The length of harmonic forms on a compact Riemannian manifold

We study -dimensional Riemannian manifolds with harmonic forms of constant length and first Betti number equal to showing that they are -step nilmanifolds with some special metrics. We also characterize, in terms of properties on the product of harmonic forms, the left-invariant metrics among them. This allows us to clarify the case of equality in the stable isosytolic inequalities in that setting. We also discuss other values of the Betti number.

     

Design of a Thin Film Infrared Barcode on a Flexible Substrate

We report the design, fabrication and characterization of an infrared barcode. This barcode is composed of a bilayer of titanium and amorphous silicon on a flexible Kapton substrate. Information encoded in the barcode shows high contrast when viewed with an infrared imaging system in the 8 to 12 m spectral region. The barcode information is concealed under visible viewing conditions, i.e., the barcode appears as an untreated, uniform metal sheet to a detector of visible radiation (400 to 700nm).     

Upper and lower bounds for the fixed spectrum frequency assignment problem

A survey of the results described in the authors PhD thesis (Montemanni 2001) is presented. The thesis, which was supervised by Prof. Derek H. Smith and Dr. Stuart M. Allen, has been defended in January 2002 at the University of Glamorgan (U.K.). The thesis proposes new heuristic algorithms, based on well-known meta-heuristic paradigms, and new lower bounding techniques, based on linear programming, for the fixed spectrum frequency assignment problem.Received: May 2003, Revised: May 2003, AMS classification: 90C27, 90C59,05C90, 90C05Roberto Montemanni: Present address: Istituto Dalle Molle di Studi sullIntelligenza Artificiale (IDSIA), Galleria 2, 6928 Manno-Lugano, Switzerland (e-mail: roberto@idsia.ch)     

Nuclear hyperfine coupling interactions in the rotational spectra of the linear and bent isomers of HF-N2O

The rotational spectra of six isotopomers of the linear and bent isomers of HF-N₂O have been collected in the 7-18 GHz region with a Fourier transform microwave spectrometer. The nuclear hyperfine structure in the spectra produced by HF spin-spin coupling interaction and nuclear quadrupole coupling interactions due to the D nucleus of DF and the nuclei of N₂O have been resolved and analyzed. In the linear isomer, H in HF is bonded to the terminal N in N₂O. The NF bond lengths are 2.9808(2) Å for the HF-containing isotopomers and 2.9732(2) Å for the DF-containing isotopomers. The zero point angles are 23.1° for HF and 31-34° for N₂O. The hyperfine constants suggest that the HF bond is lengthened by 0.0105 Å upon complexation and that the electric field gradients of the two nitrogen nuclei in N₂O are perturbed differently in the complex. In the bent isomer, the hydrogen bond is formed between HF and O in N₂O. The intermolecular distances are 3.4942(2) Å for the HF-containing isotopomers and 3.4436(2) Å for the DF-containing isotopomers, with HF and N₂O forming angles of 34° and 46°, respectively, with the intermolecular axis. The nuclear quadrupole coupling constants of the two nitrogen nuclei do not indicate electric field gradient perturbation in this isomer.     

Quantum Spectrum of Some Anharmonic Central Potentials: Wave Functions Ansatz

Based on the ansatz to the wave functions, the quasi-exact solutions of the 2D Schrödinger equation with some anharmonic potentials are reviewed and analyzed if admitting restrictions on the parameters of the potential and the angular momentum m. These potentials are taken as the screened Coulomb potential V(r)=a/r+b/(r+), the singular one-fraction power one V(r)=ar ^–1/2+br ^–3/2 and the singular two-fraction one V(r)=ar ^2/3+br ^–2/3+cr ^–4/3. The latter one is found that the hidden symmetry exists if substituting r–ir. It will reverse the signs of E and c of quantum system, leaving the remaining parameters invariant.     

Absorption Spectra of Gasolines in the Region 1090–1220 nm

The difference absorption spectra of different grades of gasoline (A-76, AI-92, and AI-95) with octane numbers lying within 76–85 have been investigated experimentally in comparison with hydrocarbons: isooctane, benzene, and n-heptane. The spectra obtained contain absorption bands of the CH₃, CH₂, and CH groups and supposedly of the olefin double bond. The possibility of determining the octane number of an unknown grade of gasoline by using the absorption of a measured difference spectrum at one selected wavelength is shown.     

Microwave Spectra of o-Fluorotoluene and Its 13C Isotopic Species: Methyl Internal Rotation and Molecular Structure

The rotational spectra of o-fluorotoluene and its seven ¹³C isotopic species were recorded in the frequency range from 4 to 20 GHz with employment of pulsed molecular beam Fourier-transform microwave (MB-FTMW) spectrometers. The analysis of the spectra in the two lowest states of methyl internal rotation (torsional ground state, A and E species) was based on a asymmetric frame-rigid symmetric top Hamiltonian with inclusion of centrifugal distortion terms, yielding structural rotational constants, as well as the threefold barrier V ₃ to internal rotation and the angle(a,i) between the principal moment of inertia a axis and the internal rotor axis i. The rotational constants of all eight isotopomeres were used to derive the seven ¹³C r _s coordinates of the molecule.     

Solid State Reactions of Hemin with Basic Substances: Formation of bis and Mixed Complexes

The solid state reactions of hemin with KCN, Na₂SxH₂O, arginine, imidazole, 1-methylimidazole, 2-methylimidazole, benzimidazole, and mixtures of these basic reagents were monitored using IR, Mössbauer, and XRD techniques. All these basic substances react at the peripheral propionic acid group of hemin-forming salts. Binary mixtures of KCN, arginine, imidazole, 1-methylimidazole, 2-methylimidazole, and benzimidazole were found to form complexes with mixed ligands at the iron site of hemin. According to the structural information obtained for these mixed complexes, mechanisms for their formation are proposed. The solid state synthesis and the properties of the obtained products reveal the specifities of the involved ligands.     

高频地波雷达频谱监测系统的前端电路设计

利用超外差式接收和直接数字合成(DDS)技术设计了高频地波雷达频谱监测系统的前端电路．该电路能够根据雷达探测距离的远近选择相对应的噪声信号接收频段,为后续的数据采集与处理提供噪声电平数据．实验证明：本系统的跳频本振信号信噪比(SNR)优于60dB;对输入信号具有60dB左右的增益和1μV的灵敏度,满足了武汉大学研制的下一代高频地波海态监测雷达对频谱监测的需要．     

准周期链状聚合物电子谱及特征

研究了链状聚合物的长短键结构呈准周期排列的电子谱。利用紧束缚近似和转移矩阵方法通过理论证明和计算表明：这种准周期排列聚合物的电子谱,当长短键长度相差很小时,具有类似于金属晶体的能带结构;相差很大时,具有无序系统一维能级结构;而对于一般情形,其电子谱与上两者均异,形成所谓的类Cantor集。这3类不同的谱结构反映在链状聚合物的宏观物理性质上也将有所不同,它无疑会影响聚合物的稳定性及相关(超)导电性能,深入研究这方面问题将有助于对有机超导的认识。