Periodic and solitary wave solutions of the three-wave problem. A different approach

We consider the inverse problem for a three-wave interaction system in a manner different from Zakharovet al. and of Kaup. Our method is an adaptation of the technique due to Date to a 3 × 3 Lax pair. The analysis leads to a system of ordinary nonlinear equations for the _ivariables linearizable through a suitable definition of differential on a Riemann surface. Next, in the degenerate case, when the _iare equal in pairs, we prove that such a set of equations is exactly integrable and leads to solitary solutions.     

Swinging atwood machine. Far- and near-resonance region

The swinging Atwood machine, a prototype nonlinear dynamical system, is analyzed following an idea of Bogoliubov and Mitropolsky. A series solution is found for the radial and angular displacement as functions of time. The analysis is repeated in the resonance case, when the frequency of the driving force maintains a fixed ratio to that of the free motion. The condition of resonance requires the mass ratio to be equal to 2j ²–1, wherej is an integer not equal to one.     

An efficient strategy for N-alkylation of benzimidazoles/imidazoles in SDS-aqueous basic medium and N-alkylation induced ring opening of benzimidazoles

A sustainable route for the N-1 alkylation of imidazole and benzimidazole derivatives has been developed under volatile organic solvent free condition in alkaline water-SDS system. Incorporation of SDS in the reaction medium enhances the reaction rate by suppressing the solubility issue that arises for different substrates. This method provides high yield of the alkylated product in a shorter reaction time. For reactive alkyl halides reaction proceeds at ambient temperature whereas in the cases of less reactive alkyl halides require 55–60?°C to complete alkylation process. N-alkylation induced ring opening of the heterocyclic ring in benzimidazole derivatives to multifunctional aromatic compounds were noticed at 60?°C when more than two equivalents of alkyl halide was used.     

Structure and associated properties of concentrated SiO2 sols in dilute salt solutions

Using the Verwey-Overbeek potential (VO) function the various liquid-state properties of SiO₂ sols in dilute salt solutions have been evaluated under the mean spherical model approximation (MSMA). The structure factors of these SiO₂ sols predicted by this model are compared with results obtained from small-angle neutron scattering experiments by Ramsay et al. Fourier transformation of these structure factors have been performed to obtain the radial distribution functions (RDF), and from these RDF's we computed coordination numbers of the sol particles. The interparticle distanced _c of sol particles has been obtained from the peak position in structure factorS(k) by using the Bragg's equation. The surface potential _s of the oxide sols has been determined from the amplitude (A) of the VO potential. The present calculations clearly indicate some sort of ordering in the sols system. It is gratifying to note that the present theoretical calculations could reproduce the available observed results very satisfactorily with respect to structure factor and other data.     

Kinetics and mechanism of aqua ligand substitution reactions from cis-diaqua-bis(bipyridine)ruthenium(II) ion by pyridine-2-aldoxime in aqueous medium

Summary The kinetic behaviour of cis-[Ru(bipy)₂(H₂O)₂]²⁺ towards the anating ligand pyridine-2-aldoxime as a function of temperature, ligand concentration, substrate complex concentration and pH is reported and the rate expression Rate = k ₁ k ₂[Ru(bipy)₂(H₂O)₂]²⁺ [LL]/(k _-1 + k ₂[LL]) is established where k ₁ is the water dissociation rate constant for the slow step, k _-1 is the rate constant for the aquation, k ₂ is the ligand-capturing rate constant of the five-coordinate intermediate [Ru(bipy)₂(H₂O)]²⁺ and LL is pyridine-2-aldoxime. The reaction is pH-dependent in the pH range 3.65–5.50. The enthalpy and entropy of activation were obtained using Eyring plots. The results are in conformity with a dissociative mechanism.     

Thermal analysis on influence of compatibilizing agents

Studies have been made on differential scanning calorimetry (DSC), thermogravimetric analysis (TG) and dynamic mechanical analysis (DMA) of binary blends of isobutylene-isoprene (IIR) copolymer and polychloroprene (CR) elastomers. Blends of IIR and CR are incompatible and showed separateT _g peaks in DSC curves similar to Tanδ peaks. However, addition of chlorinated polyethylene (CM) elastomer, as compatibilizer, imparts miscibility between IIR and CR which could be judged both through DSC as well as by dynamic loss measurements (Loss modulusE″ and Tanδ). The storage modulus (E′) showed variation of stiffness due to structural changes associated with the addition of compatibilizer. TG plots for these blends showed improvement of thermal stability both by addition of a suitable compatibilizer as well as due to formation of crosslinked structures associated with the vulcanization of the blends by standard curative package.     

Photoinduced Dynamics and Toxicity of a Cancer Drug in Proximity of Inorganic Nanoparticles under Visible Light

Drug sensitization with various inorganic nanoparticles (NPs) has proved to be a promising and an emergent concept in the field of nanomedicine. Rose bengal (RB), a notable photosensitizer, triggers the formation of reactive oxygen species under green‐light irradiation, and consequently, it induces cytotoxicity and cell death. In the present study, the effect of photoinduced dynamics of RB upon complexation with semiconductor zinc oxide NPs is explored. To accomplish this, we successfully synthesized nanohybrids of RB with ZnO NPs with a particle size of 24 nm and optically characterized them. The uniform size and integrity of the particles were confirmed by high‐resolution transmission electron microscopy. UV/Vis absorption and steady‐state fluorescence studies reveal the formation of the nanohybrids. ultrafast picosecond‐resolved fluorescence studies of RB–ZnO nanohybrids demonstrate an efficient electron transfer from the photoexcited drug to the semiconductor NPs. Picosecond‐resolved Förster resonance energy transfer from ZnO NPs to RB unravel the proximity of the drug to the semiconductor at the molecular level. The photoinduced ROS formation was monitored using a dichlorofluorescin oxidation assay, which is a conventional oxidative stress indicator. It is observed that the ROS generation under green light illumination is greater at low concentrations of RB–ZnO nanohybrids compared with free RB. Substantial photodynamic activity of the nanohybrids in bacterial and fungal cell lines validated the in vitro toxicity results. Furthermore, the cytotoxic effect of the nanohybrids in HeLa cells, which was monitored by MTT assay, is also noteworthy.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality

A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality due to Zhu [S.H. Wu, On generalizations and refinements of Jordan type inequality, Octogon Math. Mag. 12(1) (2004) 267–272] is corrected.