Journal of Mathematical Chemistry最新文献

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.

In response to the challenges posed by complex boundary conditions and singularities in molecular systems and quantum chemistry, accurately determining energy levels (eigenvalues) and corresponding wavefunctions (eigenfunctions) is crucial for understanding molecular behavior and interactions. Mathematically, eigenvalues and normalized eigenfunctions play crucial role in proving the existence and uniqueness of solutions for nonlinear boundary value problems (BVPs). In this paper, we present an iterative procedure for computing the eigenvalues ((mu )) and normalized eigenfunctions of novel fractional singular eigenvalue problems,

with boundary condition,

where (D^alpha , D^{2alpha }) represents the Caputo fractional derivative, (k ge 1). We propose a novel method for computing Lagrange multipliers, which enhances the variational iteration method to yield convergent solutions. Numerical findings suggest that this strategy is simple yet powerful and effective.

The phenomenon of isothermal supersaturation of solutions in a porous medium at ion exchange is studied on the basis of mathematical modeling. The phenomenon consists in the fact that the solution with concentration significantly higher than the maximal solubility of the substance is formed in the pores of sorbent and no precipitation occurs. The question of why sediment does not appear in the pores between the grains is investigated in the article. It is shown that the phenomenon under consideration can be explained by the effect of dynamic equilibrium between the association of condensed phase particles in the inner part of the pores, their diffusion, and decomposition near the surface of the sorbent grains caused by a change in potential. The degree of possible supersaturation of the solution is estimated depending on the process parameters. The proposed hypothesis is confirmed by quantitative studies using the available experimental data.

A fullerene graph is a 3-connected plane cubic graph in which every face is pentagonal or hexagonal. A set of hexagons (mathcal {H}) of G is called a resonant pattern if there exists a perfect matching M of G such that exactly three edges of H is contained in M for each member H of (mathcal {H}). In this paper we prove for any natural number k that almost all of the family of k disjoint hexagons are resonant patterns in sufficiently large fullerene graphs.

Throughout this research paper, we represent a highly effective Haar wavelet technique to determine the solution of the complex nonlinear dynamical system with three variables chemical reaction model. The foremost objective of this study is to represent the dynamical behavior of chemical reaction model in the sense of Caputo derivative. The convergent analysis and stability analysis of the three variable chemical reaction model are discussed. The existence and uniqueness of the given model is also verified. Furthermore, the residual error analysis for this model is also presented. In addition, graphically the numerical solutions in a 2-dimensional and 3-dimensional manner are obtained by using MATLAB (2023a).