Fiber torsion sensor demodulated by a high-birefringence fiber Bragg grating

A new high-birefringence (Hi-Bi) fiber torsion sensor demodulated by a Hi-Bi fiber Bragg grating (FBG) is proposed in this study. The twisted Hi-Bi fiber sensor characteristics are analyzed using the Jones matrix. The intensity ratio from two reflected Bragg wavelengths is associated with the twist angle of the measured Hi-Bi fiber. It is found that the twist angle resolution is estimated at around 0.3° under ±0.1 dB readout from an optical spectrum analyzer if the polarization state of the light source is stable. The advantages of this new torsion sensor are: (1) insensitivity to intensity variations from the light source, (2) insensitivity to the torsion gauge length, and (3) absolute measurement in the twist angle. However, the polarization state of light in the proposed method needs to be controlled, and any birefringence change in the twisted Hi-Bi fiber needs to be prevented.     

WZW–Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]_Schouten=H,ΠΠΠ.     

AdS/CFT duality at strong coupling

We study the strong-coupling limit of the AdS/CFT correspondence in the framework of a recently proposed fermionic formulation of the Bethe ansatz equations governing the gauge theory anomalous dimensions. We give examples of states that do not follow the Gubser-Klebanov-Polyakov law at a large ’t Hooft coupling λ, in contrast to recent results on the quantum string Bethe equations that are valid in that regime. This result indicates that the fermionic construction cannot be trusted at large λ, although it remains an efficient tool for computing the weak-coupling expansion of anomalous dimensions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 213–224, August, 2007.     

Role of structural flexibility in the fluorescence and photochromism of salicylideneaniline: the general scheme of the phototransformations

The mechanism of light-induced transformation in the salicylideneaniline molecule was studied by semiempirical PM3 calculations. The structures and energies of the minima and saddle points (transition states) on the S₀, S₁ and T₁ potential energy hypersurfaces (PESs) were obtained, together with the gradient lines on the PESs. The structure-energy scheme was compared with the experimental findings. According to the results obtained, the following principle processes are observed: fast S₁ excited state intramolecular proton transfer (ESIPT), followed by typical ESIPT fluorescence; the formation of two S₁ twisted intramolecular charge transfer (TICT) structures which quench the ESIPT fluorescence; the diabatic formation of two ground state metastable coloured “post-TICT” structures responsible for photochromism.     

环己烷中苯甲酰苯胺的双重荧光--分子内电荷转移的直接光谱证据

自从O Connell等［1］报道苯甲酰苯胺(BA)在EPA玻璃体中异常的长波长荧光发射特性以来, 已有众多学者尝试解释该"异常"荧光的发射态性质［2～12］. Kasha等［2～7］认为长波长荧光是质子转移(PT)和电荷转移(CT)两种激发态发射的叠加, 而Azumaya等［8］则认为发射态只包含分子内扭转电荷转移(TICT)态. 应该指出的是, 在上述研究中, 电荷转移态的指认并无有力的实验事实, 而主要是依据与具有CT双重荧光的对二甲氨基苯甲氰［13,14］的类比. 显然, 有关苯甲酰苯胺的长波长荧光发射态的准确性质仍待实验阐明     

Homology and cohomology intersection numbers of GKZ systems

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology intersection numbers in terms of a Laurent series. We show that the cohomology intersection number depends rationally on the parameters. We also prove a conjecture of F. Beukers and C. Verschoor on the signature of the monodromy invariant hermitian form.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.     

Solvatochromism and prototropism of diaminodiphenyl sulphones and 2-aminodiphenyl sulphone: a comparative study by electronic spectra

A comparative study of absorption and fluorescence maxima of 4,4′-diaminodiphenyl sulphone (4DADPS), 3,3′-diaminodiphenyl sulphone (3DADPS) and 2-aminodiphenyl sulphone (2ADPS) in different solvents reveals that (i) solvatochromic shifts are found to be mainly due to interaction of solvents with amino group, (ii) in any one solvent the net solvatochromic shifts of two amino groups are less than that of one amino group, (iii) fluorescence shift from cyclohexane to water is a maximum for 4DADPS and a minimum for 2ADPS and (iv) 4DADPS and 3DADPS possess more twisted intramolecular charge transfer character than 2ADPS. The excited-state acidity constants, determined by fluorimetric titration and Förster cycle methods, have been reported and discussed.     

Twisted amides: X-ray crystallographic and theoretical study of two acylated glycolurils with aromatic substituents

X-ray crystallography and theoretical analysis were applied to explore the molecular basis for the efficient and selective Claisen-like condensations of diacylglycolurils. The crystal structures of 1-acetyl-6-benzoyl-3,4,7,8-tetramethylglycoluril (4b), and of 1-(3′-oxo-3′-phenylpropionyl)-3,4,7,8-tetramethylglycoluril (5b), the product of base-promoted intramolecular condensation of 4b, were obtained by X-ray diffraction. The acetyl (Ac) group in 4b is essentially coplanar with the attached tetrahydroimidazolone ring of the glycoluril core (τ=7°), while the benzoyl (Bz) group is twisted by τ=45° relative to a plane through the ring to which it is bonded. Product 5b contains a flat amide (τ=7°). Ab initio energy optimizations of the experimental structures for 4b and 5b give optimized geometries which are not dramatically altered, suggesting that crystal packing effects are small. An atoms-in-molecules study of the delocalization of the Fermi hole reveals that electrons in the Bz C=O group of 4b are delocalized into the phenyl ring as well as into the urea moiety of the glycoluril core. This effect stabilizes the Bz over the Ac carbonyl group, and accounts for selective twisting of the Bz group. The Laplacian of the electron density reveals a non-bonded valence shell charge concentration at O of the Ac group, corresponding to a lone-pair region, aligned with a charge depletion in the valence shell of the Bz C=O carbon [(C15–O16C18)=113°]. The angle of approach [(O16C18=O19)] is 100°, equal to the angle for ideal nucleophilic attack on a carbonyl group. Oxygen atom O16 is thus poised to attack C18; only the O16C18 distance (3.248 Å) seems to prevent reaction. These results suggest that the same distance restraint may prevent O-acylation in the enolate intermediate 6b derived from4b. By contrast, the transition state for C-acylation, leading from 6b towards product 5b requires a different geometry, which may explain the observed selectivity for C-acylation in this enolate. The results show that, as 4b is converted to 5b, amide torsional strain is relieved, which may account for the high reactivity of 4b and the efficiency and irreversibility of this condensation process. This study provides a starting point for quantitative correlation of substrate structure in diacylglycolurils with kinetic data for the rearrangement reaction.     

Module Correspondences for Twisted Group Algebras

Abstract

Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K ^α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K ^α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K ^α G-modules and the set of irreducible K ^α C _G (A)-modules.