Journal of Mathematical Chemistry最新文献

One of the most important information related to molecular graphs is given by the determination (when possible) of upper and lower bounds for their corresponding topological indices. Such bounds allow to establish the approximate range of the topological indices in terms of molecular structural parameters. The purpose of this paper is to provide new inequalities relating several classes of variable topological indices including the first and second general Zagreb indices, the general sum-connectivity index, and the variable inverse sum deg index. Also, upper and lower bounds on the inverse degree in terms of the first general Zagreb are found. Moreover, the characterization of extremal graphs with respect to many of these inequalities is obtained. Finally, some applications are given.

We developed in this paper the used methodology to describe the Lennard-Jones potential of two atoms in rare gas. In this treatment we supposed that one atom could be described by a harmonic oscillator. The interaction potential is developed at short and long ranges. The results showed that the obtained physico-chemical parameters such as the oscillator frequency, the atom mass, and the atom charge well reproduce the Lennard-Jones potential. Then the potential well depth and the effective equilibrium diameter are expressed in function of the oscillator frequency, the atom mass and charge.

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Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second-order methods. The perturbation strength is parametrized by the Sommerfeld factor (the quotient of the nuclear charge and the relative velocity of the colliding particles). At each fixed impact energy, the sought sensitivity is monitored by gradually modifying the nuclear charges in the Sommerfeld factors. These factors reside in the Coulomb distortions of the unperturbed channels states. The focus is on the electronic distortions through the eikonal Coulomb logarithmic phases and the full Coulomb waves. The logarithmic phases are the constituents of the compound phases for the net charges of the two heavy scattering aggregates in relative motions. A striking perturbation strength sensitivity of the obtained total cross sections is recorded.

In this paper, a fractional differential equation with integral conditions is studied. The fractional differential equation is transformed into an integral equation with two initial values, where the initial values needs to ensure that the exact solution satisfies the integral boundary conditions. A graded mesh based on a priori information of the exact solution is constructed and the linear interpolation is used to approximate the functions in the fractional integral. The rigorous analysis about the convergence of the discretization scheme is derived by using the truncation error estimate techniques and the generalized Grönwall inequality. A quasi-Newton method is used to determine the initial values so that the numerical solution satisfies two integral boundary conditions within a prescribed precision. It is shown that the scheme is second-order convergent, which improves the results on the uniform mesh.

High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the chemical hypergraph, which relates couples of subsets (hypervertices) of an arbitrary number of vertices. Here we develop the Erdős–Rényi model for chemical hypergraphs, which corresponds to the random realisation of edges of the complete chemical hypergraph. A particular feature of random chemical hypergraphs is that the ratio between their expected number of edges and their expected degree or size is 3/2 for large number of vertices. We highlight the suitability of chemical hypergraphs for modelling large collections of chemical reactions and the importance of random chemical hypergraphs to analyse the unfolding of chemistry.

In this paper, we investigate a time two-grid algorithm to get the numerical solution of nonlinear generalized viscous Burgers’ equation, which is the first time that the two-grid method is used to solve this problem. Based on Crank–Nicolson finite difference scheme, we establish the time two-grid difference (TTGD) scheme which consists of three computational procedures to reduce the computational cost compared with the general finite difference (GFD) scheme. The cut-offf function method is applied to prove the conservation, unique solvability, the prior estimate and convergence in (L^2)-norm and (L^{infty })-norm of the TTGD scheme on the coarse grid and fine grid, respectively. Comparing our TTGD scheme with GFD scheme in Zhang et al. (Appl Math Lett 112:106719, 2021), we provided the proof the uniqueness the solution of the nonlinear scheme, direct proof of convergence in (L^2)-norm and the prior estimate both on the coarse mesh and fine mesh. The numerical results show that our TTGD scheme is more efficient than the GDF scheme in Zhang et al. (2021) in terms of the CPU time. Particularly, our method not only improves the efficiency, but also preserves the energy conservation of the original model.

A universal method, called pivotal condensation, for calculating stoichiometric factors of chemical reactions is presented. It is based on our new approach for calculating the basis of the kernel of a matrix over the field of rational numbers. This approach is referred to as kernel pivotal condensation (ker pc) and is presented in detail. It has roughly the same complexity as Gaussian elimination, but can be performed without working with fractions. It is also shown how ker pc can be adapted as a tool to solve inhomogeneous linear systems, invert matrices (this is referred to as inv pc) and determine simultaneously the four subspaces (referred to as 4 pc). Besides, the balancing by inspection method, which is widely used in practice to reduce the size of a linear system arising in chemical balancing, is formulated in a mathematical language. When calculating stoichiometric factors of chemical balancing problems with a non-unique solution the natural question arises how to determine a basis that generates all the solutions over the integers. A method, referred to as smitheration, is introduced that permits to determine such an integer basis from a basis over the rational numbers. If there are few solutions this approach is more efficient than calculating a Smith normal form directly. It is convenient to work over principal ideal domains instead of the ring of integers, so that one can treat balancing problems that depend on one parameter as well.

A high-order numerical scheme based on collocation of a quintic B-spline over finite element is proposed for the numerical solution of a class of nonlinear singular boundary value problems (SBVPs) arising in various physical models in engineering and applied sciences. Five illustrative examples are presented to illustrate the applicability and accuracy of the method. In order to justify the advantage of the proposed numerical scheme, the computed results are compared with the results obtained by two other fourth-order numerical methods, namely the finite difference method (Chawla et al. in BIT 28(1):88–97, 1988) and B-spline collocation method (Goh et al. in Comput Math Appl 64:115–120, 2012).

Convective energy and mass transfer in a non-Newtonian fluid layers a wide-spread physical phenomenon in natural and technical systems. Triple diffusive convection plays a crucial role in chemical engineering by enabling the understanding and optimisation of mass transfer processes involving multiple components. It is essential for designing efficient separation systems, optimising catalysts, predicting reaction kinetics, and improving environmental processes. The motivation of this paper is to explore an Oscillatory flow of a triple diffusive convection in a Voigt fluid layer. The governing partial differential equations are transformed into coupled ordinary differential equations with the help of the oscillation technique. The study emphasises the effects of known physical parameters, such as the thermal Grashof number, solutal Grashof number, Prandtl number, Lewis numbers and Voigt fluid parameters on velocity, temperature, concentrations and rate of heat and mass transfers. In particularly, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate.