EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.     

The stoichiometric hydrogenation of 9-methylidenefluorene and related compounds with hydridocobalt tetracarbonyl

9-Methylideneflourene (IIa) reacts rapidly with HCo(CO)₄ at -67° C to give a quantitative yield of 9-methylfluorene (IIIa); k₂  (13.4 ± 0.5) × 10^-2 l mol^-1_S^-1. Although the internal olefin, 9-ethylidenefluorene (IIb) reacts more slowly than IIa, it is hydrogenated about 2.5 times as fast as the terminal olefin, 1,1-diphenylethylene (I). Measurement of the rate of the reaction of IIb with DCo(CO)₄ and comparison with HCo(CO)₄ shows a very large inverse isotope effect k_H/k_D of 0.43.     

NMR investigation on the conformational properties of N-[2-pyridyl-N-oxide]-amino derivatives

The proton NMR spectra of N-[2-pyridyl-N-oxide]-derivatives of primary and secondary ethylamines, containing a substituent R on the C atom bearing the amino function, have been completely analysed in terms of the fundamental NMR parameters. The preferred conformations of the compounds investigated were established by the indications from NOE experiments as well as: (1) the long range coupling across the five bond between the aminic hydrogen and the proton in 4-position of the pyridine-N-oxide ring (⁵J_m^H,NH ～ 0·5 c/s), (2) the value of the vicinal coupling constant in the fragment CHNH (³J_NHCH ～ 7–9 c/s), (3) the large deshielding (Δτ ～ 1–1·5 ppm) observed for the resonance position of the proton on the asymmetric C atom in secondary amine derivatives with respect to the corresponding primary ones, and (4) the diamagnetic shielding produced on protons in position 3 and 4 of the pyridine-N-oxide ring by different aromatic groups introduced in the R substituent.The NMR data confirmed the preferred rotamers previously suggested on the basis of ORD and CD measurements.     

Electronic control of stereoselectivity. 20. Crystal and molecular structure of the ferrocene derived from tricyclo[5.2.1.02,6]Deca-2,5,8-triene

Reaction of the isodicyclopentadienide anion and its dehydro congener with Fe(II) leads to a stereochemically homogeneous ferrocene derivative in each instance. Through chemical correlation and X-ray analysis, above-plane complexation is established for both halves within the two sandwich compounds.     

Thermophysics of alkali and related azides II. Heat capacities of potassium,rubidium, cesium,and thallium azides from 5 to 350 K

The heat capacities of potassium, rubidium, cesium, and thallium azides were determined from 5 to 350 K by adiabatic calorimetry. Although the alkali-metal azides studied in this work exhibited no thermal anomalies over the temperature range studied, thallium azide has a bifurcated anomaly with two maxima at (233.0±0.1) K and (242.04±0.02) K. The associated excess entropy was 0.90 cal_th K^?1 mol^?1. The thermal properties of the azides and the corresponding structurally similar hydrogen difluorides are nearly identical. Both have linear symmetrical anions. However, thallium azide shows a solid-solid phase transition not exhibited by thallium hydrogen difluoride. At 298.15 K the values of C_p^o, S^o, and $\text{?{G}{}^{\mathrm{o}}\text{(T)?H}{}^{\mathrm{o}}\text{(0)}}\text{T}$, respectively, are 18.38, 24.86, and 12.676 cal_th K^?1 mol^?1 for potassium azide; 19.09, 28.78, and 15.58 cal_th K^?1 mol^?1 for rubidium azide; 19.89, 32.11, and 18.17 cal_th K^?1 mol^?1 for cesium azide; and 19.26, 32.09, and 18.69 cal_th K^?1 mol^?1 for thallium azide. Heat capacities at constant volume for KN₃ were deduced from infrared and Raman data.     

X-ray diffraction studies of glasses in the systems Na2OMeOSiO2 (MeMg,Zn, Ca,Ba)

X-ray diffraction studies of glasses in the following ternary systems have been made: Na₂OMgOSiO₂, Na₂OZnOSiO₂, Na₂OCaOSiO₂ and Na₂OBaOSiO₂. The following heavy atom substitutions have been used: Ag for Na and Ge for Si. The changes in the electron radial distribution curves resulting from AgNa replacement can be explained as amplifications of relatively well-defined NaSi distances, which are nearly the same in all the glasses investigated. The GeSi substitution causes changes which can be explained on the basis of isostructural GeSi substitutions.     

The condensation of methyl 2-methlylpropanoate with chiral aldehydes. X-ray crystal structure of (3rs,4sr) 3-hydroxy-4-phenyl-2,2,4-trimethylpentanoic acid

The lithium enolate derived from methyl 2-methylpropanoate reacts stereoselectively with 2-phenylpropanal and 2-(cyclohexyl)propanal, affording mainly the $\text{syn}$ β-hydroxy ester in both cases. With 2-ethylhexanal, no selectivity was observed.     

The stoichiometric hydrogenation of 1,1-diphenylethylene with hydridocobalt tetracarbonyl; differences from the hydroformylation reaction

The kinetics of the stoichiometric hydrogenation of 1,1-diphenylethylene with HCo(CO)₄ is cleanly second order, permitting a determination of the activation parameters. The rate is unaffected by the atmosphere over the reaction and is enhanced by substituting DCo(CO)₄ for HCo(CO)₄. These results contrast sharply with those secured in the hydroformylation of 1-alkenes and thus dual mechanistic pathways are available for the reaction of HCo(CO)₄ with unsaturated systems. It is very possible that the stoichiometric hydrogenation of 1,1-diphenylethylene involves a geminate free radical pair but definitive proof is still lacking.