Journal of Mathematical Chemistry最新文献

This work proposes a hybrid numerical strategy to effectively solve the singularly perturbed partial differential equations (SPPDEs) with integral boundary conditions and substantial spatial delays. For the time discretization, the Crank-Nicolson scheme was chosen because of its stability and second-order precision. In order to maximize accuracy in the vicinity of layers coming from the tiny perturbation parameter and delay parameter, the computational implementation will be carried out using a non-uniform Shishkin-type mesh for spatial discretization using cubic spline interpolation. The approach is tested numerically to verify its robustness and efficiency with respect to integral boundary conditions and delayed feedback. Applications to reaction-diffusion systems, catalytic reactions in porous media, and transport-reaction dynamics in tubular reactors are presented to illustrate the effectiveness of the proposed approach.

The Floating spherical Gaussian orbital model has existed for nearly half a century, yet it remains one of the lesser researched areas. Considering the potential of the model to address significant quantum-based or molecular problems, this article aims to bring renewed attention to this long neglected concept. This review presents, a brief overview of the background, literature and current status of the method, and concludes with suggestions for future research.

The qualitative relationship between the adsorption energy distribution of a microporous adsorbent and its total isotherms is modeled by the adsorption integral equation with Langmuir kernel. Due to the instability of the adsorption integral equation, a regularization is required. Recently, we have developed a general regularization using a transformation that will now be specialized for numerical application. In this paper, we perform the first step to this end, namely the construction of an approximation of the transformed total isotherm from finitely many measurement points. The method presented here is based on discrete convolution and is also suitable for the approximation of more general functions and their spectral functions. A full error analysis is given. In particular, the influences of the measurement error, the discretization error and the truncation error on the quality of the approximation of the transformed total isotherm are investigated.

We consider an electron confined in a quantum ring (QR) defined electrostatically within the phosphorene monolayer. A confinement potential with an elliptical shape is employed to account for the anisotropy of the effective masses. The Schrödinger equation is solved, leading to the determination of the energy levels. Subsequently, the Shannon formalism is applied to compute the probability distribution and partition function of the system. Finally, the magnetic and thermodynamic properties of the phosphorene QR are analyzed. The results reveal that the magnetic susceptibility exhibits a negative value, indicative of diamagnetic behavior. A maximum value of magnetic susceptibility is observed at low temperatures and high magnetic fields. At elevated magnetic temperatures, the specific heat remains constant, even in the absence of an external magnetic field.

The present study is on proton magnetic resonance spectroscopy (MRS), as it applies to tumor diagnostics in cancer precision medicine. The goal with the employed patients’ data, subjected to shape estimations alone with no fitting, is to reconstruct self-contained quantitative information of diagnostic relevance. This can be accomplished by proper evaluation of physical metabolites, especially cancer biomarkers (lactates, cholines, citrates,...). Such information is completely opaque in the encoded time signals, but can be transparent in the frequency domain. The optimized derivative fast Fourier transform (dFFT) can meet the challenge. The thorniest stumbling blocks in MRS are abundant overlapping resonances of low resolution and poor signal-to-noise ratio (SNR). Attempts to increase resolution are marred by decreased SNR. The long-sought strategy of MRS, simultaneous improvement of resolution and SNR, is achievable by the optimized dFFT. With the implied aid to decision-making, this is illustrated for ovarian MRS data encoded from benign and malignant human biofluid samples.

This study proposes the application of the bond dual descriptor, computed using finite difference approximation, to investigate the electron density reorganization in π-conjugated compounds upon nucleophilic/electrophilic attack. Compared to the traditional bond Fukui function analysis, this descriptor offers a simpler approach, reducing the complexity of potential rearrangement scenarios in half and simplifying the interpretation. A series of ethylene derivatives have been tested allowing to explain the activation of the double bond in ethylene derivatives, the rearrangement of the electron density and its reduction in activation energies. In addition, it is shown that it is possible to explain the reactivity on Michael acceptors, the rearrangement of cis-1,3,5-hexatriene to form 1,3-cyclohexadiene and the preference of C₆₀ to react through its [6,6] over [5,6] bonds. The bond dual descriptor complements the atomic dual descriptor, enabling a comprehensive analysis of the chemical reactivity of π-conjugated compounds.

The theory of atomic structure is conceptually built on hydrogen-like orbitals and computed using Slater or Gaussian orbitals, owing to the relative difficulty of computing integrals concerning the hydrogenic orbitals. The optimal set of hydrogenic orbitals in an atom is obtained by minimizing the energy with respect to the orbitals. The Coulomb integral is difficult to compute due to the inverse distance relationship. In this paper, we evaluate the Coulomb integral and its derivative using two expressions for the inverse distance: the Laplace expression and the Legendre expression. The two expressions for inverse distance are similar and yield different integral forms. The Laplace expression yields the Coulomb integral as a sum of hypergeometric functions while the Legendre expression yields a compact polynomial form. The derivative of the Coulomb integral (computed using both forms) with respect to the decay constant is also provided.

The methodology for calculating the phase-lag and amplification-factor for both explicit and implicit multistep methods for first-order differential equations was recently developed by one of the authors. The objective of this study is to develop low-order Adams–Bashforth–Moulton predictor–corrector algorithms that eradicate phase-lag, amplification-factor. The stability regions of the newly established methodologies will also be highlighted. Furthermore, we will examine our results from numerical experiments employing the newly developed approaches.

The paper discusses a mathematical model for non-Michaelis–Menten kinetics, which involves a substrate forming a complex with the immobilized catalyst. A new Hosoya polynomial approximation method (HPAM) is applied for solving the reaction–diffusion equations. Analytical expressions are established to the nonlinear reaction–diffusion equation arising in electro catalytic thin film with an arbitrary shape models using the Hosoya polynomials. The main idea of the proposed research work is that the nonlinear reaction–diffusion problems are converted into a system of algebraic equations using the Hosoya polynomials. Analytical expressions for substrate concentration profiles are derived in closed and simplified forms for various geometries (planar, cylindrical, and spherical), along with the corresponding steady-state amperometric current response. The proposed results are validated with the other available results. Moreover, the utility of HPAM is investigated to be simple, straight forward, efficient and flexible. Also, the paper examines how different parameters influence the substrate concentration in the above models.