Wiener's lemma for twisted convolution and Gabor frames

We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.

     

Propagation invariants of twisted Gaussian Schell-model beams

The second-order moments method is used to study the M² factor and intrinsic astigmatism of twisted Gaussian Schell-model (GSM) beams. It is shown that the M² factor of twisted GSM beams defined by the determinate of the 4×4 variance matrix is a propagation invariant and is independent of the beam twist, whereas the twist affects the intrinsic astigmatism of twisted GSM beams.     

Theoretical study of the magnetic behavior of ferric wheels.

Calculations of exchange coupling constants (J) based on density functional theory for eight complete, nonmodeled ferric wheels have been performed, and a comparison with the values obtained from magnetic susceptibility data is presented. The calculated J values obtained with a generalized-gradient approximation (GGA) functional are in good agreement with the experiment probably because the inclusion of pseudopotentials partially compensates the overestimation of the spin delocalization. The magnetostructural correlation obtained shows a strong dependence of the exchange coupling on both the Fe-O-Fe bond angle and the Fe-O bond distance. This correlation holds for both the ferric wheels and the alkoxo-bridged Fe(III) dinuclear complexes reported in the literature.     

环糊精诱导胶束形成的TICT荧光探针法研究

环糊精与表面活性剂的相互作用研究已有诸多报导，但主要涉及环糊精与表面活性剂的包络物的稳定常数和其中主客体的化学剂量比［１，２］，至于环糊精对表面活性剂胶束化性质的影响则少见涉猎，这或许与研究方法有关，分子内扭转电荷转移激发态涉及到一个完整的电荷转移，具有很高的极性，其荧光特性显示出显著的介质性质敏感性［３］，因此将ＴＩＣＴ荧光探针法用于环糊精－表面活性剂相互作用研究可能会提供一些新的信息，本文的结     

Theoretical study of non-radiative deactivation pathways for some heterocyclic compounds. I. Pyrrolyl-izoxazole derivatives

We perform an experimental and theoretical study on some pyrrolyl-izoxazole derivatives with single bridged donor (D) and acceptor (A) moieties, potentially Twisted Intramolecular Charge Transfer (TICT) state forming compounds. The emission spectra in solvent of different polarities and at different excitation wavelengths were performed. The fluorescence quantum yield is very low and the emission band shifts towards long wavelengths in polar solvents and on increasing the excitation wavelength. Solvent dependent semiempirical calculations were performed. The ground and excited states potential energy surfaces were built in terms of the torsion angle about the single bond joining D and A. The ground states have quasiplanar geometry, but the minimum of the excited states corresponds to the orthogonal conformation, stabilised in methanol due to the large charge separation between the D and A fragments. The possibility of forming TICT excited states for the studied pyrrolyl derivatives is discussed.     

Partial Crossed Products and Goldie Rings

In this paper we consider the transfer of the property of being a left Goldie ring between a ring A and its partial crossed product A*_α G by a twisted partial action α of a group G on A.     

Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces

In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to display the deeper properties of Gabor frames. Furthermore, we are able to extend results due to Connes and Rieffel on projective modules over noncommutative tori to Banach algebras, which arise in a natural manner in Gabor analysis. The main goal of this investigation is twofold: (i) an interpretation of projective modules over noncommutative tori in terms of Gabor analysis and (ii) to show that the Morita-Rieffel equivalence between noncommutative tori is the natural framework for the duality theory of Gabor frames. More concretely, we interpret generators of projective modules over noncommutative tori as the Gabor atoms of multi-window Gabor frames for modulation spaces. Moreover, we show that this implies the existence of good multi-window Gabor frames for modulation spaces with Gabor atoms in e.g. Feichtinger's algebra or in Schwartz space.     

Chern character for twisted K-theory of orbifolds

For an orbifold X and α∈H³(X,Z), we introduce the twisted cohomology and prove that the non-commutative Chern character of Connes-Karoubi establishes an isomorphism between the twisted K-groups and the twisted cohomology . This theorem, on the one hand, generalizes a classical result of Baum-Connes, Brylinski-Nistor, and others, that if X is an orbifold then the Chern character establishes an isomorphism between the K-groups of X tensored with C, and the compactly-supported cohomology of the inertia orbifold. On the other hand, it also generalizes a recent result of Adem-Ruan regarding the Chern character isomorphism of twisted orbifold K-theory when the orbifold is a global quotient by a finite group and the twist is a special torsion class, as well as Mathai-Stevenson's theorem regarding the Chern character isomorphism of twisted K-theory of a compact manifold.