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.     

New prenylated isoflavanones from the roots of <Emphasis Type="Italic">Glycyrrhiza glabra</Emphasis>

Two new prenylated isoflavanones have been isolated from the roots of Glycyrrhiza glabra L. along with the known compounds cetoleic acid, β-sitosterol, stigmasterol, lanast-5,24-dien-3β-D-glucuronopyranoside, and glucuronic acid. The structures of the prenylated isoflavanones have been established as 8-isoprenyl-7,4′-dihydroxylicoisoflavanone (glabraisoflavanone A) and 7,3′-dihydroxy-8-isoprenyl-4′-cyclogeranioloxyisoflavanone (glabraisoflavanone B) on the basis of spectral data analyses and chemical reactions.     

Far downstream analysis for the Blasius boundary-layer stability problem

In this paper, we examine the large Reynolds number (Re) asymptoticstructure of the wave number in the Orr–Sommerfeld regionfor the Blasius boundary layer on a semi-infinite flat plategiven by Goldstein (1983, J. Fluid Mech., 127, 59–81).We show that the inclusion of the term which contains the leading-ordernon-parallel effects, at O(Re^{– 1/2}), leads to a non-uniformexpansion. By considering the far downstream form of each termin the asymptotic expansion, we derive a length scale at whichthe non-uniformity appears, and compare this position with theposition seen in plots of the wave number.     

Synthesis of novel axially chiral cyclic benzopolysulfides

Novel axially chiral benzopentathiepins were synthesized by sulfurization of dithiastannole. Naphthyl moiety was introduced near the pentathiepin ring by Suzuki-Miyaura cross-coupling reaction. Pentathiepins were found as diastereomeric mixture. Rotational energy barrier for C-C bond was estimated by theoretical calculation. Energy barrier for the inversion of pentathiepin ring was experimentally determined by variable temperature ¹H NMR.     

Synthesis and thermal behaviour of silicon containing poly(ester imide)s

A series of silicon containing poly(ester imide)s [PEIs] were synthesized using novel vinyl silane diester anhydride (VSEA) and various aromatic and aliphatic dimines by two-step process includes ring-opening polyaddition reaction to form poly(amic acid) and thermal cyclo-dehydration process to obtain poly(ester imide)s. VSEA was synthesized by using dichloro methylvinylsilane and trimellitic anhydride in the presence of K₂CO₃ by nucleophilic substitution reaction. The PEIs were characterized by FTIR spectroscopy. The thermal properties of PEIs were investigated by using differential scanning calorimetry (DSC) and thermogravimetric analysis (TG) methods. The prepared PEIs showed glass transition temperatures in the range of 320–350°C and their 5% mass loss was recorded in the temperature range of 500–520°C in nitrogen atmosphere. These had char yield in the range of 45–55% at 800°C.     

Wave Propagation in a Magnetized Dusty Plasma

The properties of waves propagating in amagnetized dusty plasma are analyzed for both high andlow values of the ion-cyclotron frequency. The electronsare considered to be hot. The dispersion relation for a wave propagating through the dusty plasmaat an arbitrary angle with the external magnetic fieldis derived. This rectifies some errors in the earliertreatment of Cramer and Vladimirov (1996). Effects of the presence of the dust on thecharacteristics of wave propagation arediscussed.     

Enhanced photoresponse towards visible light in Ru doped titania nanotube

Doping of ruthenium by the ion exchange method to the hydrothermally synthesized titania nanotube (TiNT) was found to be an effective photocatalyst active under visible light for methylene blue dye decoloration. The well dispersed and well embedded ionized ruthenium particles of about ∼2-4 nm significantly reduced the band gap energy of synthesized TiNTs from 3.1 eV to 2.56 eV in (Ru(IE)/TiNT). The loading method, size of ruthenium particles and metal dispersion pattern at the nanotube textures have great influence on its photocatalytic performances exhibiting higher photocatalytic activity (>80%) of methylene blue dye. However, large aggregated ruthenium particles (sizes ∼12-60 nm) on Ru(IM)/TiNT prepared by impregnation method failed to respond in visible light. The prepared catalysts were analysed by TEM, FESEM, FE-SEMEDX, XRD, UV-vis DRS spectra, XPS and BET surface area techniques.