Superposition principle and composite solutions to coupled nonlinear Schrödinger equations

We show that the superposition principle applies to coupled nonlinear Schrödinger equations with cubic nonlinearity where exact solutions may be obtained as a linear combination of other exact solutions. This is possible due to the cancelation of cross terms in the nonlinear coupling. First, we show that a composite solution, which is a linear combination of the two components of a seed solution, is another solution to the same coupled nonlinear Schrödinger equation. Then, we show that a linear combination of two composite solutions is also a solution to the same equation. With emphasis on the case of Manakov system of two-coupled nonlinear Schrödinger equations, the superposition is shown to be equivalent to a rotation operator in a two-dimensional function space with components of the seed solution being its coordinates. Repeated application of the rotation operator, starting with a specific seed solution, generates a series of composite solutions, which may be represented by a generalized solution that defines a family of composite solutions. Applying the rotation operator to almost all known exact seed solutions of the Manakov system, we obtain for each seed solution the corresponding family of composite solutions. Composite solutions turn out, in general, to possess interesting features that do not exist in the seed solution. Using symmetry reductions, we show that the method applies also to systems of N-coupled nonlinear Schrödinger equations. Specific examples for the three-coupled nonlinear Schrödinger equation are given.     

Coordination compounds of hydrazine derivatives with transition metals. Part 26. Coordination properties of α-diketone and α-ketoaldehyde bishydrazones derived from hydrazine-S-methylcarbodithioate

Summary Metal(II) chelates with -diketone and -ketoaldehyde bishydrazones derived from hydrazine-S-methylcarbodithioate with the general formula M[-dik(hydth)₂-2H] (M=Zn^II, Cd^II, Ni^II, Cu and Pd^II) were prepared and characterized by i.r., electronic and mass spectra as well as magnetic properties. The Ni^II, Zn^II and Cd^II chelates are most probably pentacoordinated dimers whereas the Cu^II chelates are polymeric through Cu-S linkages. The Pd^II chelates are square planar monomers.     

Coordination compounds of hydrazine derivatives with transition metals. Part 21. Reaction of 1,5-thiocarbodihydrazones with nickel(II) and copper(II) salts

Summary A series of 1,5-thiocarhodihydrazones (HL) were reacted with nickel(II) acetate to give neutral bisligand nickel(II) chelates, Ni(L)₂. Reaction of nickel(H) chloride, however. results in partial hydrolysis of the dihydrazones to give Ni(RCH=NNHCSNHNH₂)₂Cl₂ chelate complexes. Deprotonation of these chelates with pyridine gave the neutral chelates Ni(RCH=NN=CSNHNH₂)₂. Copper(H) salts are readily reduced by the dihydrazone ligands to copper(I) chelates of the type CuL, Cu(HL)₂CI and Cu₂(HL)₃CI₂.     

Magneto-switchable electrocatalytic and bioelectrocatalytic transformations

Magnetic switching of redox reactions and bioelectrocatalytic transformations is accomplished in the presence of relay-functionalized magnetite particles (Fe(3)O(4)). The electrochemistry of a naphthoquinone (1), pyrroloquinoline quinone (2; PQQ), microperoxidase-11 (3), a ferrocene derivative (4) and a bipyridinium derivative (5), functionalized magnetic particles, is switched "ON" and "OFF" by an external magnet upon the attraction of the magnetic particles to an electrode or their retraction from the electrode, respectively. The magneto-switchable activation and deactivation of the electrochemical oxidation of the ferrocene-functionalized magnetic particles and the electrochemical reduction of the bipyridinium-functionalized magnetic particles are used for the triggering of mediated bioelectrocatalytic oxidation of glucose, in the presence of glucose oxidase (GOx), and bioelectrocatalytic reduction of nitrate (NO(3) (-)), in the presence of nitrate reductase (NR), respectively. Magnetic particles functionalized with a PQQ-NAD(+) dyad are used for the magnetic switching of the bioelectrocatalytic oxidation of lactate in the presence of lactate dehydrogenase (LDH). The coupling of these particles with a ferrocene-monolayer-functionalized electrode allows the dual and selective sensing of lactate and glucose in the presence of LDH and GOx, respectively, by using an external magnet to switch the detection mode.     

Metal chelates of heterocyclic nitrogen containing ketones,XIII. Cobalt(II), nickel(II) and palladium(II) complexes of 2-picolyl- and 2-lutidyl-methyl ketones

Summary The preparation and characterization of a series of new coordination compounds of cobalt(II), nickel(II) and palladium(II) containing 2-picolyl- or 2-lutidyl-methyl ketone (HPMK or HLMK) and various anions, Cl^–, Br^–, NO ₃ ^– , NCS^– or BF ₄ ^– , are reported. Complexes of square planar, tetrahedral and octahedral stereochemistry as well as five-coordinate species were isolated. The reaction products were found to be dependent on the molar ratios, pH and the temperature at which the reaction takes place. Cobalt(II) thiocyanate was found to form a complex of the type [CoL₃][Co(NCS)₄] (L = HPMK or HLMK). Also complexes containing coordinated BF₄ were isolated. The ligand field parameters (Dq, B and ) for the cobalt(II) and nickel(II) complexes were calculated using the averaged-ligand-field approximation. The influence of the substituents of theses parameters and on the stereochemistry are discussed.     

Structure based design of simplified analogues of insect kinins

Based on a receptor interaction model, simplified analogues of insect kinins were prepared. The compounds were templated on a conformationally restricted amino piperidinone carboxylate scaffold. The conformation of the analogues was studied by NMR and the biological activity of the compounds was tested in a bio-assay.     

Polarographic analysis. III

Summary Reduction of U^VI in H₃PO₄ solution passes to U^IV, the behaviour of the polarogram depends upon the acidity of the medium. In 0.1 M H₃PO₄ solution, a single wave is obtained which is characterised by a minimum due to the formation of an insoluble U^III phosphate. In 0.6 M H₃PO₄ and 1 M H₃PO₄ solutions two waves appear. The two waves join together to form a single wave representing the reduction of U^VI to the U^IV, by increasing the acidity of the medium or by the addition of gelatin. The diffusion coefficient of the phosphate complex varies with the concentration of H₃PO₄. It possesses a maximum value of 6.25×10^–6 cn²/sec in 0.5 M H₃PO₄ solution in absence of gelatin and of 5.59×10^–6 cm²/sec in presence of 0.005% gelatin.Part II: See Z. analyt. Chem. 176, 250 (1960).     

Determination of cimetidine,famotidine, and ranitidine hydrochloride in the presence of their sulfoxide derivatives in pure and dosage forms by high-performance thin-layer chromatography and scanning densitometry

A selective, precise, and accurate method was developed for the determination of cimetidine (C), famotidine (F), and ranitidine hydrochloride (R x HCl) in the presence of their sulfoxide derivatives. The method involves quantitative densitometric evaluation of mixtures of the drugs and their derivatives after separation by high-performance thin-layer chromatography on silica gel plates (10 x 20 cm) with ethyl acetate-isopropanol-20% ammonia (9 + 5 + 4, v/v) as the mobile phase for both C and F and ethyl acetate-methanol-20% ammonia (10 + 2 + 2, v/v) as the mobile phase for R x HCl; Rf values for C, F, and R x HCl and their corresponding derivatives were 0.85 and 0.59, 0.73 and 0.41, and 0.56 and 0.33, respectively. Developing time was approximately 20 min. For densitometric evaluation, peak areas were recorded at 218, 265, and 313 nm for C, F, and R x HCl, respectively. The relationship between concentration and the corresponding peak area was plotted for the ranges of 5-50 microg/spot for C and 2-20 microg/spot for F and R x HCl. Mean recoveries were 100.39 +/- 1.33, 99.77 +/- 1.30, and 100.09 +/- 0.69% for C, F, and R x HCl, respectively. The proposed method was used successfully for stability testing of the pure drugs in the presence of up to 90% of their degradates, in bulk powder and dosage forms. The results obtained were analyzed statistically and compared with those obtained by the official methods.     

Synthesis and Crystal Structures of Bromo(1,10-phenanthroline- N , N ′)tris(2-cyanoethyl)phosphinocopper(I) and Bromo(2,2′-bipyridine- N , N ′)tris(2-cyanoethyl)phosphinocopper(I)

The two new complexes bromo(1,10-phenanthroline-N,N′)tris(2-cyanoethyl)phosphinocopper(I) and bromo(2,2′-bipyridine-N,N′)tris(2-cyanoethyl)phosphinocopper(I) were synthesized and their X-ray crystal structures were determined. The first complex crystallizes in the triclinic space group P-1 with the crystal cell parameters a = 7.7596(7) ?, b = 11.470(1) ?, c = 12.803(1) ?, α = 78.884(1)^°, β = 79.759(1)^°, γ = 86.867(1)^°, V = 1100.0(2) ?³ and Z = 2. The second complex crystallizes in the orthorhombic space group Pbca with the crystal cell parameters a = 10.614(1) ?, b = 12.345(1) ?, c = 31.903(3) ?, V = 4180.3(7) ?³ and Z = 8. In both compounds, the copper(I) ion is four-coordinate with a distorted tetrahedral geometry. In the 1,10-phenanthroline complex, an intermolecular dipole–dipole interaction between two cyano groups stabilizes an unfavorable synclinal conformation of one cyanoethyl group of the phosphine ligand.     

Spectrofluorimetric and spectrophotometric stability-indicating methods for determination of some oxicams using 7-chloro-4-nitrobenz-2-oxa-1,3-diazole (NBD-Cl)

Two sensitive and selective spectrofluorimetric and spectrophotometric stability-indicating methods have been developed for the determination of some non-steroidal anti-inflammatory oxicam derivatives namely lornoxicam (Lx), tenoxicam (Tx) and meloxicam (Mx) after their complete alkaline hydrolysis. The methods are based on derivatization of alkaline hydrolytic products with 7-chloro-4-nitrobenz-2-oxa-1,3-diazole (NBD-Cl). The products showed an absorption maximum at 460 nm for the three studied drugs and fluorescence emission peak at 535 nm in methanol. The color was stable for at least 48 h. The optimum conditions of the reaction were investigated and it was found that the reaction proceeds quantitatively at pH 8, after heating in a boiling water bath for 30 min. The methods were found to be linear in the ranges of 1-10 microg ml(-1) for Lx and Tx and 0.5-4.0 microg ml(-1) for Mx for spectrophotometric method, while 0.05-1.0 microg ml(-1) for Lx and Tx and 0.025-0.4 microg ml(-1) for Mx for the spectrofluorimetric method. The validity of the methods was assessed according to USP guidelines. Statistical analysis of the results revealed high accuracy and good precision. The suggested procedures could be used for the determination of the above mentioned drugs in pure and dosage forms as well as in the presence of their degradation products.