The Balian-Low theorem and regularity of Gabor systems

For any positive real numbers A, B, and d satisfying the conditions , d>2, we construct a Gabor orthonormal basis for L²(ℝ), such that the generating function g∈L²(ℝ) satisfies the condition:∫_ℝ|g(x)|²(1+|x| ^A )/log ^d (2+|x|)dx < ∞ and .     

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

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.     

Laser cleaning of copper roofing sheets subjected to long-lasting environmental corrosion

The study was concerned with the effect of the laser fluence and pulse duration on the microstructure of copper roofing of the Wilanów Palace in Warsaw (Poland) subjected to environmental degradation since the turn 19th century. The techniques used for the microstructure examinations included: SEM+EDS, X-ray diffraction analysis, surface profiling and colour analysis. The measurements of colour of the laser-cleaned surfaces showed that series of 100-μs pulses offer the most effective cleaning. It was also found that by controlling the number of laser pulses it is possible to control the roughness of the cleaned surface.