Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

Resonance Raman and DFT studies of tetra-tert-butyl porphine: Assignment of strongly enhanced distortion modes in a ruffled porphyrin

The free-base form of tetra-tert-butyl porphine (TtBP), which has extremely bulky meso substituents, is severely distorted from planarity, with a ruffling angle of 65.5degrees. The resonance Raman spectrum of TtBP (lambda(ex) = 457.9 nm) and its d(2), d(8), and d(10) isotopomers have been recorded, and while the spectra show high-frequency bands similar to those observed for planar meso-substituted porphyrins, there are several additional intense bands in the low-frequency region. Density functional calculations at the B3-LYP/6-31G(d) level were carried out for all four isotopomers, and calculated frequencies were scaled using a single factor of 0.98. The single factor scaling approach was validated on free base porphine where the RMS error was found to be 14.9 cm(-1). All the assigned bands in the high-frequency (> 1000 cm(-1)) region of TtBP were found to be due to vibrations similar in character to the in-plane skeletal modes of conventional planar porphyrins. In the low-frequency region, two of the bands, assigned as nu(8) (ca. 330 cm(-1)) and nu(16) (ca. 540 cm(-1)), are also found in planar porphyrins such as tetra-phenyl porphine (TPP) and tetra-iso-propyl porphine (IPP). Of the remaining three very strong bands, the lowest frequency band was assigned as gamma(12) (pyr swivel, obsd 415 cm(-1), calcd 407 cm(-1) in do). The next band, observed at 589 cm-1 in the do compound (calcd 583 cm(-1)), was assigned as a mode whose composition is a mixture of modes that were previously labeled gamma(13) (gamma(CmCaHmCa)) andy gamma(11) (pyr fold(asym)) in NiOEP. The final strong band, observed at 744 cm(-1) (calcd 746 cm(-1)), was assigned to a mode whose composition is again a mixture of gamma(11) and gamma(13), although here it is gamma(11) rather than gamma(13) which predominates. These bands have characters and positions similar to those of three of the four porphyrin ring-based, weak bands that have previously been observed for NiTPP. In addition there are several weaker bands in the TtBP spectra that are also

Efficient analysis, design, and filter applications of EBG waveguide with periodic resonant loads

An efficient analysis and design of an electromagnetic-bandgap (EBG) waveguide with resonant loads is presented. Equivalent-circuit analysis is employed to demonstrate the differences between EBG waveguides with resonant and nonresonant loadings. As a result of the resonance, transmission zeros at finite frequencies emerge. The concept is demonstrated in E-plane waveguides. A generic fast and efficient formulation is presented, which starts from the generalized scattering matrix of the unit cell and derives the dispersion properties of the infinite structure. Both real and imaginary parts of the propagation constant are derived and discussed. The Floquet wavelength and impedance are also presented. The theoretical results are validated by comparison with simulations of a finite structure and experimental results. The application of the proposed EBG waveguide in the suppression of the spurious passband of a conventional E-plane filter is presented by experiment.

X-ray diffraction, optical microscopy, and microhardness studies of gas nitrided titanium alloys and titanium aluminide

Thermochemical surface gas nitriding of ß21s, Timetal 205 and a Ti–Al alloy was conducted using differential scanning calorimeter equipment, in nominally pure nitrogen at 850 °C and 950 °C (ß21s), 730 °C and 830 °C (Timetal 205), and 950 °C and 1050 °C (Ti–Al) for 1 h, 3 h and 5 h. X-ray diffraction analyses showed new phases formed in the nitrided layer, depending on the alloy and the time and the temperature of nitriding. Microstructures were analyzed using optical microscopy. Cross-sectional microhardness profiles of cross-sectional samples after nitriding were obtained using a Knoop indenter.

Structural and kinetic studies of spin crossover in an Iron(II) complex with a novel tripodal ligand

Configurational and ligand conformational influences on the kinetics of (1)A(1) reversible arrow T-5(2) spin crossover in the Fe(II) complex with the novel tripodal ligand, 1,1,1-tris((N-(2-pyridylmethyl)-N-methylamino)methyl)ethane (tptMetame), have been explored. Despite having six chelate rings and three chiral nitrogen atoms, only one enantiomeric pair of isomers, Delta, SSS, and Lambda, RRR, of the complex ion is observed. The conformation of the three rings forming the upper ''cap'' of the complex structure can be assigned delta or lambda with respect to the 3-fold molecular axis. X-ray data at 300 and 153 K, above and below the critical temperature for the spin transition, show that the conformation of the ligand ''cap'' is the same as the absolute configuration of the complex, with the same Lambda lambda(CAP)(or Delta delta(CAP)) combination prevailing for both the LS ((1)A(1)) and HS (T-5(2)) isomers. Molecular mechanics calculations further show that the ligand energy remains lowest for this Lambda lambda(CAP) (or Delta delta(CAP)) combination at all Fe-N distances over the range spanning the LS and HS isomers. Measurements of the spin crossover relaxation time have been carried out in solution over the temperature range 293-170 K. The observed monophasic relaxation traces are also consistent with the absolute configuration of the complex remaining unaltered during the spin crossover.

Theoretical and photoemission studies of the band structure of CdI

The band structure of CdI has been calculated using a modified semi-empirical tight-binding method and the results obtained have been compared with both angularly averaged and angularly resolved photoemission spectra. The theoretically computed density of states distribution is in excellent agreement with angularly averaged results and all the main features observed experimentally are reproduced in the theory. Angularly resolved spectra have been used to draw up energy band dispersion curves directly and agreement with calculated bands in both the Gamma M and Gamma K directions of the Brillouin zone is good.

Design and experimental validation of liquid crystal-based reconfigurable reflectarray elements with improved bandwith in F-band

A reconfigurable reflectarray which exploits the dielectric anisotropy of liquid crystals (LC) has been designed to operate in the frequency range from 96 to 104 GHz. The unit cells are composed of three unequal length parallel dipoles placed above an LC substrate. The reflectarray has been designed using an accurate model which includes the effects of anisotropy and inhomogeneity. An effective permittivity that accounts for the real effects of the LC has also been used to simplify the analysis and design of the unit cells. The geometrical parameters of the cells have been adjusted to simultaneously improve the bandwidth, maximize the tunable phase-range and reduce the sensitivity to the angle of incidence. The performance of the LC based unit cells has been experimentally evaluated by measuring the reflection amplitude and phase of a reflectarray consisting of 52x54 identical cells. The good agreement between measurements and simulations validate the analysis and design techniques and demonstrate the capabilities of the proposed reflectarray to provide beam scanning in F band.