Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral <Emphasis Type="Italic">su</Emphasis>(2) WZNW Model

A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.      

Twisted Poincaré Duality for some Quadratic Poisson Algebras

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier. This research of the first author was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme. The second author was supported by EPSRC Grant EP/D034167/1.     

The Sixth Painlevé Equation as Similarity Reduction of $${\widehat{\mathfrak{gl}}_3}$$ Generalized Drinfel’d–Sokolov Hierarchy

Scaling symmetry of -type Drinfel’d–Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n + 1) regular singularities. Especially in the case of n = 3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painlevé VI equation. We also discuss Weyl group symmetry of the hierarchy.      

Probing the electronic structure of ZnO nanowires by valence electron energy loss spectroscopy

Valence electron energy loss spectroscopy in a transmission electron microscope is employed to investigate the electronic structure of ZnO nanowires with diameter ranging from 20 to 100 nm. Its excellent spatial resolution enables this technique to explore the electronic states of a single nanowire. We found that all of the basic electronic structure characteristics of the ZnO nanowires, including the 3.3 eV band gap, the single electron interband transitions at approximately = 9.5, approximately = 13.5,and approximately = 21.8 eV, and the bulk plasmon oscillation at approximately 18.8 eV, resemble those of the bulk ZnO. Momentum transfer resolved energy loss spectra suggest that the 13.5 eV excitation is actually consisted of two weak excitations at approximately = 12.8 and approximately = 14.8 eV, which originate from transitions of two groups of the Zn 3d electrons to the empty density of states in the conduction band, with a dipole-forbidden nature. The energy loss spectra taken from single nanowires of different diameters show several size-dependent features, including an increase in the oscillator strength of the surface plasmon resonance at approximately = 11.5 eV, a broadening of the bulk plasmon peak, and splitting of the O 2s transition at approximately = 21.8 eV into two peaks, which coincides with a redshift of the bulk plasmon peak, when the nanowire diameter decreases. All these observations can be well explained by the increased surface/volume ratio in nanowires of small diameter.     

Solvent and pH Effects on the Fluorescence of 7-(Dimethylamino)-2-Fluorenesulfonate

A novel water-soluble solvatochromic molecule, 7-(dimethylamino)-2-fluorenesulfonate (2,7-DAFS), was prepared by a three-step reaction from 2-nitrofluorene in good overall yield. The pH and solvent effects on the UV-VIS absorption and fluorescence spectra of 2,7-DAFS have been studied. Protonation of the dimethylamino group switches the absorption from intramolecular charge-transfer (ICT) to π → π* transition. The ground state pKa value of 2,7-DAFS was determined as 4.51. The fluorescence spectrum of the excited basic form, *(DAFS), shows a structureless single band with a large Stokes shift, whereas that of the acidic form, *(⁺HDAFS), exhibits a structured band with a small Stokes shift. The emission intensities of the basic and acidic forms versus pH/Ho plots show stretched sigmoidal curves and indicate that (1) the rate of deprotonation of *(⁺HDAFS) is comparable to the fluorescence decay of the species, and (2) the efficient proton-induced quenching of *(DAFS) fluorescence occurs. The pKa* was estimated as −1.7 from the fluorescence titration curve. The fluorescence maximum of *(DAFS) is blue-shifted as the polarity of solvent decreases. However, no clear dependency of the emission intensity and spectral half width, and thus fluorescence quantum yield, on the solvent polarity was revealed. It appears that the fluorescence sensitivity of 2,7-DAFS is 15 ∼ 25 times greater than the sensitivity of a widely utilized fluorescent probe, 5-(dimethylamino)-1-naphthalenesulfonate. This higher sensitivity, together with the ease of derivatization, would provide the fluorene-based fluorescent molecules significant advantages for a variety of applications.     

Stress-Induced Alteration of Chlorophyll Fluorescence Polarization and Spectrum in Leaves of <Emphasis Type="Italic">Alocasia macrorrhiza</Emphasis> L. Schott

The value of intrinsic chlorophyll fluorescence polarization, and the intensity in emission spectrum were investigated in leaf segments of Alocasia macrorrhiza under several stress conditions including different temperatures (25–50°C), various concentrations of NaCl (0–250 mM), methyl viologen (MV, 0–25 μM), SDS (0–1.0%) and NaHSO₃ (0–80 μM). Fluorescence emission spectrum of leaves at wavelength regions of 500–800 nm was monitored by excitation at 436 nm. The value of fluorescence polarization (P value), as result of energy transfer and mutual orientation between chlorophyll molecules, was determined by excitation at 436 nm and emission at 685 nm. The results showed that elevated temperature and concentrations of salt (NaCl), photooxidant (MV), surfactant (SDS) and simulated SO₂ (NaHSO₃) treatments all induced a reduction of fluorescence polarization to various degrees. However, alteration of the fluorescence spectrum and emission intensity of F₆₈₅ and F₇₃₁ depended on the individual treatment. Increase in temperature and concentration of NaHSO₃ enhanced fluorescence intensity mainly at F₆₈₅, while an increase in MV concentration led to a decrease at both F₆₈₅ and F₇₃₁. On the contrary, NaCl and SDS did not cause remarkable change in fluorescence spectrum. Among different treatments, the negative correlation between polarization and fluorescence intensity was found with NaHSO₃ treatments only. We concluded that P value being measured with intrinsic chlorophyll fluorescence as probe in leaves is a susceptible indicator responding to changes in environmental conditions. The alteration of P value and fluorescence intensity might not always be shown a functional relation pattern. The possible reasons of differed response to various treatments were discussed.     

Quantitative Time-Resolved Fluorescence Spectrum of the Cortical Sarcoma and the Adjacent Normal Tissue

The difference in time-resolved fluorescence spectrum between the cortical sarcoma and the adjacent normal tissue was studied in both experimental and theoretical ways. The Clinical data were obtained in vivo using a time-resolved fluorescence spectrometer employing a single fiber-optic probe for excitation and detection. Tissue was modeled as s-180 sarcoma tumor surrounded with normal muscle and was mediated by the Palladium-porphyrin photosensitizer (Pd-TCPP). The emitted fluorescence was considered as arising from the tumor tissue or the normal muscle, due to the presence of the photosensitizer. A computational code which could simulating time-resolved fluorescence emission was presented and applied to comparing fluorescence decay of photosensitizer in different stages of tumor growth. In this code the different stages of the tumor was modeled through changing the time τ, the delay of the fluorescence photon emission and z _max, the thickness of the tumor. It was found in the in vivo experiment that the fluorescence from tumor tissue decayed more quickly than from the adjacent normal muscle. For the ten rats in the first experiment day, the mean decay constant of tumor T _s and normal tissue T _n were 554 and 526 μs, respectively. And T _s increased with the tumor growth, from 554 μs in the first day to 634 μs in the eighth day while T _s kept steady. It was believed that the more adequate oxygen supplied by the normal tissue can more effectively quench the fluorescence and in the normal tissue the photosensitizer lifetime is smaller. As a result the simulated time-resolved fluorescence spectrum of normal tissue showed more quickly decay. And the thickness of the tumor can also delay the fluorescence decay. Both the experimental and simulated results indicated that the germination of the tumor would increase the decay constant of the time-resolved fluorescence spectrum. So decay constant of the tumor tissue spectrum should be larger than that of adjacent normal tissue for the reason of hypoxia and overgrouth. This fact could be of use in the tumor diagnoses.     

Calcium Ion-Induced Stabilization and Refolding of Agkisacutacin from <Emphasis Type="Italic">Agkistrodon Acutus</Emphasis> Venom Studied by Fluorescent Spectroscopy

Agkisacutacin isolated from the venom of Agkistrodon acutus is a coagulation factor IX / coagulation factor X-binding protein with marked anticoagulant- and platelet-modulating activities. Ca²⁺ ion-induced stabilization and refolding of Agkisacutacin have been studied by following fluorescent measurements. Ca²⁺ ions not only increase the structural stability of agkisacutacin against GdnHCl denaturation, but also induce its refolding. The GdnHCl-induced unfolding of the apo-agkisacutacin and the purified agkisacutacin is a single-step process with no detectable intermediate state. Ca²⁺ ions play an important role in the stabilization of the structure of agkisacutacin. Ca²⁺-stabilized agkisacutacin exhibits higher resistance to GdnHCl denaturation than the apo-agkisacutacin. It is possible to induce refolding of the unfolded apo-agkisacutacin merely by adding 1 mM Ca²⁺ ions without changing the concentration of the denaturant. The kinetic result of Ca²⁺-induced refolding provides evidences for that agkisacutacin consists of at least two refolding phases and the first phase of Ca²⁺-induced refolding should involve the formation of the compact Ca²⁺-binding site regions, and subsequently, the protein undergoes further conformational rearrangements to form the native structure.     

Exponential stabilization of chaotic systems with delay by periodically intermittent control

This paper studies the exponential stabilization problem for a class of chaotic systems with delay by means of periodically intermittent control. A unified exponential stability criterion, together with its simplified versions, is established by using Lyapunov function and differential inequality techniques. A suboptimal intermittent controller is designed with respect to the general cost function under the assumption that the control period is fixed. Numerical simulations on two chaotic oscillators are presented to verify the theoretical results.