Journal of Mathematical Chemistry最新文献

We present combinatorial cum group theoretical generating function methods for vertex and face colorings of a dodecahedron for all irreducible representations of the icosahedral group. We demonstrate the usefulness of the Mȍbius inversion method. We consider several types of distortions arising from the highly symmetric dodecahedron, in particular, to an elongated dodecahedron and a pyrithohedron (T_h). Elaborate combinatorial enumerations and tables of combinatorial numbers are explicitly constructed for all irreducible representations of both the distorted and the parent undistorted structures. It is shown that the combinatorial cum computational techniques provide new insights into the dynamic chirality arising from such distortions which include the pentagonal distortions, elongated distortions and so forth. We point out applications to the dynamic NMR and ESR spectroscopies as well to the dynamic stereochemistry of topological metamorphosis through a combination of combinatorics and group theory.

By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The cost-efficient approach is a new strategy whose aims are to boost algebraic order (AOR) and reduce function evaluations (FEVs). The symbolic representation of the one-of-a-kind approach is PF6DPHFITN142SPS. This method is infinitely periodic since it is P-Stable. The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires (5 , FEVs), the new method could be seen as a cost-effective strategy. With a AOR of 14, we can greatly enhance our current situation.

Extensive studies have investigated second-order singular differential equations to model various phenomena in astrophysics, reaction-diffusion processes, and electrohydrodynamics. However, finding numerical and analytical solutions for these problems with appropriate boundary conditions is challenging due to their inherent nonlinearity. Our current study explores singular second-order differential equations (SSODEs) with boundary conditions, specifically those modelling the distribution of heat sources in the human head and the steady-state temperature distribution in a vessel before a thermal explosion. The fundamental idea behind our approach is initially transforming the differential equation into an equivalent integral form, thereby circumventing the singular behaviour. Subsequently, the optimal homotopy analysis method is employed to scrutinize two distinct models, i.e., the heat conduction model, the thermal explosion model and the spherical catalyst equation. Further, a detailed convergence analysis is conducted in a Banach space framework to ensure the method’s reliability. The accuracy of the new approach is checked by considering various numerical examples with different values of thermogenesis heat production, the Biot number, and metabolic thermogenesis slope. It has been shown that the proposed approach qualitatively and quantitatively approximates the solutions with higher precision than the existing Adomian decomposition method.

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.

In this manuscript, a possible local softness and local molecular quantum similarity relationship is postulated. These outcomes were obtained using softness, Fukui functions and the Molecular Quantum Similarity context, to obtain a possible way to relate the local softness between molecules A and B. This methodology offers a potential approach for identifying systematic relationships within each molecular ensemble by using selectivity defined in the Density Functional Theory framework.

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.