Gel growth of α and γ glycine and their characterization

The microbial free single crystals of α and γ glycine were grown from gel at room temperature in a new chemical route. These crystals showed a superior quality than the solution grown crystals. The metastable α-form and the stable γ-form of glycine were crystallized in silica gel by solubility reduction method. The form of crystallization is confirmed by single crystal and powder X-ray diffraction analyses. The crystals of α and γ glycine were found to crystallize in monoclinic and hexagonal crystal systems, respectively. For analyzing the functional group and thermal stability of α and γ glycine crystals, spectroscopic and thermal analyses have been carried out. The dielectric studies were performed to find the dielectric constant of the grown crystals and the results are discussed. Second harmonic generation efficiency of the crystal was measured by Kurtz’s powder method using Nd:YAG laser and it was found to be 2.68 times that of potassium dihydrogen phosphate crystals.     

Some Algebraic Operators and the Invariant Subspace Problem

We consider the resolvent algebra ${R_A=\{T\in\mathcal{L} (X):\sup_{m \geq 0}\|(1+\,mA)T(1+\,mA)^{-1}\| < \infty \}}$ , and Deddens?? algebra ${B_A= \{T\in \mathcal{B}(H) : \sup_{n\geq 0}\|A^nTA^{-n}\|<\infty\}}$ . It is shown that both R _A and B _A?CI possess non-trivial invariant subspaces when A is an algebraic operator of degree 2. This assertion becomes stronger than the existence of a hyper-invariant subspace for R _A whenever R _A ?? {A}??. Investigation of the relationship between these two algebras is addressed for different classes of operators A. Also, a complete characterization of the algebra R _A when A is an algebraic operator is given. For the finite dimensional case, we present an elementary example showing that R _A contains properly {A}?? whenever A has an eigenvalue other than zero.     

Approche analytique de la convection forcée des fluides de Bingham dans un tubeAnalytical approach for forced convection of Bingham fluids in a tube

The asymptotic behaviour of laminar forced convection for Bingham fluid in a circular tube subjected to an axially varying wall heat flux is studied analytically. The effect of viscous dissipation is taken into account while the axial heat conduction in the fluid is considered as negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial wall heat flux distributions which yield a thermally developed region. The results obtained show a diminution in asymptotic Nusselt number when the Brinkman number and the dimensionless radius of the plug flow region increase. Comparisons with the results in the literature for Newtonian fluids show the validity of the present analysis. To cite this article: R. Khatyr et al., C. R. Mecanique 330 (2002) 69–75.     

Electric susceptibility of unsolvated glycine-based peptides

The DC electric susceptibilities of unsolvated glycine-based peptides, WGn (W = tryptophan and G = glycine) with n = 1-5, have been measured by deflection of a molecular beam in an electric field. These are the first electric deflection measurements performed on peptides. At 300 K the susceptibilities are in the range of 200-400 A(3). By far the largest contribution to the susceptibilities is from the permanent dipole moment of the peptides. The results indicate that the peptides do not have rigid conformations with fixed dipoles. Instead the dipole is averaged as the peptides explore their energy landscape. For a given WGn peptide, all molecules have almost the same average dipole, which suggests that they all explore a similar energy landscape on the microsecond time scale of the measurement. The measured susceptibilities are in good overall agreement with values calculated from the average dipole moment deduced from Monte Carlo simulations.     

Raman and resonance-Raman spectra of CsI/I−3

Raman and resonance-Raman spectra of the I^?₃ ion isolated within CsI crystals have been studied using 647 nm and 488 nm exciting radiation. Sample temperatures between 300 and 20 K have been used. Eleven overtones of the symmetric stretching mode (nν₁) have been observed in the resonance-Raman spectrum excited by the 488 nm Ar⁺ laser line. Bands centred at 153, 170, 264 and 304 cm^?1 have been assigned as ν₃, 2ν₂, ν₁+ν₃ and 2ν₃(Σ⁺) respectively. The remaining structure between the nν₁ lines has been assigned as due to combinations of these lines with the lattice vibrations of the CsI crystal.     

Spectral Properties of the Cauchy Operator and Its Product with Bergman's Projection on a Bounded Domain

In this paper exact asymptotic formulae are found for singularvalues of the Cauchy operator and the logarithmic potentialtype operator (on a bounded domain), as well as their productswith Bergman's projection. It is shown that these spectral characteristicsdetect geometric properties of a domain (area and the lengthof the boundary). The hypothesis "can we hear the shape of adrum", from a paper by J.M. Anderson, D. Khavinson, and V. Lomonosov[‘Spectral properties of some integral operators arisingin potential theory’, Quart. J. Math. Oxford (2) 43 (1992)387-407], is correct in the above sense. 1991 Mathematics SubjectClassification: 47B10.