Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.     

Characterization of measures by potentials

Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f _E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l _∞ ⁿ and wheref(t)=|t| ^p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ _∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ _∞) is positive definite only iff is a constant function.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Best possibility of the Furuta inequality

Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but .

     

Correlations of13C chemical shifts and geometry modifications

The effect of geometry modifications of¹³C chemical shifts has been investigated in a small subset of molecules using both LO-INDO and Gaussian 70 (4–31) calculations. The Gaussian calculations, while known to give poor absolute shifts, compare well to the reparameterized semi-empirical INDO determinations in calculated shift changes. In virtually all cases the signs of the shift changes were found to be opposite to that of the changes in the calculated electronic energy.     

Ab initio molecular modeling of 13C NMR chemical shifts of polymers. 1. Ethylene–norbornene copolymers

Cycloolefin copolymers (COC) have recently raised much interest because of their excellent thermal and optical properties, largely determined by the chain composition and stereochemistry. Previous force‐field computations allowed us to define the main conformational characteristics of ethylene–norbornene (E–N) copolymers and to contribute to the elucidation of their microstructure on the basis of empirical relationships between conformation and ¹³C nuclear magnetic resonance (NMR) chemical shifts. A thorough test of ab initio ¹³C chemical shifts computations [gauge‐invariant atomic orbitals (GIAO)] on known cases shows that the agreement with experimental data is quite good, especially with the MPW1PW91 density functional theory (DFT), using the 6‐311+G(2d,p) basis set on properly energy‐minimized structures. We applied this method on proper model compounds to confirm the signal assignment of the spectra of E–N copolymers in the presence of norbornene microblocks, where strong effects arising from ring distortions are expected to occur. The results nicely confirm the latest assignment of norbornene signals belonging to ENNE sequences. This shows the great potentialities of GIAO/DFT computations with regard to complex spectra interpretation and polymer microstructural investigations. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.     

Electronic Structure, Aromaticity, and Physicochemical Characteristics of Carbene, Radical, and Ionic Forms of Compounds of the Imidazole Series, and their Oxo and Thio Analogs

The effects of benzannellation, phenyl substitution at the nitrogen atom, protonation at the carbene carbon, ionization, and the state of the carbene center (² or ²) on the electronic structure, diamagnetic susceptibility, induced -electron ring currents, the ¹H, ¹³C, and ¹⁴N chemical shifts, and the energies of the lowest electronic transitions of imidazol-2-ylidenes and their oxo and thio analogs were examined in the bound version of -electron perturbation theory. The calculated and experimental data are compared.     

15N NMR spectral parameters of compounds of the N-methylpyrazole series

The¹⁵N NMR chemical shifts and¹⁵N-¹H SSCCs are presented for substituted N-methylpyrazoles with substituents such as CH₃, NO₂, Br, Cl, NH₂, O=CNH₂, O=CPh, and COOH at the carbon atoms. The¹⁵N chemical shifts of the cyclic atoms of nitrogen and the nitro groups are discussed as well as the geminal and vicinal SSCCs of the ring nitrogen atoms with the hydrogen atoms of the CH and CH₃ fragments.N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117334 Moscow. D. I. Mendeleev Chemico-Technological Institute, Moscow, Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 11, pp. 2554–2561, November, 1992.     

Nuclear magnetic resonance spectroscopic study on ionic liquids of 1-alkyl-3-methylimidazolium salts

Chemical shifts of ¹H and ¹³C NMR of series of methylimidazolium salts (MIM⁺, X=Br⁻, BF₄⁻ and PF₆⁻) function on the length of alkyl groups on the ring, type of solvents and the concentration. The bromides series demonstrate more chemical shift variation on H2 upon the change of solvents and concentration. Unexpected H-D exchange reactions were also observed in the MIM⁺Br⁻ by using CD₃OD and D₂O. The exchange rates strongly depend on the length of the alkyl group, which could cause more steric factor to reduce the interaction between deuterium atom from solvent and C2 of the ring.