Relating Total π-Electron Energy and Resonance Energy of Benzenoid Molecules with Kekulé- and Clar-Structure-Based Parameters

Summary. Within classes of isomeric benzenoid hydrocarbons various Kekulé- and Clar-structure-based parameters (Kekulé structure count, Clar cover count, Herndon number, Zhang–Zhang polynomial) are all mutually correlated. This explains why both the total π-electron energy (E), the Dewar resonance energy (DRE), and the topological resonance energy (TRE) are well correlated with all these parameters. Nevertheless, there exists an optimal value of the variable of the Zhang–Zhang polynomial for which it yields the best results. This optimal value is negative-valued for E, around zero for TRE, and positive-valued for DRE. A somewhat surprising result is that TRE and DRE considerably differ in their dependence on Kekulé- and Clar-structure-based parameters.     

Estimation of very narrow bounds to the behavior of nonlinear incompressible elastic composites

Variational bounds for the effective behavior of nonlinear composites are improved by incorporating more-detailed morphological information. Such bounds, which are obtained from the generalized Hashin–Shtrikman variational principles, make use of a reference material with the same microstructure as the nonlinear composite. The geometrical information is contained in the effective properties of the reference material, which are explicitly present in the analytical formulae of the nonlinear bounds. In this paper, the variational approach is combined with estimates for the effective properties of the reference composite via the asymptotic homogenization method (AHM), and applied to a hexagonally periodic fiber-reinforced incompressible nonlinear elastic composite, significantly improving some recent results.     

Pointwise Growth and Uniqueness of Positive Solutions for a Class of Sublinear Elliptic Problems where Bifurcation from Infinity Occurs

In this paper we analyze the uniqueness and the pointwise growth of the positive solutions of a nonlinear elliptic boundary‐value problem of general sublinear type with a weight function multiplying the nonlinearity. When this function vanishes on some subdomain, the problem exhibits a bifurcation from infinity. In this case almost nothing is known about the pointwise growth of the positive solutions as the parameter approaches the critical value where the bifurcation from infinity occurs. In this work we show that the positive solutions grow to infinity in the region where the weight function vanishes and that on its support they stabilize to the minimal positive solution of the original equation subject to infinite Dirichlet boundary conditions. This behavior provides us with the uniqueness of the positive solution near the value of the parameter where the bifurcation from infinity occurs. Also, we solve the problem using spectral collocation methods coupled with path‐following techniques to show how the main uniqueness result is optimal. Throughout the paper the mathematical analysis aids the numerical study, and the numerical study confirms and illuminates the analysis. (Accepted February 17, 1998)     

Dynamics of Nonlinear Random Walks on Complex Networks

Journal of Nonlinear Science - In this paper, we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition...     

The 1,3-dipolar cycloaddition of 1H-pyridinium-3-olate and 1-methylpyridinium-3-olate with methyl acrylate: a density functional theory study

The 1,3-dipolar cycloaddition reaction of 1-substituted pyridinium 3-olates with methyl acrylate is studied using density functional theory (DFT) method at the B3LYP/6-31G(d) level. The molecular mechanisms of the possible stereo- and regio-chemical pathways are characterized and explored. Solvent effects are also evaluated by the polarizable continuum model (PCM). Analysis of the results shows that there are relevant differences in the reaction pathways between the gas phase and with solvent. Only results in solvent phase are in accord with literature experimental results where 6-substituted 8-azabicyclo[3.2.1]oct-3-en-2-ones are formed preferentially. These polar cycloaddition reactions take place through highly asynchronous transition states in which nucleophilic attack by C2/C6 of the pyridinium-3-olates on the more electrophilic centre of the methyl acrylate initiates the process. Analysis of global and local indexes of the reactants is evaluated in order to explain the observed regioselectivity. Rate constants are calculated at room temperature using conventional transition state theory.     

Carbonization of electrospun poly(acrylonitrile) nanofibers containing multiwalled carbon nanotubes observed by transmission electron microscope with in situ heating

Composite nanofibers with 5% w/w multiwalled carbon nanotubes (MWCNTs) in polyacrylonitrile (PAN) were fabricated using the electrospinning technique. Morphological development during the carbonization process was characterized by transmission electron microscopy (TEM) with in situ heating. It was found that the orientation of graphitic layers increases with temperature and does not change significantly with time during our TEM measurement, except the 750 °C. In the heating stage at 750 °C noticeable enhancement of orientation with time was observed. The presence of embedded CNTs enhances the order of the formed graphitic structures even when the CNTs are irregular or entangled. The results indicate that embedded MWCNTs in the PAN nanofibers nucleate the growth of carbon crystals during PAN carbonization. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Quinine‐Derived Imidazolidin‐2‐imine Ligands: Synthesis,Coordination Chemistry,and Application in Catalytic Transfer Hydrogenation

Two new optically active bidentate N,N‐ligands, DMIQCI ( 3a ) and DMIQCD ( 3b ), containing a quinuclidine core and an imidazolidin‐2‐imine unit, were synthesized. The reaction of these ligands with [(η⁵‐C₅Me₅)RuCl]₄ afforded the brick‐red ruthenium(II) complexes [(η⁵‐C₅Me₅)Ru(DMIQCI)Cl] ( 4 ) and [(η⁵‐C₅Me₅)Ru(DMIQCD)Cl] ( 5 ), which were used as catalysts in the transfer hydrogenation of acetophenone in boiling 2‐propanol. The reactions of 3a and 3b with [(COD)PdCl₂] (COD = 1,5‐cycloocta‐diene) and with [(DME)NiBr₂] (DME = 1,2‐dimethoxyethane) afforded the square‐planar palladium(II) complexes [(DMIQCI)PdCl₂] ( 7 ) and [(DMIQCD)PdCl₂] ( 8 ) or the tetrahedral nickel(II) complexes [(DMIQCI)NiBr₂] ( 9 ) and [(DMIQCD)NiBr₂] ( 10 ), respectively. The X‐ray crystal structures of 4 , 7 , 9· THF, and 10 are reported.     

On the stability of the linear differential equation of higher order with constant coefficients

We obtain a result on stability of the linear differential equation of higher order with constant coefficients in Aoki-Rassias sense. As a consequence we obtain the Hyers-Ulam stability of the above mentioned equation. A connection with dynamical sytems perturbation is established.