The spectrum of twisted Dirac operators on compact flat manifolds

Let be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of , and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group , we give a very simple expression for the multiplicities of eigenvalues that allows us to compute explicitly the -series, in terms of values of Hurwitz zeta functions, and the -invariant. We give the dimension of the space of harmonic spinors and characterize all -manifolds having asymmetric Dirac spectrum.

Furthermore, we exhibit many examples of Dirac isospectral pairs of -manifolds which do not satisfy other types of isospectrality. In one of the main examples, we construct a large family of Dirac isospectral compact flat -manifolds, pairwise nonhomeomorphic to each other of the order of .

     

High-resolution infrared and theoretical study of gaseous 1,2,5-selenadiazole in the 600-1400 cm range

The Fourier transform gas-phase IR spectrum of natural isotopic 1,2,5-selenadiazole, C₂H₂N₂Se, has been recorded with a resolution of ca. 0.0025 cm⁻¹ in the wavenumber region 600-1400 cm⁻¹. The three a-type bands, ν₂ (A₁), ν₄ (A₁), ν₅ (A₁), the two b-type bands ν₁₁ (B₁), ν₁₂ (B₁), and the c-type band ν₁₄ (B₂) for each of the isotopologues C₂H₂N₂⁸⁰Se and C₂H₂N₂⁷⁸Se have been analyzed using the Watson model. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from the fits. The rotational constants, harmonic and anharmonic frequencies, and vibration-rotation constants (alphas, ) have been predicted by quantum chemical calculations using a cc-pVTZ basis at the MP2 and B3LYP methodology levels, and compared with the present experimental data. Although the rotation constants are marginally closer to experiment from the MP2 calculations, in general the B3LYP frequencies and alphas are closer to experiment.     

Browder spectra of upper-triangular operator matrices

Let be a 2×2 upper triangular operator matrix acting on the Hilbert space H⊕K. In this paper, for given operators A and B, we prove that

     

The ideal property, the projection property, continuous fields and crossed products

Let A be the C^∗-algebra associated to an arbitrary continuous field of C^∗-algebras. We give a necessary and sufficient condition for A to have the ideal property and, if moreover A is separable, we give a necessary and sufficient condition for A to have the projection property. Some applications of these results are given. We also prove that “many” crossed products of commutative C^∗-algebras by discrete, amenable groups have the projection property, generalizing some of our previous results.     

Application of LC/MS and ICP/MS for establishing the fingerprint spectrum of the traditional Chinese medicinal preparation Gan-Lu-Yin

We developed a method to analyze the fingerprint spectrum qualitatively and quantitatively for the traditional Chinese herbal medicinal preparation Gan-Lu-Yin with HPLC combined with photodiode array detection, and MS, and to identify the preparation's 14 main components including baicalin, baicalein, oroxylin A-7-O-glucuronide, wogonin-7-O-glucuronide, wogonin, and oroxylin A in Radix Scutellariae; naringin and neohesperidin in Aurantii fructus; liquiritigenin, liquiritin, and glycyrrhizic acid in Radix Glycyrrhizae. In LC/UV assay, a Cosmosil 5C18-MS-II column was used as the stationary phase, and a gradient of potassium dihydrogen phosphate, ACN, and water as the elute solution. The UV detection wavelengths were 250 and 280 nm. In LC/MS assay, a gradient of phosphoric acid, ACN, and water was used as the elute solution, and electrospray positive ion mode ((+)-ESI) as the analytic mode. In order to explore the distribution of trace metal elements effectively in Gan-Lu-Yin, a microwave digestion method was used for sample treatment, and an inductively coupled plasma MS assay was used to analyze fingerprint spectra of the inorganic metals in Gan-Lu-Yin. Combined with fingerprint spectra of organic compounds by LC/UV and LC/MS, it was expected to provide effective quality control in the production of Gan-Lu-Yin.     

邻二甲苯分子结构和红外光谱的DFT研究

用 Onsager 模型和密度泛函B3LYP方法在6-31G^＊基组水平上对邻二甲苯分子的几何构型进行了全优化，计算了最优构型的红外光谱．将计算所得的邻二甲苯的红外频率与其Sadtler标准红外光谱进行了比较，确定了邻二甲苯的分子结构，并对红外光谱进行了归属．同时，对 Onsager 模型的适用性进行了讨论，进而得出了 Onsager 模型适于研究纯液态的邻二甲苯分子结构和红外光谱的结论．     

High Power THz Undulator Radiation from Linear Accelerator

A 30-MeV femto-second electron linac is built at the Shanghai Institute of Applied Physics, which can produce high power, coherent THz undulator radiation. We report the experimental facility and measurement of the power, frequency spectrum. First experiments show the averaged power at THz to be about 20mW.     

Magnetic spectra of Fe-based nanocrystalline wires with axial or transverse domains

The circular permeability μ′=μ′−jμ″ of two Fe-based soft magnetic wires with axial and transverse domains, has been determined from the measurements of impedance Z=R+jX as functions of frequency (f=10-10⁵ Hz) and AC current amplitude (I=0.1-100 mA). From the magnetic spectra of μ′−f and μ″−f for a few circular fields (H_φ=0.4, 1.2, 4, 12, 40 A/m), we found that the sample with axial domain structure exhibits a relaxational feature, while for the one with transverse domain resonance-like spectra were observed when the circular field H_φ≥4 A/m. These results have been discussed in terms of domain structure and circular magnetization processes.     

Surface‐enhanced Raman scattering and density functional theory studies of bis(4‐aminophenyl)sulfone

Raman and surface‐enhanced Raman scattering (SERS) spectra of dapsone by using colloidal silver nanoparticles have been recorded. Density functional theory was used for the optimization of ground state geometries and simulation of the vibrational spectrum of this molecule. The SERS spectrum with a large silver cluster as a model metallic surface was simulated for the first time. Taking into account the experimental and calculated Raman as well as the SERS normal modes and the corresponding assignments, along with the modeling of the free dapsone and the one in the presence of the colloidal silver nanoparticles, the importance of the sulfone group on the SERS effect in dapsone was inferred. Copyright © 2009 John Wiley & Sons, Ltd.     

Study of asymmetric wavenumber shift of the Fermi doublet ν1 − 2ν2 in the Raman spectrum of liquid carbon disulfide

The Raman spectra of liquid carbon disulfide (CS₂) diluted with benzene (C₆H₆) have been measured. By changing the CS₂, the concentration, we found an asymmetric wavenumber shift phenomenon. With decreasing concentration of CS₂, the position of the ν₁ (655 cm⁻¹) band remains practically unchanged, and the 2ν₂ (796 cm⁻¹) band shifts toward higher wavenumbers. To interpret this asymmetric wavenumber shift phenomenon of the Fermi doublet ν₁ − 2ν₂ in the Raman spectra satisfactorily, we propose a modified Bertran model. The values of the Fermi resonance (FR) parameters of CS₂ at different concentrations were calculated using the Bertran equations. In addition, we found the fundamental ν₂, which should be independent of the FR interaction, shifted to higher wavenumbers as the concentration decreased. This shift was probably driven by the tuning of the FR. Copyright © 2009 John Wiley & Sons, Ltd.