Optical properties of polarization-dependent geometric phase elements with partially polarized light

The behavior of geometric phase elements illuminated with partially polarized monochromatic beams is investigated both theoretically and experimentally. The element discussed in this paper is composed of wave plates with π-retardation and a space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders; right-and left-handed circularly polarized states with conjugate geometric phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix includes a “vectorial interference matrix” which contains information concerning the correlation between the two orthogonal, circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. In addition, we found that the equivalent mutual intensity of the emerging beam is modulated according to the geometric phase induced by the element. Other interesting phenomena concerning propagation will be discussed theoretically and demonstrated experimentally. The experiment made use of a spherical geometric phase element that was realized by use of a space-variant subwavelength grating illuminated with CO₂ laser radiation of 10.6 μm wavelength.     

A geometric formula for Haefliger knots

Haefliger has shown that a smooth embedding of the (4k−1)-sphere in the 6k-sphere can be knotted in the smooth sense. In this paper, we give a formula with which we can detect the isotopy class of such a Haefliger knot. The formula is expressed in terms of the geometric characteristics of an extension, analogous to a Seifert surface, of the given embedding. In particular, the Hopf invariant associated to the extension plays a crucial role. This leads us to a new characterisation of Haefliger knots.     

Thermal isomerization of trifluoromethyl trifluorovinyl ether to pentafluoropropionyl fluoride

The thermal rearrangement of trifluoromethyl trifluorovinyl ether (MVE) to pentafluoropropionyl fluoride (PPF) under pressure with and without radical initiators has been studied. The reaction typically gives a mixture of different acyl fluorides. The influence of the reaction parameters (pressure, temperature, concentration, type of initiator and contact time) on the conversion and the selectivity of the process has been carefully examined. In addition, a mechanism which accounts for the formation of all the products has been proposed.     

Theoretical study of cyclization of 2′-hydroxychalcone

The isomerization mechanism of 2′(OH)chalcone (1) in flavanone (2) was studied. The calculations were performed with the semiempirical method AM1, using totally optimized molecular geometries. A 6-step mechanism including several equilibrium states was proposed. It was concluded that: (a) At the conformational equilibrium of 1 there could be 43.9% of s-cis conformer; (b) The acid dissociation of 1 trans-s-trans is considerable; (c) The E_E, ΔH_f and net charges show that the rotation of ring A of 1 and the formation of ring C of 2 occurs without greater impairments; (d) Although the keto structure is the most stable one, the enolate of 2 is present in the reaction medium; (e) The conversion of enol of 2 in the keto form would be the limiting step of the analyzed isomerization rate.     

一类广义Lanchester模型的数值解及若干结论

本讨论了一类广义的Lanchester模型在一些限制条件下的近似解，并给出了若干结论。     

Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.     

Polynomial expansion of basis sets: Alternatives to fully optimized exponents

Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry.     

长叶烯通过异构化,氧化和Prins反应合成新型香料

本文报道综合利用长叶烯（１）催化异构化为异长叶烯（２）及合成系列香料的方法；通过氧化反应合成不同香型烯醇酯类等；Ｐｒｉｎｓ反应合成系列化合物。鉴定了１０种香料化合物的香型。