A turn-on fluorescent chemosensor for Hg based on phenanthroline fluorophore

Dipyrido[3,2-a:2′,3′-c]-phenazine (L) was employed as a selectively fluorescent chemosensor for Hg²⁺ in DMF solution under buffered conditions with its fluorescence being strongly increased. The fluorescence increasing was attributed to the formation of L–Hg²⁺ by 1:1 complex ratio (K=3.7×10⁵ M⁻¹), which constitutes the basis for the determination of Hg²⁺ with the prepared chemosensor. The experiment results also show that the response behavior of L to Hg²⁺ is pH independent in the range of pH 6.0–9.0 and show excellent sensitivity and selectivity for Hg²⁺ over other examined metal ions.     

Carbon-13 and Fluorine-19 NMR Spectroscopy of the Supramolecular Solid p-tert-Butylcalix[4]arene ·α,α,α-trifluorotoluene

The supramolecular 1 : 1 host–guest inclusion compound, p-tert-butylcalix[4]arene ·α,α,α-trifluorotoluene, 1, is characterized by ¹⁹F and ¹³C solid-state NMR spectroscopy. Whereas the ¹³C NMR spectra are easily interpreted in the context of earlier work on similar host–guest compounds, the ¹⁹F NMR spectra of solid 1 are, initially, more difficult to understand. The ¹⁹F{¹H} NMR spectrum obtained under cross-polarization and magic-angle spinning conditions shows a single isotropic resonance with a significant spinning sideband manifold. The static ¹⁹F{¹H} CP NMR spectrum consists of a powder pattern dominated by the contributions of the anisotropic chemical shift and the homonuclear dipolar interactions. The ¹⁹F MREV-8 experiment, which minimizes the ¹⁹F–¹⁹F dipolar contribution, helps to identify the chemical shift contribution as an axial lineshape. The full static ¹⁹F{¹H} CP NMR spectrum is analysed using subspectral analysis and subsequently simulated as a function of the ¹⁹F–¹⁹F internuclear distance (D_FF = 2.25 ± 0.01 Å) of the rapidly rotating CF₃ group without including contributions from additional libration motions and the anisotropy in the scalar tensor. The shielding span is found to be 56 ppm. The width of the centerband in the ¹⁹F{¹H} sample-spinning CP NMR spectrum is very sensitive to the angle between the rotor and the magnetic field. Compound 1 is thus an attractive standard for setting the magic angle for NMR probes containing a fluorine channel with a proton-decoupling facility.     

Some remarks on -invariant Fedosov star products and quantum momentum mappings

In these notes we consider a slightly generalized Fedosov star product * on a symplectic manifold (M,ω), emanating from the fibrewise Weyl product and the triple (,Ω,s) consisting of a symplectic torsion free connection on M, a formal series ΩνZ²_dR(M)[[ν]] of closed two-forms on M, and a certain formal series s of symmetric contravariant tensor fields on M. We prove necessary and sufficient conditions for certain classical symmetries to become symmetries of the star product, only sufficient conditions having been published in special cases when this letter was written (note, however, the different proofs in [S. Gutt, J. Rawnsley, Natural star products on symplectic manifolds and quantum moment maps, 2003. math.SG/0304498 v1]). For a given symplectic vector field X on M, it is well known that (= is a sufficient condition for the Lie derivative to be a derivation of *. We prove that these conditions are in fact necessary ones, also providing a very simple proof for their being sufficient. Moreover, we prove a criterion that has first been presented by Gutt [S. Gutt, Star products and group actions, Contribution to the Bayrischzell Workshop, April 26–29, 2002] (see also [S. Gutt, J. Rawnsley, Natural star products on symplectic manifolds and quantum moment maps, 2003. math.SG/0304498 v1] for a different proof) and which specifies a necessary and sufficient condition for to be a quasi-inner derivation. The statement that this condition is a sufficient one dates back to Kravchenko [O. Kravchenko, Compos. Math. 123 (2000) 131]. Applying our results, we find necessary and sufficient criteria for a Fedosov star product to be -invariant and to admit a quantum Hamiltonian. Finally, supposing the existence of a quantum Hamiltonian, we present a cohomological condition on Ω that is equivalent to the existence of a quantum momentum mapping. In particular, our results show that the existence of a classical momentum mapping in general does not imply the existence of a quantum momentum mapping and thus give a negative answer to Xu’s question posed in [P. Xu, Commun. Math. Phys. 197 (1998) 167].     

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.     

Calcul d'un Invariant de Star-Produit Fermé sur une Variété Symplectique

Let M be a symplectic manifold over $ℝ. In [CFS] the authors construct an invariant ϕ in the cyclic cohomology of M for any closed star-product. They compute this invariant in the de Rham complex of M when M=T ^* V. We generalize this result by computing the image of ϕ in the de Rham complex for any symplectic manifold and any star-product and we show how this invariant is related to the general classification of Kontsevich. The proof uses the Riemann–Roch theorem for periodic cyclic chains of Nest–Tsygan.

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Calcul d'un Invariant de Star-Produit Fermé sur une Variété Symplectique

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Received: 30 November 1998 / Accepted: 15 February 1999     

Cycloaddition of 2′-azidoethyl glycosides to fullerene[C60] under ultrasonic irradiation

The reactions of fullerene[C₆₀] with 2′-azidoethyl 2,3,4,6-tetra-O-acetyl-α-d-mannopyranoside (2a) and 2′-azidoethyl 2,3,4,6-tetra-O-acetyl-β-d-galactopyranoside (2b) under ultrasonic irradiation cause the cycloaddition of 2′-azidoethyl glycosides to fullerene[C₆₀] and lead to d-glycosyl fullerene[C₆₀] derivatives 3a and 3b, respectively. The glycosyl fullerene[C₆₀] derivatives were characterized by ¹H and ¹³C NMR, UV–vis, FAB-MS, FT-IR spectra and were a 1:1 glycoside fullerene [C₆₀]-adduct.     

Quantization of the Lie Bialgebra of String Topology

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincaré duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra.     

Non-Perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group G × U(1) over a Riemannian manifold M without boundary. The total connection on the vector bundle naturally splits into a G-connection and a U(1)-connection, which is assumed to have a parallel curvature F. We find a new local short time asymptotic expansion of the off-diagonal heat kernel U(t|x, x′) close to the diagonal of M × M assuming the curvature F to be of order t ⁻¹. The coefficients of this expansion are polynomial functions in the Riemann curvature tensor (and the curvature of the G-connection) and its derivatives with universal coefficients depending in a non-polynomial but analytic way on the curvature F, more precisely, on tF. These functions generate all terms quadratic and linear in the Riemann curvature and of arbitrary order in F in the usual heat kernel coefficients. In that sense, we effectively sum up the usual short time heat kernel asymptotic expansion to all orders of the curvature F. We compute the first three coefficients (both diagonal and off-diagonal) of this new asymptotic expansion.     

Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M × F, where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.     

Condition for adiabatic passage in the earth’s-field NMR technique

The equation of motion dM/dt=γ M×B(t) is solved for the case B(t)=jB_p(t)+kB_e. The field B_e is a small static field, typically the earth’s field. The field B_p(t) decays exponentially toward zero with time constant T. This decay is produced by an overdamped switching transient that occurs near the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed that B_p is initially large compared to B_e, and that magnetization M is initially along the resultant field B. Exact solutions are obtained numerically for several decay time constants of B_p, and the motion of M is depicted graphically. It is found that for adiabatic passage, the final cone angle β of the precession in field B_e is related to the decay time constant of B_p by β=2e^{−(π/2)ω_eT}. This is confirmed by measurements of the amplitudes of the ensuing free-precession signals for various decay rates of B_p. Near-perfect adiabatic passage (magnetization aligned within 2° of the earth’s field) can be achieved for time constants T2.6/ω_e. For the case of sudden passage, an approximate analytic solution is developed by linearizing the equation of motion in the laboratory frame of reference. For the adiabatic case, an approximate analytic solution is obtained by linearizing the equation of motion in a rotating frame of reference that follows the resultant field B=B_p+B_e.     

The set of equivalent classes of invariant star products on (G; β1)

This article, in conjunction with a previous one, proves Drinfeld's theorems about invariant star products, ISPS, on a connected Lie group G endowed with an invariant symplectic structure β₁ ε ²( ). In particular, we prove that every formal 2-cocycle · ² ( ))[[ ]] determines an ISP, , and conversely any ISP, F, determines a formal 2-cocycle fx360-1 such that F is equivalent to . We also prove that two ISPS and are equivalent if and only if the cohomology classes of and coincide. These properties define a bijection between the set of equivalent classes of ISP on (G; β₁) and the set · ²( )[[ ]].     

Non-holonomic and semi-holonomic frames in terms of Stiefel and Grassmann tangent bundles

We prove that the bundles of non-holonomic and semi-holonomic second-order frames of a real or complex manifold M can be obtained as extensions of the bundle F²(M) of second-order jets of (holomorphic) diffeomorphisms of into M, where or . If and is the bundle of -linear frames of M we will associate to the tangent bundle two new bundles and with fibers of type the Stiefel manifold and the Grassmann manifold , respectively, where . The natural projection of onto defines a -principal bundle. We have found that the subset of given by the horizontal n-planes is an open sub-bundle isomorphic to the bundle of semi-holonomic frames of second-order of M. Analogously, the subset of given by the horizontal n-bases is an open sub-bundle which is isomorphic to the bundle of non-holonomic frames of second-order of M. Moreover the restriction of the former projection still defines a -principal bundle. Since a linear connection is a horizontal distribution of n-planes invariant under the action of it therefore determines a -reduction of the bundle , in a bijective way. This is a new proof of a theorem of Libermann.     

Convergence of an Exact Quantization Scheme

It has been shown by Voros [V1] that the spectrum of the one-dimensional homogeneous anharmonic oscillator (Schrödinger operator with potential q^2M, M=2,3,...) is a fixed point of an explicit non-linear transformation. We show that this fixed point is globally and exponentially attractive in spaces of properly normalized sequences.Partially supported by Faperj and CNPq, BrazilCurrent address:Laboratoire de Probabilités et Modéles aléatoires, Université Pierre et Marie Curie–Boi te courrier 188, 75252–Paris Cedex 05, France. E-mail: artur@ccr.jussieu.fr     

Hermitian Star Products are Completely Positive Deformations

Let M be a Poisson manifold equipped with a Hermitian star product. We show that any positive linear functional on C^∞(M) can be deformed into a positive linear functional with respect to the star product.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Linear Perturbations of Quaternionic Metrics

We extend the twistor methods developed in our earlier work on linear deformations of hyperkähler manifolds [1] to the case of quaternionic-Kähler manifolds. Via Swann’s construction, deformations of a 4d-dimensional quaternionic-Kähler manifold ${\mathcal{M}}We extend the twistor methods developed in our earlier work on linear deformations of hyperk?hler manifolds [1] to the case of quaternionic-K?hler manifolds. Via Swann’s construction, deformations of a 4d-dimensional quaternionic-K?hler manifold M{\mathcal{M}} are in one-to-one correspondence with deformations of its 4d + 4-dimensional hyperk?hler cone S{\mathcal{S}}. The latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space Z_S{\mathcal{Z}_\mathcal{S}}, with a suitable homogeneity condition that ensures that the hyperk?hler cone property is preserved. Equivalently, we show that the deformations of M{\mathcal{M}} can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space Z_M{\mathcal{Z}_\mathcal{M}} of M{\mathcal{M}}, by-passing the Swann bundle and its twistor space. We specialize these general results to the case of quaternionic-K?hler metrics with d + 1 commuting isometries, obtainable by the Legendre transform method, and linear deformations thereof. We illustrate our methods for the hypermultiplet moduli space in string theory compactifications at tree- and one-loop level.     

Explicit form and convergence of 1-differential formal deformations of the poisson Lie algebra

Introducing the notion of an admissible graded Lie subalgebra A of the Nijenhui-Richardson algebra A(V) of the vector space V, it is shown that each cohomology class of a subcomplex C _A of the Chevalley-Eilenberg complex (C ⁰ M), extends in a cononical way as a graded cohomology class of weight — 1 of A. Applying this when V is the space N of smooth functions of a smooth manifold M, shows that the de Rham cohomology of M is induced by the graded cohomology of weight — 1 of the Schouten graded Lie algebra of M. This allows us to construct explicitly all 1-differential, nc formal deformations of the Poisson bracket of a symplectic manifold. The construction also applies for an arbitrary Poisson manifold but leads to only part of these deformations when the structure degenerates, as shown by an example.     

Visible laser spectroscopy of cobalt monofluoride

The laser-induced fluorescence excitation spectrum of jet-cooled CoF molecules has been studied in the range of 18 800–22 000 cm⁻¹. Ten observed vibronic bands have been classified into three transitions with the 0–0 band at 18 909, 19 236, and 20 654 cm⁻¹, assigned as the [18.8]³Φ₄–X³Φ₄, [19.2]³Φ₄–X³Φ₄, and [20.6]³Γ₅–X³Φ₄ transition, respectively, the two ³Φ states, [18.8]³Φ and [19.2]³Φ, are consistent with Adam’s results (10). The previously unanalyzed [20.6] state is identified in the current work. A rotational analysis of [20.6]³Γ₅–X³Φ₄ transition has been performed and effective equilibrium molecular constants have been determined for the first time. In addition, lifetime measurements of the three electronic transitions were carried out under the collision-free condition. From the lifetime analysis, we consider that the V=1, 2, and 3 vibrational levels of [18.8]³Φ state are perturbed by another state.     

On the Buchdahl Inequality for Spherically Symmetric Static Shells

A classical result by Buchdahl [6] shows that for static solutions of the spherically symmetric Einstein equations, the ADM mass M and the area radius R of the boundary of the body, obey the inequality 2M/R ≤ 8/9. The proof of this inequality rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl’s hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in [R ₀, R ₁], R ₀ > 0, of matter models for which the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1. We show a Buchdahl type inequality for shells which are thin; given an there is a κ > 0 such that 2M/R ₁ ≤ 1 − κ when . It is also shown that for a sequence of solutions such that R ₁/R ₀ → 1, the limit supremum of 2M/R ₁ of the sequence is bounded by ((2Ω + 1)² − 1)/(2Ω + 1)². In particular if Ω = 1, which is the case for Vlasov matter, the bound is 8/9. The latter result is motivated by numerical simulations [3] which indicate that for non-isotropic shells of Vlasov matter 2M/R ₁ ≤ 8/9, and moreover, that the value 8/9 is approached for shells with R ₁/R ₀ → 1. In [1] a sequence of shells of Vlasov matter is constructed with the properties that R ₁/R ₀ → 1, and that 2M/R ₁ equals 8/9 in the limit. We emphasize that in the present paper no field equations for the matter are used, whereas in [1] the Vlasov equation is important.     

La première valeur propre de l'opérateur de Dirac sur les variétés kählériennes compactes

K.D. Kirchberg [Ki1] gave a lower bound for the first eigenvalue of the Dirac operator on a spin compact Kähler manifoldM of odd complex dimension with positive scalar curvature. We prove that manifolds of real dimension 8l+6 satisfying the limiting case are twistor space (cf. [Sa]) of quaternionic Kähler manifold with positive scalar curvature and that the only manifold of real dimension 8l+2 satisfying the limiting case is the complex projective spaceCP ^4l+1.