On eigenfunctions of nonlinear heat generation

Summary We consider the equation u+ expu=0, >0,u(boundary)0 in the formv= exp (K,v), whereK ^–1=–. We give bounds on for the latter equation to be solvable by the contraction mapping principle, and estimate theL ² norm of the solution so obtained. We also give a bound on for the topological index of the solution to be non-zero and apply Krasnoselskii's results to the least squares method of approximating the solution.

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Sommario Consideriamo l'equazione u+ expu=0, >0,u(frontiera)=0 nella formav= exp (Kv), doveK ^–1=–. In questo lavoro diamo limitazioni per per cui la seconda equazione e risolubile col metodo delle contrazioni, e diamo una stima della norma inL ² della soluzione cosi ottenuta. Diamo anche una limitazione per per cui l'indice topologico della soluzione diventa non zero, e applichiamo i risultati di Krasnoselskii al metodo dei minimi quadrati per approssimare la soluzione.

     

Nonlinear evolution of thin liquid films dewetting near soft elastomeric layers

The nonlinear evolution of thin liquid films dewetting near soft elastomeric layers is examined in this work. Evolution equations are derived by applying the lubrication approximation and assuming that van der Waals forces in the liquid cause the dewetting and that the solid can be described as a linear viscoelastic material. Two cases are examined: (i) a liquid layer resting on an elastomer bounded from below by a rigid substrate, and (ii) an elastomer overlying a thin liquid film bounded from below by a rigid substrate. Linear stability analysis is carried out to obtain asymptotic relations which are then compared against solutions of the full characteristic equations. In the liquid-on-solid case, numerical solutions of the evolution equations show that van der Waals forces cause thinning of the liquid film and thickening of the elastomeric solid beneath film depressions. Inclusion of a short-range repulsive force suggests that regular patterns may form in which ridges of fluid rest on depressions in the solid. In the solid-on-liquid case, the van der Waals forces cause the solid layer to break up before the liquid film can dewet. The results presented here support the idea that the dewetting of thin liquid films might be exploited to create topographically patterned surfaces on soft polymeric solids.     

ETC and Thermal Ligand Substitution in PhCCo3(CO)9 with 2,3-Bis(diphenylphosphino)-N-phenylmaleimide(bppm). X-Ray Diffraction Structure of Co3(CO)6[μ2,η2, η1-C(Ph)(O)](μ2-PPh2)

The reactivity of the bidentate ligand 2,3-bis(diphenylphosphino)-N-phenylmaleimide (bppm) with the tetrahedrane cluster PhCCo₃(CO)₉ under thermolysis and ETC conditions has been studied and found to ultimately give Co₃(CO)₆[μ₂,η²,η¹-C(Ph) ${\text{C}}{\text{ = }}{\text{ = }}{\text{C(PPh}}_{\text{2}} {\text{)C(O)NPhC}}$ (O)](μ₂-PPh₂) as the final product. The intermediate cluster compound PhCCo₃(CO)₇(bppm), which was observed by IR and ³¹P NMR spectroscopies, readily and rapidly transforms into the product cluster under the reactions conditions. The solid-state structure of Co₃(CO)₆[μ₂,η²,η¹-C(Ph)fptt(O)](μ₂-PPh$_{2})$ was unequivocally determined by X-ray crystallography. Co₃(CO)₆[μ₂, η², η¹-C(Ph)Õ(O)](μ₂-PPh₂) crystallizes in the monoclinic space group P2(1)/n, a = 11.825(5) Å, b = 31.20(1) Å, c = 11.831(5) Å, β = 108.720(7)°, V = 4134(7) ų, Z = 4, d _calc = 1.567 Mg/m³; R = 0.0350, R _w = 0.0817 for 4747 observed reflections with I > 2σ(I). The X-ray structure confirms the coupling of the benzylidyne ligand with the bppm ligand in Co₃(CO)₆[μ₂,η²,η¹-C(Ph)Õ(O)](μ₂-PPh₂). The course of the thermolysis reaction is identical to those reactions carried out with the related diphosphine ligands bma and bpcd. The utility of electron-transfer catalysis (ETC) in the preparation of PhCCo₃(CO)₇(bppm) is discussed relative to the reduction potential of the bppm ligand and the tricobalt cluster PhCCo₃(CO)₉.     

A simple and reliable semipreparative high-performance liquid chromatography technique for the isolation of marker-grade hyperforin from Hypericum perforatum L extract

The present work describes isolation of bioactive lipophilic constituent [namely, hyperforin from St. John's wort (Hypericum perforatum L.)], of approximately 98% purity by semipreparative high-performance liquid chromatography (LC). The extraction, isolation, and analysis of the collected compound is performed without the use of antioxidants and inert gas atmospheres at all the stages. Hyperforin, separated isocratically on a 12microm semiprep column, is obtained in high purity, lyophilized after the removal of the organic phase, and preserved at a low temperature. The purity of the collected marker compound is estimated by the use of LC-mass spectrometry and spectroscopic techniques.     

1,1,1,1-Tetrakis(o-fluorophenylamino)silane tris[titanium(IV) chloride]. Evidence for a new titanium cation [Ti2Cl7]+

Si(NHC₆H₄F-o)₄ · 3TiCl₄ (1) has been obtained from the disproportionation of (CF₃CH₂O)₃SiNHC₆H₄F-o and TiCl₄ in petroleum ether (40–60 °C) at –10 °C. The analytical (elemental analysis, molar conductance) and spectral (i.r., ¹H- and ¹⁹F-n.m.r.) data suggested that (1) behaves as [Si(NHC₆H₄F-o)₄ · Ti₂Cl₇]⁺ [TiCl₅]^–. The presence of these ions has been confirmed by characterising the products of metathetical reactions of (1) with R₄NX (R = Bu and Et; X = I and Br) and with AgNO₃. The data suggest the presence of a new titanium cation [Ti₂Cl₇]⁺.     

Novel reactions of phosphorus(III) azides and isocyanates: unusual modes of cycloaddition with dipolarophiles and an unexpected case of ring expansion

New modes of 1,3-dipolar cycloaddition are uncovered by the isolation of [CH2(6-t-Bu-4-Me-C6H2O)2]P(C(CO2Me)C(CO2Me)N[NP(N3)(OC6H2-6-t-Bu-4-Me)2CH2]N) (3) and [CH2(6-t-Bu-4-Me-C6H2O)2]P(C(CO2Me)C(CO2Me)C(O)N) (4) on treating [CH2(6-t-Bu-4-Me-C6H2O)2]P-X [X = N3 (1) and NCO (2)] with the dipolarophile MeO2CC identical to CCO2Me; compound 4 undergoes an unprecedented ring expansion upon addition of 2-(methylamino)ethanol to afford the spirocycle [CH2(6-t-Bu-4-Me-C6H2O)2]P(OCH2CH2N(Me)CH(CO2Me)CH(CO2Me)C(O)N) (5).     

Ammonium tetraphenylborate-naphthalene adsorbent for the preconcentration and trace determination of uranium in standard alloys and synthetic samples using 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol by fourth-derivative spectrophotometry

A solid ion-pair material produced from ammonium tetraphenylborate (ATPB) and naphthalene has been used for the preconcentration of uranium from the large volume of its aqueous complex samples. Uranium reacts with 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP) to form a water insoluble, coloured complex. This complex is quantitatively retained on the ATPB-naphthalene adsorbent filled in a column in the pH range 7.0–9.5 and at a flow rate of 2 ml/min. The solid mass from the column is dissolved with 5 ml of dimethylformamide (DMF) and uranium is determined by fourth-derivative spectrophotometry. The calibration curve is linear over the concentration range of 0.13–15.0 g of uranium in 5 ml of the final DMF solution. Seven replicate determinations of 6 g of uranium gave a mean peak height (peak-to-peak signal between 592 nm and 582 nm) of 1.02 with a relative standard deviation of 0.95%. The sensitivity is 0.8419 (d⁴A/d⁴)/(g ml^–1) found from the slope of the calibration curve. The interference of a large number of anions and cations on the estimation of uranium has been studied and the method applied for the determination of uranium in coal fly ash, Zr-base alloy and some synthetic samples corresponding to standard alloys.     

Reaction of 3,6-diphenyl-1,2,4,5-tetrazine with cis,cis-1,5-cyclooctadiene : An attempt at preparing some dihydropyridazine derivatives

The reaction of 3,6-diphenyl-1,2,4,5-tetrazine 1 with cis,cis-cycloocta-1,5-diene 7 has been studied with a view to preparing some interesting dihydropyridazine derivatives. Refluxing a mixture of 1 with excess of 7 in benzene solution for 8hr resulted in the formation of a mixture of products consisting of 1,4-diphenyl-10a-hydroperoxy-4a, 5,6,9,10,10a-hexahydrocycloocta[d]pyridazine (8, 27%) and 2,4a,5,6,8,10a,11,12-octahydro-1,4,7,10-tetraphenyldipyridazo[4,5-a:4',5'-e]cyclooctene ( However, when the reaction of 1 with 7 was carried out in refluxing benzene for nearly 40 hr, the products formed were a 14% yield of 8, a 17% yield of 9 and a 37% yield of 1,4-diphenyl-5,6,9,10-tetrahydrocycloocta[d]pyridazine (10). Neat heating of 1 with 7 around 150° for 10 hr, on the other hand, gave a 20% yield of 9, as the only isolable product. Thermolysis of 8 around 155° gave a mixture of products consisting of 2-oxocyclooct-5-enyl phenyl ketone N-benzoylhydrazone (15,30%) and 1H-3-phenyl-4,5,8,9-tetrahydrocycloocta[d]pyrazole (16, 22%). Nickel peroxide-oxidation of the adduct 9 gave a 67% yield of 1,4,7,10-tetraphenyldipyridazo[4,5-a:4',5'-e]cyclooctene (27). Acetylation of 9, on the other hand, gave a 70% yield of 2,3,8,9-tetraacetyl-2,3,5,6,8,9,11,12-octahydro-1,4,7,10-tetraphenyldipyridazo[4,5-a:4',5'-e]cyclooctene(28).     

Polarographic determination of cadmium, lead, nickel, thallium and uranium(VI) in isoquinoline formate

Summary The polarographic behaviour of Cd, Pb, Ni, Tl and U(VI) has been described in 0.1 M isoquinoline formate as base electrolyte. In all cases well defined reversible waves were obtained and determinations are possible in the presence of Mo, Co, Zn, Mn, Te, In, Se, Fe, Cr, V, Th, Zr, As, Sb, Ag, Hg and Cu.

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Polarographische Bestimmung von Cadmium, Blei, Nickel, Thallium und Uran(VI) in Isochinolinformiat

Zusammenfassung Das polarographische Verhalten von Cd, Pb, Ni, Th. und U(VI) in 0,1 M Isochinolinformiatlösung wird beschrieben, Bestimmungsmöglichkeiten werden aufgezeigt. In allen Fällen werden gut definierte reversible Stufen erhalten. Folgende Elemente stören nicht: Mo, Co, Zn, Mn, Te, In, Se, Fe, Cr, V, Th, Zr, As, Sb, Ag, Hg, Cu.

     

Spectroscopic studies of bridged binuclear complexes of Co(II), Ni(II), Cu(II) and Zn(II)

Binuclear cobalt(II), nickel(II), copper(II) and zinc(II) complexes of general composition [M₂L^1-2(μ-Cl)Cl₂] · nH₂O with the Schiff-base ligands (where L¹H and L²H are the potential pentadentate ligands derived by condensing 2,6-diformyl-4-methylphenol with 4-amino-3-antipyrine and 2-hydroxy-3-hydrazinoquinoxiline, respectively) have been synthesized and characterized. Analytical and spectral studies support the above formulation. ¹H-NMR and IR spectra of the complexes suggest they have an endogenous phenoxide bridge, with chloride as the exogenous bridge atom. The electronic spectra of all the complexes are well characterized by broad d–d and a high intensity charge-transfer transitions. The complexes are chloro-bridged as evidenced by two intense far-IR bands centered around 270–280 cm⁻¹. Magnetic susceptibility measurements show that complexes are antiferromagnetic in nature. The compounds show significant growth inhibitory activity against fungi Aspergillus niger and Candida albicans and moderate activity against bacteria Bacillus cirroflagellosus and Pseudomonas auresenosa.