Journal of Mathematical Chemistry最新文献

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.

To calculate the entropy of three-coordinated ice-like systems, a simple and convenient approximate method of local conditional transfer matrices using 2 × 2 matrices is presented. The exponential rate of convergence of the method has been established, which makes it possible to obtain almost exact values ​​of the entropy of infinite systems. The qualitatively higher rate of convergence for three-coordinated systems compared to four-coordinated systems is due to less rigid topological restrictions on the direction of hydrogen (H-) bonds in each lattice site, which results in a significantly weaker the system’s total correlations. Along with the ice hexagonal monolayer, other three-coordinated lattices obtained by decorating a hexagonal monolayer, a square lattice, and a kagome lattice were analyzed. It is shown that approximate cluster methods for estimating the entropy of infinite three-coordinated systems are also quite accurate. The importance of the proposed method of local conditional transfer matrices for ice nanostructures is noted, for which the method is exact.

Kinetic chemical reactions find applications across various fields. In industrial processes, they drive the production of essential materials like fertilizers and pharmaceuticals. In environmental science, they are crucial to understanding pollution dynamics. Additionally, in biochemistry, they underpin vital cellular processes, offering insights into disease mechanisms and drug development. In this work, we present a new advancement of a dynamical system for kinetically controlled chemical reactions and the dependency of its solution on the initial conditions using mathematical techniques for fractional orders. By utilizing this fixed-point approach, we can derive the existence and uniqueness theorem of the proposed model. We further show that the chemical kinetics of the fractional model are stable through the Hyers-Ulam stability condition. We finally run a numerical simulation to verify our conclusions. The manuscript concludes with demonstrative examples.

This work is based on the productive idea of Mulliken about the alignment of electronegativities of atoms in the process of bond formation to their geometric mean value. The paper considers in detail the case of a binary molecule and obtains formulas for the dependence of the current values of the electronegativities of the two atoms forming the molecule on time, and finds a mathematical connection between the current and initial values of electronegativities. Also, in the work the theorem on the relation between the rates of alignment of electronegativities of atoms entering into chemical bonding is formulated and proved, and a special case of this theorem is considered.