Iranian Journal of Mathematical Chemistry
Year:2014 | Volume:5 | Issue:1|Papers Count:7

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In the present study we compute some bounds of multiplicative Zagreb indices and then we study these topological indices by using concept of chromatic number and clique number.

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

In the present study an alternative model allows the extension of the Debye- Huckel Theory (DHT) considering time dependence explicitly. From the Electro-Quasistatic approach (EQS) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.This leads to a new formulation of the meaning of the nonlinear Poisson-Boltzmann Equation (PBE). If a concentration and/or flux gradient of particles is considered the original structure of the mPBE will be modified leading to a new nonlinear partial differential equation (nPDE) of the third order. It is shown how one can derive classes of solutions for the potential function analytically by application of an algebraic method. The benefit of the mathematical tools used here is the fact that closed-form solutions can be calculated without any numerical approximations.

boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad’e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for solving singular boundary value problems arising in the reaction cum diffusion process in a spherical biocatalyst. ChFD method can be regarded as a non-uniform finite difference scheme and DTM is a numerical method based on the Taylor series expansion, which constructs an analytical solution in the form of a polynomial. The main advantage of DTM is that it can be applied directly to nonlinear ordinary without requiring linearization, discretization or perturbation. Therefore, it is not affected by errors associated to discretization. The results obtained, are in good agreement with those obtained numerically or by optimal homotopy analysis method.

In this paper, we calculate the eccentric connectivity index and the eccentricity sequences of two infinite classes of fullerenes with 50+10k and 60+12k (kÎN) carbon atoms.

Let H be a finite dimensional complex Hilbert space, B(H)+ be the set of all positive semi-definite operators on H and j is a (not necessarily linear) unital map of B(H)+ preserving the Entropy-Gibbs transformation. Then there exists either a unitary or an anti-unitary operator U on H such that j(A)=UAU* for any AÎB(H)+.