On some global well-posedness and asymptotic results for quasilinear parabolic equations

We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+.     

Synthesis and Structural Studies of Platinum Complexes Containing Monodentate, Bridging, and Chelating Formamidine Ligands

The reactions of K(2)PtCl(4) with N,N'-diphenylformamidine (HDPhF) and N,N'-di-p-tolylformamidine (HDTolF) produce the trans square-planar compounds PtCl(2)(HDPhF)(2), 1a, and PtCl(2)(HDTolF)(2), 1b. Compound 1a crystallizes as yellow parallelepipeds in the space group P2(1)/c with two independent molecules in the asymmetric unit and unit cell dimensions a = 23.427(7) ?, b = 16.677(6) ?, c = 12.980(4) ?, and beta = 96.10(2) degrees. These compounds are soluble in common organic solvents and have been used as starting materials for the preparation of diplatinum compounds. Treatment of 1a and 1b with NaOMe and the halide abstraction reagent TlPF(6) produces the compounds Pt(2)(&mgr;-DArF)(2)(eta(2)-DArF)(2), Ar = Ph (2a) and Tol (2b), respectively. Compound 2a crystallizes as yellow rods in the space group P&onemacr; with unit cell dimensions a = 12.296(3) ?, b = 12.310(4) ?, c = 15.374(4) ?, alpha = 90.75(2) degrees, beta = 91.02(2) degrees, and gamma = 110.20(2) degrees. Compound 2b crystallizes with a molecule of THF, as yellow rods in the space group P2(1)/c with a = 17.883(3) ?, b = 14.517(3) ?, c = 22.581(3) ?, and beta = 98.17(1) degrees. These compounds contain two cis bridging formamidinato ligands and two formamidinato ligands that are chelated to separate Pt centers. Upon heating, they further react to give the tetrabridged compounds Pt(2)(&mgr;-DArF)(4), Ar = Ph (3a), Tol (3b). Compound 3a crystallizes as orange cubes in the cubic space group I432 with a = 19.671(1) ?. On going from the bis-bridged, bis-chelate structure in 2a to the tetrabridged structure in 3a, the metal-metal separation decreases from 2.910(1) to 2.649(1) ?. Both 2band 3b have been oxidized to give the Pt(II)-Pt(III) compound Pt(2)(&mgr;-DTolF)(4)(PF(6)), 4. Compound 4 crystallizes as cubes in the tetragonal space group P4/ncc with a = 14.392(1) ? and c = 14.436(1) ?. The Pt-Pt distance in 4 is 2.5304(6) ?.     

Electrofugal Fragmentation of Alkylcobalamin Derivatives Using Cob(I)Alamin and Heptamethyl Cob (I)yrinate as Catalysts

The cob (I)alamin- ( 1(I) ) and the heptamethyl cob(I)ynnate- ( 2(I) ) catalyzed transformation of an epoxide to the corresponding saturated hydrocarbon 3→4→5 is examined (see Schemes 1 and 3–5). Under the reaction conditions, the epoxyalkyl acetate 3 is opened by the catalysts with formation of appropriate (b?-hydroxyalkyl)-corrinoid derivatives ( 13 , 14 , 17 , 18 , see Schemes 12 and 14). Triggered by a transfer of electrons to the Co-corrin-π system, the Co, C-bond of the intermediates is broken, generating the alkenyl acetate 4 (cf. Schemes 12 and 14) following an electrofugal fragmentation (cf. Schemes 2 and 12). The double bond of 4 is also attacked by the catalysts, leading to the corresponding alkylcorrinoids ( 15 , 19 , see Schemes 12 and 14) which in turn are reduced by electrons from metallic zinc, the electron source in the system, inducing a reductive cleavage of the Co, C-bond with production of the saturated monoacetate 5 (see Schemes 2, 5 and 12). In the cascade of steps involved, the transfer of electrons to the intermediate alkylcorrinoids ( 13–15 , 17–19 , see Schemes 12 and 14) is shown to be rate-limiting. Comparing the two catalytic species 1(I) and 2(I) , it is shown that the ribonucleotide loop protects intermediate alkylcobalamins to some extent from an attack by electrons. The protective function of the ribonucleotide side-chain is shown to be present in alkylcobalamins existing in the base-on form (cf. Chap. 4 and see Scheme 14).     

On the regiochemistry of the methylphenylcyclopropenone dimer. A reinvestigation

The regiochemistry of the previously reported dimer of methyhlphenylcyclopropenone is corrected through analysis of the long-range ¹H, ¹³C correlated (COLOC) 2D nmr spectrum.     

Salting-in of alcohols in aqueous solutions by tetraalkylammonium bromides at the freezing temperature

The freezing-point depression of the ternary systems tetraalkylammonium bromides-t-butanol-water for the first five homologs of R₄NBr was measured. In the case of Bu₄NBr, the effect of size of the alcohol (methahol ton-butanol) was also investigated. From the corresponding freezing-point data for the binary systems the apparent salting constants were calculated. The true salting constantsk _s were obtained by extrapolation to infinite dilution. These are all very close to zero at the freezing temperature. From the corresponding thermochemical data the temperature dependence ofk _s was calculated, and above 5°C all the R₄NBr salts int-butanol; the salting-in increases with temperature and with the size of the hydrophobic cations. The scaled-particle theory is at present the only one which can account semiquantitatively for the temperature dependence of the salting-in effect. On leave of absence from Chemistry Department, The University, Sheffield S3 7HF, England To whom correspondence should be addressed.     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.     

Thermodynamic properties of alkali halides. IV. Apparent molal volumes,expansibilities, compressibilities,and heat capacities in urea-water mixtures

The apparent molal volume φ_v, expansibility φ_E, compressibility φ_K, and heat capacity φ_c of NaCl were measured in urea-water mixtures, as a function of salt (<1.5m) and urea (<13m) concentrations at 25°C. At a fixed urea concentration, the transfer functions from H₂O to 3m urea are linear functions of the NaCl aquamolality. At a fixed salt aquamolality, (0.1m), the sign of the transfer functions is in the direction of a decrease in the structure-breaking effect, and the absolute values of the transfer functions tend to level off at high urea concentrations (13m). The functions φ_v, φ_E, φ_K, φ_c, and (?φ_v/?T)_p were measured for the sodium halides and alkali, bromides (chlorides in the case of φ_K) at a fixed salt aquamolality of 0.1m and fixed urea molality of 3m. The corresponding transfer functions from H₂O to 3m urea are opposite those from H₂O to D₂O and similarly are relatively independent of ionic size. This suggests that urea, shows no specific interaction affinity for ions and that the overall number of water molecules influenced by the ions is relatively constant for all alkali halides. The lithium halides are an exception in that Li⁺ seems to have hardly any structure-breaking effect.     

Anionic graft polymerization of methyl methacrylate on starch and dextrin

The anionic graft polymerization of methyl methacrylate on the potassium alkoxide derivative of starch or dextrin in DMSO was studied. The effects of monomer and alkoxide concentrations as well as temperature were investigated. The yield of graft polymer increased with increasing alkoxide concentration. With increasing monomer concentration and with increasing temperature the extent of homopolymer formation increased. The composition of the graft polymers was found to depend on the reaction conditions. Graft polymers having about 10–40% poly(methyl methacrylate) were obtained. There were quantitative differences in yield of isolated graft polymer between starch and dextrin and these were ascribed to differences in the solubility properties of the carbohydrates. Evidence on the structure of the graft polymers and on the mechanism of the graft polymerization was obtained from acid hydrolysis of the graft polymers and determination of the molecular weights of the cleaved side chains.     

Structure and reactivity of xanthocorrinoids. Part V. Formation of trans-diol derivatives of 5,6-dihydrocobyrinic acid from xanthocorrinoids under acidic conditions

On treatment with H₂SO₄/MeOH, epimerization of hexamethyl cis-5,6-dihydroxycobyrinate c,8-lactam ( 3 ) takes place quantitatively at C(6), yielding the corresponding trans-diol 4 . The corresponding lactone 7 , whose structure has been established by X-ray analysis, is obtained from xanthocorrinoids 5 and 6 under similar conditions.