A diffusion approximation result for two parameter processes

Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010     

An efficient phosphine-free palladium coupling for the synthesis of new 2-arylbenzo[b]thiophenes

Straightforward and rapid access to 2-arylbenzo[b]thiophenes has been developed. It involved a catalytic coupling of 3-activated benzo[b]thiophenes with several aryl halides in the presence of a phosphine-free palladium system. In case of fragile functional groups such as aldehydes, a quaternary ammonium was used as an additive as with the other substrates, the coupling performed better and faster in the presence of a crown ether, the best one being DCH-18-C-6, with good yields and low reaction times. This method would provide a direct access to novel structures of biological interest.     

PHOTOEFFECTS OF VISIBLE AND ULTRAVIOLET RADIATION ON THE TWO-SPOTTED SPIDER MITE, TETRANYCHUS URTICAE

Abstract— The ability of the two-spotted spider mite, Tetranychus urticae Koch, to detect and avoid various wavelengths was examined. The mites were given a choice between two regions: an area on a leaf exposed to light of defined spectral composition or an area protected from certain selected wavelength components. The mites showed little avoidance of visible, UV-A or UV-C wavelengths. In contrast, the animals strongly avoided the UV-B spectral region, indicating that this arthropod can discriminate and respond to the presence of UV-B wavelengths. The adult mites did not appear to be killed by the amount of UV-B they could receive on a sunny summer day in Kentucky (i.e. 20 SU). However, the egg laying capacity of the females was reduced in a linear fashion as dose increased. Thus, avoidance of high UV-B regions on a leaf may contribute to the survival of the species in nature.     

Convex polynomial and spline approximation in C[−1, 1]

We prove that a convex functionf C[–1, 1] can be approximated by convex polynomialsp _n of degreen at the rate of ₃(f, 1/n). We show this by proving that the error in approximatingf by C² convex cubic splines withn knots is bounded by ₃(f, 1/n) and that such a spline approximant has anL third derivative which is bounded by n³₃(f, 1/n). Also we prove that iff C²[–1, 1], then it is approximable at the rate ofn ^–2 (f, 1/n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore.     

Benzo[b]thiophene as a template for substituted quinolines and tetrahydroquinolines

An original methodology starting from 3-aroyl-2-(2′-nitro-4′-methoxyphenyl)-benzo[b]thiophene allows the synthesis of unusual fused heterocycles. Direct hydrogenation with nickel catalysts followed by desulfurisation led to 2,3-diarylquinolines or 2,3-diaryltetrahydroquinolines.     

Structure and properties of hydrophobically end-capped poly(ethylene oxide) solutions in the presence of monovalent and divalent cations

Hydrophobically modified poly(ethylene oxide), HMPEO, was studied in concentrated salt solutions. The influence of salts was compared to the effect of temperature on poly(ethylene oxide), PEO. As expected, the addition of monovalent cations (Na(+), K(+)) has the same effect as an increase in temperature in agreement with the thermodynamic properties of PEO: a decrease in solubility, micelle size, and viscosity was observed. Moreover, the intensity of neutron scattering peaks (characteristic of the semi-dilute solutions of these associative polymers) increases due to the collapse of PEO coronae in micelles. Very peculiar behavior was observed in the presence of divalent cations (Ca(2+), Mg(2+)): larger micelle aggregates and higher viscosities, relaxation times, and activation energies were observed by dynamic rheology. This behavior is attributed to interactions between divalent cations and oxygen in PEO backbones close to the micelle core, which may reinforce intermicellar bridges.     

Apparent Molar Volume, Heat Capacity, and Conductance of Lithium Bis(trifluoromethylsulfone)imide in Glymes and Other Aprotic Solvents

Lithium bis(trifluoromethylsulfone)imide (LiTFSI) is a promising electrolyte for high-energy lithium batteries due to its high solubility in most solvents and electrochemical stability. To characterize this electrolyte in solution, its conductance and apparent molar volume and heat capacity were measured over a wide range of concentration in glymes, tetraethylsulfamide (TESA), acetonitrile, -butyrolactone, and propylene carbonate at 25°C and were compared with those of LiClO₄ in the same solvents. The glymes or n(ethylene glycol) dimethyl ethers (nEGDME), which have the chemical structure CH₃–O–(CH₂–CH₂–O) _n –CH₃ for n = 1 to 4, are particularly interesting since they are electrochemically stable, have a good redox window, and are analogs of the polyethylene oxides used in polymer-electrolyte batteries. TESA is a good plasticizer for polymer-electrolyte batteries. Whenever required, the following properties of the pure solvents were measured: compressibilities, expansibilities, temperature and pressure dependences of the dielectric constant, acceptor number, and donor number. These data were used in particular to calculate the limiting Debye-Hückel parameters for volumes and heat capacities. The infinite dilution properties of LiTFSI are quite similar to those of other lithium salts. At low concentrations, LiTFSI is strongly associated in the glymes and moderately associated in TESA. At intermediate concentrations, the thermodynamic data suggests that a stable solvate of LiTFSI in EGDME exists in the solution state. At high concentrations, the thermodynamic properties of the two lithium salts approach those of the molten salts. These salts have a reasonably high specific conductivity in most of the solvents. This suggests that the conductance of ions at high concentration in solvents of low dielectric constant is due to a charge transfer process rather than to the migration of free ions.     

Polynomial approximation inL p (0<p<1)

We prove that forf∈L _p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP _n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω _k ^? (f,t)p is the Ditzian-Totik modulus of smoothness off inL _p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP _n can also be taken to be nondecreasing.     

Bimetallic Gold(I) Complexes with Ethynyl‐Helicene and Bis‐Phosphole Ligands: Understanding the Role of Aurophilic Interactions in their Chiroptical Properties

Monometallic gold(I)‐alkynyl‐helicene complexes ( 1 a , b ) and bimetallic gold(I)‐alkynyl‐helicene architectures featuring the presence ( 2 a , b ) or absence ( 3 a , b ) of aurophilic intramolecular interactions were prepared by using different types of phosphole ligands (mono‐phosphole L1 or bis‐phospholes L2 , 3 ). The influence of the Au^I d¹⁰ metal center(s) on the electronic, photophysical, and chiroptical properties of these unprecedented phosphole‐gold(I)‐alkynyl‐helicene complexes was examined. Experimental and theoretical results highlight the importance of ligand‐to‐ligand‐type charge transfers and the strong effect of the presence or absence of Au^I–Au^I interactions in 2 a , b .