Painlevé analysis,conservation laws,and symmetry of perturbed nonlinear equations

We consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generator. When the perturbed KdV equation is subjected to Painlevé analysisa la Weiss, it is found that the resonance position changes compared to the unperturbed one. We prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter to be small. We determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation we determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painlevé analysis does not produce a positive answer for the perturbed NLS equation. So here we have two contrasting examples of perturbed nonlinear equations: one passes the Painlevé test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painlevé test, though its Lax pair is found in another way.     

Electrical conduction in copper vanadate

A.C. and d.c. electrical conductivities, thermoelectric power and dielectric constant of copper vanadate (CuV₂O₆) have been measured in the temperature range 300–1000 K in order to discuss the electrical conduction in the compound. The extrinsic conduction, which takes place below 500 K, has been explained by small polaron hopping mechanism while intrinsic conduction, which takes place above 500 K, has been explained by large polaron band mechanism in view of the values of activation energy and charge carrier mobility in the temperature ranges 300–500 K and 500–1000 K.     

Mössbauer spectroscopy study of iron corrosion underneath painting system

The effect of pigments on the development of corrosion products between the painting system and metal surface when exposed to marine environments has been discussed. The pigments studied were; Red Mud Zinc chromate, Zinc chromate, Red oxide Zinc Phosphate, Manganese Phosphate Barium chromate and Basic Lead Silico Chromate. Mossbauer Spectroscopy revealed that the upper rust layer in all the cases consisted of-Fe203,-FeOOH and-FeOOH. The lower rust layer immediately in contact with the metal surface consisted of an asymmetrical doublet due to -FeOOH.     

Kinetics and mechanism of the complex formation between oxalatopentaamminecobalt(III) and aluminium(III) and gallium(III); a comparative study

Summary The reversible complex formation between oxalatopentaammine cobalt(III), aluminium(III) and gallium(III) was investigated by the stopped flow technique at 30 ± 0.1 °C and I = 1.0 mol dm^–3. The reactivity sequence: Ga^III > Al^III is observed, however, the major path for gallium(III) was (NH3)₅CoC₂O₄H²⁺ + GaOH²⁺ (NH₃)₅CoC₂O₄-Ga⁴⁺ + H₂O. The formation and dissociation rate constants of the binuclear species have been compared with the analogous data for iron(III) and nickel(II) reported earlier. The results reflect the fact that the half-bonded exalato moiety of (NH₃)₅CoC₂O _inf4 ^p+ acts as a chelating agent for the metal ions.Author to whom all correspondence should be directed.     

Complex formation of isocytosine tautomers with PdII and PtII

Isocytosine (ICH) exists in solution as two major tautomers, the keto form with N1 carrying a proton (1a) and the keto form with N3 being protonated (1b). In water, 1a and 1b exist in equilibrium with almost equal amounts of both forms present. Reactions with a series of Pd(II) and Pt(II) am(m)ine species such as (dien)Pd(II), (dien)Pt(II), and trans-(NH(3))(2)Pt(II) reveal, however, a distinct preference of these metals for the N3 site, as determined by (1)H NMR spectroscopy. Individual species have been identified by the pD dependence of the ICH resonances. pK(a) values (calculated for H(2)O) for deprotonation of the individual tautomers complexes are 6.5 and 6.4 for the N3 linkage isomers of dienPd(II) and dienPt(II), respectively, as well as 6.2 and 6.0 for the N1 linkage isomers. The dimetalated species [(dienM)(2)(IC-N1,N3)](3+) (M = Pd(II) or Pt(II)) are insensitive over a wide range of pD. The crystal structure analysis of [(dien)Pd(ICH-N3)](NO(3))(2) is reported. Ab initio calculations have been performed for tautomer compounds of composition [(NH(3))(3)Pt(ICH)](2+), cis- and trans-[(NH(3))(2)PtCl(ICH)](+), as well as trans-[(NH(3))(2)Pt(ICH)(2)](2+). Without exception, N3 linkage isomers are more stable, in agreement with experimental findings. As to the reasons for this binding preference, an NBO (natural bond orbital) analysis for [(NH(3))(3)Pt(ICH-N3)](2+)strongly suggests that intramolecular hydrogen bonding between trans-positioned NH(3) ligands and the two exocyclic groups of the ICH is of prime importance. The calculations furthermore show a marked pyramidalization of the NH(2) group of ICH in the complex once the heterocyclic ligand forms a dihedral angle <90 degrees with the Pt coordination plane.     

Site-specific cleavage of human telomerase RNA using PNA-neocuproine.Zn(II) derivatives

Here we report the synthesis of a novel PNA based neocuproine.Zn RNA cleaving agent; we demonstrate that such agents sequence specifically cleave a synthetic RNA target and in particular the RNA component of human telomerase.     

Reactions of Titanium Alkoxides with N-Methylaminoalcohols

N-methylaminoalkoxides of titanium of the type Ti(OR)_4?n(O · CHR′ · CH₂ · NR″R?)_n where R = Et and Pr¹; n = 1–4; and R′ = R″ = H, R? = Me; R′ = H, R″ = R? = Me; R′ = R″ = R? = Me, synthesized by the reactions of titanium alkoxides with aminoalcohols, show interesting variations in their properties like physical state, volatility and molecular complexity. I.r. and p.m.r. spectra of these derivatives have been recorded. A few interchange reactions with methanol and tert-butanol have also been carried out. These aminoalkoxides get cleaved with acetyl chloride and undergo insertion reactions with phenylisocyanate, thus providing the first examples of insertion reactions in such derivatives.     

Thermal analysis of lanthanide polyphosphates

Summary A study of thermal analysis of some lanthanide polyphosphates has been reported. The DTA curves of Ce, Pr and Sm polyphosphates were of similar nature. They exhibited a sharp exothermic peak indicating crystallization temperature (T _c) around 520 °C. However, no peak indicatingT _m was observed upto 800 °C. TG curves of Ce, La, Pr, Sm, Y polyphosphates indicated weight loss occurring in three stages. The integral procedural decomposition thermal analysis (ipdt) indicated that these materials had refractory nature.With 4 figures and 2 tables     

Kinetics of oxidation of some disaccharides in ammoniacal medium

Kinetics of oxidation of lactose, maltose, cellobiose and melibiose has been studied by hexacyanoferrate(III) in the presence of ammonia. A general mechanism involving the formation of intermediate enodiol anion has been suggested. The effects of dielectric constant and salts have been studied in detail. The oxidation products have been characterised by descending paper chromatography. Compensation effects have been observed.