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.     

Bianchi VI cosmological models representing perfect fluid and radiation with electric-type free gravitational fields

A homogeneous Bianchi type VI_h cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (–1) is imposed in the particular case of Bianchi VI₀ string models. Various physical and kinematical properties of the models are discussed.     

Processing and properties of sintered submicron IR transparent alumina derived through sol–gel method

For the first time, sintered alumina with high transparency in mid infrared region, composed of submicron grains, has been fabricated using sol–gel processing. Commercially available boehmite powder was used to prepare the stable sol. The sol was mixed with appropriate amount of sintering aids and alumina seeds. The sol was further gelled, dried, and heat treated at 1000?°C for producing alumina powder. The powder was further shaped into pellets by compaction and sintered at temperatures between 1200 and 1400?°C in air. Sintered samples were further pressed hot isostatically to produce sintered submicron transparent alumina. The synthesized powder was characterized for its morphology and phase. The sintered and hot isostatically pressed samples were characterized for their physical, mechanical, and optical properties. The present method produced transparent alumina with transparency upto 87% in mid-wave infrared region. These transparency values were at par with the transparency of single crystal sapphire in the mid-wave infrared region and the hardness values were even superior than sapphire.

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Nanoisozymes: Crystal‐Facet‐Dependent Enzyme‐Mimetic Activity of V2O5 Nanomaterials

Nanomaterials with enzyme‐like activity (nanozymes) attract significant interest owing to their applications in biomedical research. Particularly, redox nanozymes that exhibit glutathione peroxidase (GPx)‐like activity play important roles in cellular signaling by controlling the hydrogen peroxide (H₂O₂) level. Herein we report, for the first time, that the redox properties and GPx‐like activity of V₂O₅ nanozyme depends not only on the size and morphology, but also on the crystal facets exposed on the surface within the same crystal system of the nanomaterials. These results suggest that the surface of the nanomaterials can be engineered to fine‐tune their redox properties to act as “nanoisozymes” for specific biological applications.     

Gene Expression on DNA Biochips Patterned with Strand‐Displacement Lithography

Lithographic patterning of DNA molecules enables spatial organization of cell‐free genetic circuits under well‐controlled experimental conditions. Here, we present a biocompatible, DNA‐based resist termed “Bephore”, which is based on commercially available components and can be patterned by both photo‐ and electron‐beam lithography. The patterning mechanism is based on cleavage of a chemically modified DNA hairpin by ultraviolet light or electrons, and a subsequent strand‐displacement reaction. All steps are performed in aqueous solution and do not require chemical development of the resist, which makes the lithographic process robust and biocompatible. Bephore is well suited for multistep lithographic processes, enabling the immobilization of different types of DNA molecules with micrometer precision. As an application, we demonstrate compartmentalized, on‐chip gene expression from three sequentially immobilized DNA templates, leading to three spatially resolved protein‐expression gradients.     

Synthesis,characterization, and antimicrobial studies of some palladium complexes with an octamethyl tetraazacyclotetradecadiene ligand and isomers of its reduced form

Biologically important tetraaza-macrocyclic ligand 3,10-C-meso-3,5,7,7,10,12,14,14-octamethyl-1,4,8,11-tetraazacyclotetradeca-4,11-diene dihydroperchlorate, Me₈[14]diene·2HClO₄ (L₁·2HClO₄) was synthesized by the condensation of 1,2-diaminopropane with acetone in presence of quantitative amount of HClO₄ and three isomeric ligands designated as L_A, L_B and L_C were separated by the reduction of L₁·2HClO₄ with NaBH₄ and fractional crystallization from xylene. The nitrato, nitro, bromido, and iodido complexes of palladium with diene ligand L₁ were prepared by the interaction of L₁·2HClO₄ with K₂[Pd(NO₃)₄], K₂[Pd(NO₂)₄], K₂[PdBr₄], and K₂[PdI₄] (prepared by the reactions with PdCl₂ with KNO₃, KNO₂, KBr, and KI, respectively), respectively. The bromide and iodido complexes of L_A were prepared by the axial substitution reactions with [PdL_ACl₂]Cl₂. By contrast, similar complexes of other isomeric ligands L_B and L_C were prepared by axial addition reactions of [PdL^?][PdCl₄] (L′?=?L_B or L_C) with KBr and KI, respectively. The complexes were characterized on the basis of elemental analysis: IR, ¹H-NMR, UV–Vis spectroscopic analysis, and magnetic and molar conductivity data. The antifungal and antibacterial activities of these compounds have been studied against some phyto-pathogenic fungi and bacteria.