays recorded at 460 nm when exciting at 250 nm and those obtained when exciting at 394 nm are reported. When exciting at 394 nm, the fluorescence anisotropy decay is bi-exponential, while on exciting at 250 nm a mono-exponential fluorescence anisotropy decay is observed. We interpret this in terms of different directions of the absorption dipole at 394 and 250 nm with the emission dipole respectively, which is experimentally validated and further analysed as a prolate model of ellipsoid.     

关系模式关键字的一个求解算法

本文给出了关系数据库模式中求解关键字的一个算法。算法很简洁并且对于[1]定义的一大类问题,执行时间是多项式级的。     

Spectral and voltammetric studies on titanium substituted Keggin-type heteropolyanions

Bonding and redox properties of mono- and dititanium substituted 12-heteropolytungsto-phosphates and their complexes with bivalent Mn, Co, Ni and Cu are studied by UV-Vis, ESR and cyclicvoltammetric techniques. The heteropoly blue analogue [Ti^IIITi^IVW₁₀PO₄₀]⁸⁻ is unstable and its presence in solution is proved by optical and ESR spectroscopy. ESR results reveal that the odd electron is trapped on the titanium atom at 77 K. The optical electronegativity of Ti(III) in this heteropoly blue is estimated to be 2.4 from the intervalence charge transfer (IVCT) bands. X-ray powder diffraction results show that the complexes K₅M^II[Ti₂W₁₀PO₄₀].xH₂O(M^II = Cu or Mn) are isomorphous with K₇[Ti₂W₁₀PO₄₀].6H₂O. Electronic spectroscopy indicates very high symmetry around the bivalent metal ion M in the K₅M^II[Ti₂W₁₀PO₄₀].xH₂O complexes. This high symmetry is confirmed in K₅Cu[Ti₂W₁₀PO₄₀] by the observation of dynamic Jahn-Teller (JT) distortion at 300 K and static JT distortion at 77 K.     

Sliding spark spectroscopy

Summary A new analytical radiation source combined with fiber optics linked to a diode array detection device with modified software is described. The direct-reading spectrometer simultaneously covers the wavelength range 185–510 nm with a spectral resolution of <1.5 nm. Intense optical emission is observed when positionally stable high-current surface sparks supplied by a pulse-generator with definite discharge parameters (max. 800 Ampere/pulse) are sliding over compact non-conductive materials such as plastics, glasses, quartz filters or powder pellets. Substrate vaporization, ionization and excitation processes in the surface discharge plasma channel generate emission corresponding to neutral and ionic states. The spectra are essentially composed of lines emitted by the electrode material (e.g. copper, silver), from the substrate under investigation, radiation continuum as well as structured background from the surrounding air atmosphere. Due to the occurrence of emission lines of reactive fillers, inorganic pigments and stabilizers, a rapid multi-element screening method is demonstrated. A rapid identification system (mix-up test) of PVC or fire-retardant thermoplastics within one second has been realized from the atomic emission line intensity originating from the sputtered copper electrode material according to its increased volatility in the presence of chlorine (modified Beilstein test).Puls-Plasma-Technik GmbH, Dortmund     

Chiroptical properties of steroid 1,3-diaxial diols in the presence of [Mo2(OAc)4]

Summary Bidentate complexes of dimolybdenum tetraacetate with 1,3-diaxial diols show Cotton effects around 490–540 nm (CD band I), 400–440 nm (II), 350–380 nm (III), 320 nm (IV) and 280 nm (V). The sign of the Cotton effect II can be predicted by a proposed sector rule. It seems that from the Cotton effects for cyclic 1,3-diols the absolute configurations or conformations can be obtained.A part of this material was presented at III-rd International Conference on CD Spectroscopy [1]     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Trimode ladar/radar transponder systems for tracking long range cooperative targets

Detection and tracking of cooperative airborne targets are very important for military and also for civilian purposes. Previous research has shown that detection and tracking LASER offer high precision but their operation range is limited to less than 40 km even in good visibility propagation conditions. For long operation ranges, high power and bulky RADAR are required which can be significantly reduced by using active transponders on the cooperative target. A trimode LADAR/RADAR/Transponder system is investigated providing optimum performances. A L band Radar with active transponder is operated for all weather long ranges up to Low Earth Orbit satellites. The L mode is switched to a Mm wave mode RADAR for operation distances lower than 350 km and to an accurate LASER mode for the final tracking steps.     

Erratum: Preparation of size‐controlled In2O3 nanoparticles

The article referenced above was first published online on 7 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.