Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.     

RADICAUX LIBRES INDUITS PAR L''ACTION DU RAYONNEMENT ULTRAVIOLET SUR CERTAINS CONSTITUANTS DE L''ACIDE DEOXYRIBONUCLEIQUE

The action of ultra violet rays of 260 nm on aqueous solutions of bases, nucleosides and nucleotides of DNA at 77°K is studied by electron spin resonance. It is shown that the free radicals observed are similar, with a few noteworthy exceptions to those induced by X-rays, under the same conditions of temperature, in the solid state. Contrary to what might be excepted on the basis of the results obtained by X-rays, the variation in the yield in paramagnetic centres in each sequence studied does not seem to be important.     

ETUDE PAR RESONANCE PARAMAGNETIQUE ELECTRONIQUE DE LA PHOTOSENSIBILISATION DES ACIDES AMINES PAR LA PROFLAVINE

Abstract— –The photosensitization of amino acids by proflavine is studied using the technique of electron spin resonance spectroscopy. The analysis of the line shape as a function of the incident microwave power (both in the presence and absence of oxygen) and the dependence of the numbers of free radicals on the intensity of the incident light allow one to suggest that two types of radicals are formed. One is formed by a biphotonic process, the nature of the radicals being the same as in the case of ionising radiation, while the other is probably the RO₂ radical formed as a result of photodynamic action.     

A Popov-theory-based approach to digital H{infty} control with measurement feedback for Pritchard-Salamon systems

In this paper, we deal with the digital output-measurement-feedbackH control problem for Pritchard-Salamon infinite-dimensionalsystems with unbounded input and output operators. A discretePopov-theory-based solution is given in terms of the solvabilityof Kalman-Szegö-Popov-Yakubovitch systems associated withthe equivalent discrete-time time-invariant system obtainedby lifting the T-periodic continuous-time system.     

Concise and enantioselective synthesis of the aminocyclitol core of hygromycin A

[reaction: see text] Stereoselective aminohydroxylation and dihydroxylation using osmium(VIII) oxidants enabled the short and efficient synthesis of the aminocyclitol core of hygromycin A. In addition to allowing the selective introduction of the heteroatoms N and O, the use of osmium (via an osmate ester) as a protecting group for a 1,2-glycol is also reported. This tactic allowed efficient differentiation of otherwise equivalent hydroxyl groups and allowed us to complete the synthesis in short order (14 steps) and excellent overall yield (12%).     

Efficient acyclic stereocontrol using the tethered aminohydroxylation reaction

[reaction: see text] The tethered aminohydroxylation (TA) of acyclic allylic carbamates has been achieved in a stereospecific and stereoselective manner. Unusually high levels of stereocontrol were observed in the oxidation of 1,1-disubstituted substrates.     

ELLIPSOMETRY OF BLACK LIPID MEMBRANES OF EGG LECITHIN AND CHLOROPLAST EXTRACTS

Abstract— Ellipsometric angles and reflectivity of black lipid membranes containing either egg lecithin or chloroplast extracts were measured at a wavelength of 6328 Å. Evidence was found for positive uniaxial anisotropy in membranes of lecithin. If the thickness of those films is assumed to be 62 Å, the refractive index normal to the film surface is 1.471 ± 0.004, and the refractive index parallel to the film surface is 1.454 ± 0.003. The results for membranes of chloroplast extracts also indicate a positive anisotropy in the indices of absorption.     

Synthesis and mesomorphic properties of perfluorinated rod-like liquid crystals with sulphur-containing spacers

In order to determine the influence of 'sulphur-containing' spacers on the formation of mesophases in low molecular mass compounds, we have examined the mesomorphic behaviour of molecules which consists of a 4-biphenyl unit linked to an unbranched fluorinated chain via a short spacer including at least a sulphur atom. The synthesis of these compounds has been carried out from 2-F-butylethyl iodide or from the 2-F-alkylethyl mercaptans in the case of the F-hexyl and F-octyl tails. The mesomorphic properties have been characterized by polarized light microscopy and by differential thermal analysis showing the peculiar contribution of each of the spacers. The influence of the fluorinated chain and the shape of the connector on the stability of the mesophases has been investigated. The compounds with a thioether or a hemithioacetal spacer showed no mesomorphic properties, whereas the structures with a thioester spacer showed a very interesting enantiotropic behaviour of the smectic A type over a wide temperature range. Furthermore from the series exhibiting liquid crystalline behaviour, increasing the number of fluoromethylene units simultaneously increases both the melting and the clearing temperature. These mesomorphic properties within the fluorinated series are compared with those of their monocatenar hydrocarbon homologues.     

Forward scattering theory of electric-field-gradient-induced birefringence

We attempt to resolve the discrepancy between the Buckingham—Longuet-Higgins (BLH) and Imrie—Raab (IR) theories of linear birefringence induced in a gas of dipolar molecules by an electric field gradient. To this end we present a new calculation of the effect, based on forward scattering of a light beam incident on a thin lamina of gas molecules. We work to electric quadrupole—magnetic dipole order. The beam undergoes a time delay which is proportional to the thickness of the lamina and the electric field gradient, and can therefore be interpreted in terms of a contribution to the refractive index of the gas due to the field gradient. The birefringence is obtained by considering appropriate polarizations of the incident beam. To avoid the occurrence of a divergent quantity, such as appears in the BLH theory, it is essential to take account of the finite beam width. Calculations are performed using both primitive (traced) and traceless molecular quadrupole moments; as required on basic grounds, these results are equivalent. They are also identical to the BLH result. By contrast, the IR result is physically unacceptable because it is not invariant with respect to the use of traced and traceless moments. The source of error in the IR theory remains unclear.     

On the theory of the Buckingham effect

We apply general arguments (based on spatial transformation properties, intrinsic symmetry and dimensional analysis) to the theory of the Buckingham effect (electric-field–gradient-induced birefringence in a gas). These yield, in a simple manner, the temperature-dependent and temperature-independent terms in the birefringence (each to within a numerical factor), and also the expression, derived by Buckingham and Longuet-Higgins, for the effective quadrupole centre of a molecule. We show in addition how the calculation of the two numerical factors can be simplified in our approach.