Journal of Mathematical Chemistry最新文献

We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz method are increasingly accurate upper bounds to the exact ones. To this end, we resort to the variational principle and to a set of suitable projection operators.

This paper presents a qualitative study of a reversible biochemical reaction model with cross-diffusion and Michalis saturation. For the system without diffusion, the existence, stability and Hopf bifurcation of the positive equilibrium have been clearly determined. For the cross-diffusive system, the stability and Turing instability driven by cross-diffusion are studied according to the relationship between the self-diffusion and the cross-diffusion coefficients. Stability and cross-diffusion instability regions are theoretically determined in the plane of the cross-diffusion coefficients. The amplitude equation is derived by using the technique of multiple time scale. With the help of numerical simulation, we verify the analysis results.

It is possible to eliminate phase-lag and all of its derivatives up to order five by employing a method that takes fading phase-lag into consideration. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new method called the cost-efficient approach. The unique method is illustrated by the symbol PF5DPHFITN142SPS. This approach is P-Stable, which means it is infinitely periodic. A wide variety of periodic and oscillatory issues can be solved using the suggested approach. The challenging problem of Schrödinger-type coupled differential equations in quantum chemistry was tackled using this novel approach. With only (5,FEvs) needed to complete each step, the new method could be considered as a cost-effective approach. An AOR of 14 allows us to significantly improve our present condition.

This paper presents a novel approach for constructing the lower and upper boundaries of closed regions where solutions to the singular nonlinear diffusion problems

exist. This existence result is proved using the method of lower and upper solutions with monotone iterative technique under the restriction that f(x, y) is continuous in (x in [0,1]) and non-increasing in y in such regions. Additional uniqueness criteria is also established. The approach is illustrated on four singular nonlinear diffusion problems including some real life applications.

This study employs Molecular Dynamics (MD) simulations to investigate the mechanical properties of single-layer X-graphene and Y-graphene in both armchair and zigzag configurations, as well as multi-walled nanotubes with varying stacking orders. The nanotubes are constructed using various combinations of armchair and zigzag configurations for the X-graphene and Y-graphene layers, arranged in distinct stacking patterns. Analysis of fracture and stress distribution in the X-graphene and Y-graphene nanotubes indicates a soft mechanical behavior. Additionally, stress–strain curve analysis shows that, within the initial elastic range, the curves coincide, suggesting that nanotube length does not significantly affect behavior in this region. The ultimate stress and strain of the X-graphene and Y-graphene nanotubes decrease with increasing length, while the toughness also diminishes as the length of the nanotubes increases. Notably, for double-walled nanotubes with both layers oriented in the zigzag configuration, the stress–strain response is slightly higher compared to other configurations.

Metal organic frameworks (MOFs) are not only fundamentally interesting due to their intricate and complex network structures but also due to their applied significance in enhancing the performance of various technologies, owing to their porous nature, large surface areas, and tunable structural architecture. Hence, they find applications in energy storage, catalysis, gas separation, and sensing technologies. Oxalates play a key role in the sequestration of toxic metal ions through efficient MOFs with tunable pores. This paper investigates graph descriptors, entropy, and spectral properties of oxalate-based MOFs. We have developed innovative mathematical methods to calculate distance based graph descriptors for a series of interconnected pentagonal networks that represent MOFs. We also compute the spectral based graph energies and the entropies of MOFs using techniques of graph theory. We have presented a regression technique for the efficient generation of the graph energies of these networks from their graph descriptors.

Differential cross sections for simultaneous capture of both electrons by alpha particles from helium targets are computed. Employed are several quantum-mechanical distorted wave four-body methods of first- and second-orders. The main focus is on the cross section sensitivity as a function of different perturbation interactions and scattering states. Two aspects are considered. One is for theories with the same perturbation interactions and different scattering states. The other is for theories with the same scattering states and different perturbation interactions. In this context, the interference effect on two levels is examined. One compares the yields from the internuclear potential and the interactions between nuclei and two electrons. The other contrasts the contributions from the channel states with and without the distorted waves generated by the relative motions of nuclei. Depending on the employed theory, differential cross sections can be strongly or mildly influenced by the variability in all the mentioned frameworks. The salient illustrations are reported at intermediate energies 180-900 keV for which the experimental data are available. It is found that the second-order theories are in much better agreement with the measured cross sections than the first-order theories.

We simplify some proposed formulas for hydrostatic pressure on a molecule by G. Subramanian, N. Mathew and J. Leiding, J. Chem. Phys. 143, 134109 (2015). We apply the formulas to an artificial triatom ABC whose potential energy surface is formed by a combination of Morse curves.

Let (G=(V(G),E(G))) be a simple graph and denote by (d_{u}) the degree of the vertex (uin V(G)). Using a geometric approach, Gutman introduced a new vertex-degree-based topological index, defined as

and named Sombor index. It is a molecular descriptor with an impressive research activity in recent years. In this paper we propose and initiate the study of a family of topological indices, also conceived from a geometric point of view, called irregularity integral Sombor indices, that generalize the Sombor index. Also, we study the application of these indices in QSPR/QSAR research.

As is known that many existing numerical methods for time fractional nonlinear subdiffusion equations (TFNSEs) often suffer from the phenomenon of order reduction, because the solution of TFNSEs usually has the initial singularity. To overcome this order reduction problem, in this paper, an improved Euler method is proposed for solving TFNSEs based on the technique of variable transformation in time. Then, it is proved that the temporal convergence order of the proposed method is the first order for any fractional order (alpha in (0,1)), which achieves the optimal convergence order of the Euler method. Finally, numerical experiments are given to verify the correctness of our theoretical results.