Quantum Spheres and Projective Spaces as Graph Algebras

 The C ^* -algebras of continuous functions on quantum spheres, quantum real projective spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras corresponding to suitable directed graphs. Structural results about these quantum spaces, especially about their ideals and K-theory, are then derived from the general theory of graph algebras. It is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively. Received: 31 January 2001 / Accepted: 29 July 2002 Published online: 7 November 2002 RID="*" ID="*" Supported by grant No. R04–2001–000–00117–0 from the Korea Science & Engineering Foundation. RID="**" ID="**" Partially supported by the Research Management Committee of the University of Newcastle.     

Intrinsic optical bistability for low-frequency rigid layer modes in MoS2 crystal

A study of the parametric optical excitation of overtones of rigid layer modes in a MoS₂ crystal is presented. This effect, resulting from the modulation of the vibrational frequency by a biharmonic optical field, is shown to lead to a significant intrinsic optical bistability, which can be registered in a four-wave mixing process.     

The emission spectrum of the CΣ–XΣ system of AlH

The ultraviolet spectrum of AlH has been investigated at high resolution between 42 000 and 45 000 cm⁻¹ using a conventional spectroscopic technique. The AlH molecules were formed and excited in an aluminium hollow-cathode lamp with two anodes, filled with a mixture of Ne carried gas and a trace of NH₃. The emission from the discharge was observed with a plane grating spectrograph and recorded by a photomultiplier tube. The 0–0, 1–1 and 1–2 bands of the C¹Σ⁺–X¹Σ⁺ transition have been identified and rotationally analyzed. The new data were elaborated with help of recent X¹Σ⁺ state parameters reported by White et al. [J. Chem. Phys. 99 (1993) 8371–8378] and by Szajna and Zachwieja [Eur. Phys. J. D. 55 (2009) 549–555]. Determined constants of the excited C¹Σ⁺ state include: T_e = 44 675.3711(57) cm⁻¹, ω_e = 1575.3357(42) cm⁻¹, ω_ex_e = [125.5] cm⁻¹, B_e = 6.66804(32) cm⁻¹, α_e = 0.55839(56) cm⁻¹, D_e = 2.23(13) × 10⁻⁴ cm⁻¹, β_e = 6.13(25) × 10⁻⁴ cm⁻¹ and r_e = 1.613132(39) Å. The C¹Σ⁺ state is found to be extensively perturbed in the v = 0 and 1 vibrational level at J = 20, 22 − 27 and J = 5 − 9, respectively. This was probably caused by the interaction with the vibrational levels of the outer minimum.     

Random quantum operations

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Φ and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.     

Determination of T1-spin-lattice relaxation time in a two-level system by continuous wave multiquantum electron paramagnetic resonance spectroscopy in a presence of tetrachromatic microwave irradiation

Applicability of continuous wave multiquantum EPR methods to study relaxation times at X-band is examined. Multiquantum transitions excited in a two-level system by tetrachromatic irradiation are used for these studies. The Bloch equation model is applied to simulate lineshapes of the three quantum transitions as a function of frequency difference between exciting fields. The dependence of multiquantum transition signals on relaxation times and microwave amplitude is shown. On this basis a method of deducing relaxation times from these signals is formulated. The case of a homogeneously and inhomogeneously broadened resonance line is considered. Two experimental methods are used to verify the proposed hypothesis: the X-band continuous wave multiquantum EPR with four frequencies microwave field and saturation recovery EPR. The values of T₁ obtained from CW MQ EPR and SR EPR are compared.     

Approximate analytical solution to normal emittance of semi-transparent layer of an absorbing, scattering, and refracting medium

A two-step approximate analytical solution for the normal emittance of a plane layer of an absorbing, scattering and refracting medium is derived analytically. The analysis is based on the transport approximation and the two-step solution method for radiative transfer. The high accuracy of the approximate solution, examined by comparing its results to those obtained independently by the discrete ordinates and Monte Carlo methods, makes it suitable for application in combined experimental-analytical studies to identify selected spectral radiative properties of dispersed media in the range of semi-transparency.     

Applicability of the film-diffusion model for description of the adsorption kinetics at the solid/solution interfaces

The adsorption kinetics at the solid/solution interfaces has been described by using the kinetic model based on accepting the existence of the concentration gradient in the region of bulk solution close to the solid surface (external film-diffusion model). This model has also been adopted to explain some behaviours observed in the real adsorption systems. Simultaneously, the pseudo-first order (Lagergren) equation can be derived applying this model. The results indicate that the necessary condition to state that the “diffusion across the liquid film” mechanism is involved in controlling the rate of adsorption process is the linearity of the initial parts of kinetic isotherms plotted as the amount adsorbed vs. the time. The two methods have been proposed to distinguish between this mechanism and the classical Langmuir kinetics. The results presented here might be useful in identifying if the concentration gradient in the bulk solution influences the overall adsorption rate.     

6,7‐diaza‐1‐methoxy‐ 5‐methyl‐2, 8‐dioxabicyclo[3.2.1]oct‐6‐ene. An unstable bicyclic precursor of a dioxa carbonyl ylide and carbenes by ylide ring opening

Synthesis of a bicyclic 2,2‐dioxa oxadiazoline (6,7‐diaza‐1‐methoxy‐5‐methyl‐2,8‐dioxabicyclo[3.2.1]oct‐6‐ene) is reported. Its thermolysis at 27°C is about 200 times as fast as the thermolysis of a monocyclic oxadiazoline model system. Presumably, a cyclic dioxa carbonyl ylide is formed initially and the ylide then undergoes a bond scission to afford either a dioxacarbene or a dialkylcarbene or it cyclizes to an oxirane. A small fraction of a dialkylcarbene was trapped as the product of addition to dimethyl acetylenedicarboxylate (DMAD). Computations of the barriers to the loss of N₂ from the oxadiazolines and to the formation of the carbenes from the carbonyl ylide resulting from thermolysis of the bicyclic oxadiazoline are compared to corresponding barriers for a similar monocyclic oxadiazoline. The rate acceleration is accounted for in terms of geometric factors. The complex products from the decomposition of the bicyclic oxadiazoline were not studied. Copyright © 2007 John Wiley & Sons, Ltd.     

Two-dimensional imaging of two types of radicals by the CW-EPR method

New EPR resonators were developed by using a ceramic material with a high dielectric constant, epsilon=160. The resonators have a high quality factor, Q=10(3), and enhance the sensitivity of an EPR spectrometer up to 170 times. Some advantages of the new ceramic resonators are: (1) cheaper synthesis and simplified fabricating technology; (2) wider temperature range; and (3) ease of use. The ceramic material is produced with a titanate of complex oxides of rare-earth and alkaline metals, and has a perovskite type structure. The resonators were tested with X-band EPR spectrometers with cylindrical (TE(011)) and rectangular (TE(102)) cavities at 300 and 77K. We discovered that EPR signal strength enhancement depends on the dielectric constant of the material, resonator geometry and the size of the sample. Also, an unusual resonant mode was found in the dielectric resonator-metallic cavity structure. In this mode, the directions of microwave magnetic fields of the coupled resonators are opposite and the resonant frequency of the structure is higher than the frequency of empty metallic cavity.