Journal of Mathematical Chemistry最新文献

An oxide of the perovskite type, barium zirconate (BaZrO3), has attracted a lot of interest for use as a potential candidate for electrolyte of solid oxide fuel cells (SOFCs) that conduct protons. The perovskite crystal structure of BaZrO3 is well-known for its adaptability in accepting various dopants and preserving stability in a range of circumstances. BaZrO3 is appropriate for the severe operating conditions of SOFCs because it is chemically stable in both reducing and oxidizing environments. When doped, BaZrO3 acts as an electrolyte that conducts protons. Protons (H+), which travel through the crystal structure to complete the fuel cell circuit, are the main charge carriers in these materials. BaZrO3 can function at lower temperatures, which lessens thermal stress and lengthens the life of fuel cells. Additionally, a greater variety of fuels, including ones with higher hydrogen contents, are permitted. The examination of the mechanism underlying the enhanced performance requires the atomic knowledge. We have used the ab-initio DFT computation for that. Band-gap and electrochemical stability assessments have been made more accurate by using Grimme d3 dispersion correction and PBE. A distinct metric, the global instability index (GII), was employed to evaluate the thermodynamic stability of BaZrO3 and the doped structures. It bases its calculation on the bond valence sum technique utilized in SoftBV. All DFT calculations were carried out using Quantum ESPRESSO pwscf codes. XCrySDen and VESTA, two open-source programs, were used to create all of the visuals.

This paper investigates the temporally loaded time-fractional diffusion equation with initial and Dirichlet-type boundary conditions. To begin with, a solution form is established using the method of eigenfunction expansions, and its existence and uniqueness are examined along with some apriori estimates. Thereafter, a finite difference approximation is performed using the so-called L1 method for the Caputo fractional derivative, resulting in a loaded difference scheme. The superposition property of systems of linear algebraic equations is applied to solve the loaded difference scheme by appointing an appropriate solution representation. The unique solvability of the proposed scheme is set up. The stability and convergence of the proposed difference scheme are analysed by the discrete energy method with an order of accuracy (mathcal {O}(tau ^{2-alpha }+h^2)). Numerical results via two test problems are presented to validate the theoretical findings of the proposed scheme by observing the errors.

The first inverse Nirmala index is a novel degree-based topological descriptor that was introduced in 2021. Preliminary QSPR investigations suggest that this index deserves further consideration because of its unusually good predictive potential. This paper investigates the relations between this index with some elementary graph quantities and some related degree-based topological index. Further, the computational analysis will reveal extremal graphs among trees, molecular trees, all connected graphs, and their molecular counterparts.

In this work, we introduce the q-Rényi’s divergence, which results from the conjunction of Rényi’s divergence and Jackson’s integral. The resultant equation can be employed as a measure of chemical similarity, which consists of comparing two or more chemical species with a set of molecules that have been characterized to find two or more molecules that could have similar chemical or physical properties. To carry out our study, we applied q-Rényi’s divergence using a set of Tetrodotoxin variants and a set of 1641 organic molecules. Our results suggest that q-Rényi’s divergence could be a valuable tool to complement chemical similarity studies.

In present research work, numerical approx. of one- and two-dimensional Hyperbolic Telegraph equations is fetched with aid of Modified Cubic and Quartic Hyperbolic B-spline Differential Quadrature Methods. Modified cubic B-spline is used in Differential Quadrature Method to find weighting coefficients for Method I. Modified Quartic Hyperbolic B-spline is utilized to attain weighting coefficients for Method II. After spatial discretization partial differential equations got reduced in the system of ODEs, which later on tackled with SSPRK43 regime. Total ten Examples are discussed to check the efficacy and robustness of the implemented method. For comparison of results, error norms are evaluated. Graphical presentation of the results is also provided. It got noticed that, in most of the cases, exact solutions and present numerical solutions were compatible. The present scheme is easy to implement and it is a better approach to solve some complex natured partial differential equations. The cubic Hyperbolic B-spline has produced much better errors than the Quartic Hyperbolic B-spline. The statistical validation of the parameters is also provided via generating the correlation matrix heatmap.

The goal of this paper is to characterize the existence of positive equilibria of power law systems through their kinetics-based decompositions. To achieve this, we consider subclasses of power law systems: PL-RDK and PL-TIK systems. PL-RDK systems are those in which the kinetic order vectors are reactant-determined, that is, branching reactions have identical vectors. PL-TIK systems are characterized by having linearly independent kinetic order vectors per linkage class. We first introduced the notion of Zero Kinetic Deficiency Decomposition of cycle terminal power law systems. Then, by considering non-cycle terminal power law systems, we extend this by introducing the notion of PL-TIK decomposition. Through these novel decomposition classes, we showed that PL-RDK systems with weakly reversible decompositions admit positive equilibria. Moreover, to ensure the existence of PL-TIK decomposition, we developed an algorithm in which any power law system can generate a PL-TIK decomposition. Lastly, we applied the algorithm to Schmitz’ Global Carbon Cycle Model.

The normalization of the polar functions (Theta _{ell , m} (theta )) for the solution of Schrödinger’s equation for the Coulomb potential usually proceeds by appealing to the properties of Associated Legendre polynomials. We show how to achieve the normalization directly from the overall form of the solution and the recursion relation for its series part. When combined with a previous such normalization for the radial part of the solution, the entire hydrogen atom solution can be normalized without having to invoke any properties of special functions.