Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators

A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions. This research was partially supported by a grant from CEA, Commissariat à l’énergie atomique and by the National Science Foundation under grant DMS-0705247.     

Camphor-derived sulfonylhydrazines: catalysts for Diels-Alder cycloadditions

Camphor-derived sulfonylhydrazines proved to be very active for organocatalyzed Diels-Alder cycloadditions with cyclopentadiene. Good chemical yields and enantiomeric excesses up to 89% and 88% are obtained for endo/exo adducts.     

Influence of water on localized and delocalized molecular mobility of cellulose

The influence of hydration on cellulose molecular mobility is investigated by two dielectric methods at different molecular scale. The mobility of side groups, assigned to γ mode, for dried cellulose increases. The water molecules have an anti-plasticizer effect on γ mode due to the water–polymer hydrogen bonding. For the β relaxation mode, only observed by the Thermo Stimulated Current technique, the hydration plays a role of plasticizer. The α relaxation mode assigned to the delocalized cooperative mobility of long chain segments of cellulose is plasticized by water. The study of activated parameters deduced from fractional polarization procedure, shows an increase of the activation enthalpy range with dehydration. It permits to conclude that reduction of hydrogen bonds density leading to a more extended cooperative mobility.     

Instability of mercury in specimens of human urine for external quality assessment

An under-recovery of inorganic mercury added to urine and a wide range of results is observed in quality assessment schemes (EQAS) for trace elements. Furthermore, the under-recoveries are inconsistent suggesting features associated with the urine matrix may make the mercury unavailable for measurement. To investigate the instability of mercury in urine the following experiments were set up: (1) a sample of Hg²⁺ in water with various ‘stabilizers’ added was sent to UK external quality assessment scheme participants. (2) Urine was collected from volunteers who also completed a 3-day food diary. Hg, Ca, Mg, Se, uric acid, phosphate, creatinine, reducing substances and protein were measured. Inorganic mercury was spiked into the urine, stabilizers were added and the mercury determined following storage. The results confirmed under-recovery of mercury in association with the urine matrix. Further investigations of how urinary components affect the measurement of mercury are necessary.     

Synthesis of new boron analogues of cyclic carboxylic α-amino acids using ring-closing metathesis reactions

Ruthenium catalyzed ring-closing metathesis has been used as a key step for the synthesis of cyclic α-aminoboronic esters as, for example, boron-containing mimics of pipecolic, 2-azepanecarboxylic acid or baikiain.     

Polymorphism of Anhydrous Cadmium Iodate Structure of ε‐Cd(IO3)2

The investigation of CdCl₂‐HIO₃ system, in aqueous and HNO₃ solutions, revealed that anhydrous cadmium iodate presents a marked polymorphism. No less than four new Cd(IO₃)₂polymorphs have been isolated and characterized, two of which showing second harmonic generation activity. Single crystals of ε‐Cd(IO₃)₂ are obtained by slowly evaporating, at 60 °C, a saturated solution of γ‐Cd(IO₃)₂ in 30 % nitric acid. This compound crystallizes in the orthorhombic space group Pca2₁ [a = 17.581(2), b = 5.495(2), c = 11.163(2) Å]. The basic structural unit can be described as the connection of two cadmium polyhedrons with a short metal – metal distance of 3.88Å. These units are further linked through two other iodate bridges resulting in layers parallel to the (100) plane. The 3D linkage is ensured by short bonds of the fourth iodate group.     

PHOTOTHERMAL DEFLECTION SPECTROSCOPY OF PHOTOSYNTHETIC PIGMENTS in vivo and in vitro

Abstract— This Technical Note describes the design of a photothermal beam deflection apparatus which allows the easy and rapid measurement of thermal dissipation of absorbed light energy in various photosynthetic materials including whole plant leaves. This system is based on the "mirage effect" in which the refractive index gradient induced in a fluid in contact with the sample, irradiated with an intensity-modulated light, causes the periodic deflection of a laser beam parallel to the sample surface. The deflection of the probe laser beam is detected by a position sensor, the output of which is processed by a lock-in amplifier. Photothermal deflection signals can be monitored in vivo in intact leaves placed in various (liquid or gaseous) environments with a satisfactory signal-to-noise ratio between 100 (in water) and 50 (in air) at low modulation frequencies (ca 30 Hz). It is shown that this new and simple photothermal technique is a very sensitive tool for the measurement of absorption spectra of photosynthetic pigments both in vivo (leaves, algae or chloroplasts) and in model systems (Langmuir-Blodgett and solid films of chlorophyll).     

Semiclassical dynamics of Dirac particles interacting with a static gravitational field

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy–Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime metric is realized. In this representation the Hamiltonian provides for a coupling between spin and gravity through the torsion of the gravitational field. In the specific case of a symmetric gravitational field we retrieve the Hamiltonian previously found by other authors. But our formalism provides for another effect, namely, the spin hall effect, which was not predicted before in this context.     

General Adiabatic Evolution with a Gap Condition

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable. The presence of eigenilpotents in the spectral decomposition of the generator typically leads to solutions which grow exponentially fast in some inverse power of the adiabaticity parameter, even for real spectrum. In turn, this forbids the evolution to follow all instantaneous eigenprojectors of the generator in the adiabatic limit. Making use of superadiabatic renormalization, we construct a different set of time-dependent projectors, close to the instantaneous eigenprojectors of the generator in the adiabatic limit, and an approximation of the evolution semigroup which intertwines exactly between the values of these projectors at the initial and final times. Hence, the evolution semigroup follows the constructed set of projectors in the adiabatic regime, modulo error terms we control.     

Self‐association in {2‐[3,4‐alkylenedioxy‐5‐(3‐pyridyl)]‐thienyl}alkanols: an NMR,IR, and single‐crystal X‐ray study

syn‐2,2,4,4‐Tetramethyl‐3‐{2‐[3,4‐alkylenedioxy‐5‐(3‐pyridyl)]thienyl}pentan‐3‐ols self‐associate both in the solid state and in solution. Single‐crystal X‐ray diffraction study of the 3,4‐ethylenedioxythiophene (EDOT) derivative shows that it exists as a centrosymmetric head‐to‐tail, syn dimer in the solid state. The IR spectra of the solids display only a broad OH absorption around 3300 cm^?1, corresponding to a hydrogen‐bonded species. ¹H Nuclear Overhauser Effect Spectroscopy (NOESY) NMR experiments in benzene reveal interactions between the tert‐butyl groups and the H2 and H6 protons of the pyridyl group. Two approaches have been used to determine association constants of the EDOT derivative by NMR titration, based on the concentration dependence of (i) the syn/anti ratio and (ii) the OH proton shift of the syn rotamer. Reasonably concordant results are obtained from 298 to 323 K (3.6 and 3.9 M^?1, respectively, at 298 K). Similar values are obtained from the syn OH proton shift variation for the 3,4‐methylenedioxythiophene (MDOT) derivative. Concentration‐dependent variation of the anti OH proton shift in the latter suggests that the anti isomer associates in the form of an open, singly hydrogen‐bonded dimer, with a much smaller association constant than the syn rotamer. Self‐association constants for 3‐pyridyl‐EDOT‐alkanols with smaller substituents vary by a factor of 4 from (i‐Pr)₂ up to (CD₃)₂, while the hetero‐association constants for the same compounds with pyridine vary slightly less. Copyright © 2007 John Wiley & Sons, Ltd.