Journal of Mathematical Chemistry最新文献

We study single-voxel in vivo proton magnetic resonance spectroscopy (MRS) of white matter in the brain of a 25 year old healthy male volunteer. The free induction decay (FID) data of short length (0.5KB) are encoded at a long echo time (272 ms) with and without water suppression at a clinical scanner of a weak magnetic field (1.5T). For these FIDs, the fast Fourier transform (FFT) gives sparse, rough and metabolically uninformative spectra. In such spectra, resolution and signal to noise ratio (SNR) are poor. Exponential or Gaussian filters applied to the FIDs can improve SNR in the FFT spectra, but only at the expense of the worsened resolution. This impacts adversely on in vivo MRS for which both resolution and SNR of spectra need to be very good or excellent, without necessarily resorting to stronger magnetic fields. Such a long sought goal is at last within reach by means of the optimized derivative fast Fourier transform (dFFT), which dramatically outperforms the FFT in every facet of signal estimations. The optimized dFFT simultaneously improves resolution and SNR in derivative spectra. They are presently shown to be of comparably high quality irrespective of whether water is suppressed or not in the course of FID encodings. The ensuing benefits of utmost relevance in the clinic include a substantial shortening of the patient examination time. The implied significantly better cost-effectiveness should make in vivo MRS at low-field clinical scanners (1.5T) more affordable to ever larger circles of hospitals worldwide.

The effect of defects on the thermal properties of Ψ-Graphene Nanotubes (Ψ-GNTs) is investigated in this study using Molecular Dynamics simulations. The results reveal that the thermal properties of Ψ-GNTs are profoundly impacted by the presence of defects. Specifically, a significant reduction in thermal conductivity is observed with increasing defect concentrations. This reduction is attributed to the scattering of phonons by the defects, which leads to increased phonon–phonon interactions and decreased thermal transport efficiency. Furthermore, the effect of temperature on the thermal properties of defective Ψ-GNTs is investigated. The findings demonstrate a nonlinear decrease in thermal conductivity with increasing temperature.

Recently, fractional derivatives have become increasingly important for describing phenomena occurring in science and engineering fields. In this paper, we consider a numerical method for solving the fractional Burgers’ equations (FBEs), a vital topic in fractional partial differential equations. Due to the difficulty of the fractional derivatives, the nonlinear FBEs are linearized through the Rubin–Graves linearization scheme combined with the implicit the third-order Adams–Moulton scheme. Additionally, in the spatial direction of the FBEs, the fourth-order central finite difference scheme is used to obtain more accurate solutions. The convergence of the proposed scheme is theoretically and numerically analyzed. Also, the efficiency is demonstrated through several numerical experiments and compared with that of existing methods.

Exact analytical energy formula for the rotating Kratzer–Fues oscillator with (v, J)-dependent potential parameters is obtained. It was used to reproduce the spectral data generated by the vibrational transitions (vrightarrow v+1, v=0, 1 ldots 7) in (J=0,1ldots 47) rotational states of dinitrogen (^{14})N(_2) and (^{15})N(_2) in the ground electronic state (X^1Sigma _g^+). Calculations performed for two isotopic variants enabled the selection of the mass-dependent and independent potential parameters defining the model. To check the ability of the eigenenergies derived to reproduce rotational transitions measured with kHz accuracy, calculations for (^{74})Ge(^{32})S, (^{79})Br(^{35})Cl and (^{1})H(^{35})Cl were performed, obtaining agreement between theoretical and experimental results. Minimum uncertainty coherent states and ladder operators for the rotating improved Kratzer–Fues oscillator are also constructed.

This article deals with a coupled system of singularly perturbed convection-diffusion parabolic partial differential equations (PDEs) possessing overlapping boundary layers. As the thickness of the layer shrinks for small diffusion parameter, efficient capturing of the solution and the diffusive flux (i.e., scaled first-order spatial derivative of the solution) leads to a difficult task. It is well-known that the classical numerical techniques have deficiencies in estimating the solution and the diffusive flux on equidistant mesh unless the mesh-size is adequately large. We aim to generate an efficient numerical approximation to the coupled system of PDEs by employing the implicit-Euler method in time and a classical finite difference scheme in space on a layer-adapted Shishkin mesh. Firstly, we discuss about parameter-uniform convergence of the numerical solution in (C^0)-norm followed by the error analysis for the scaled discrete space derivative and the discrete time derivative. Subsequently, the parameter-uniform error bound is established in weighted (C^1)-norm for global approximation to the solution and the space-time solution derivatives. The theoretical findings are verified by generating the numerical results for two test examples.

In this paper, a fourth-order energy-preserving time integrator is derived by improving the classical average vector field integrator. Combining the proposed novel time integrator with the Fourier pseudo-spectral spatial discretisation, we develop and analyze an energy-preserving fully discrete scheme for the sine-Gordon equation with periodic boundary conditions. Numerical results verify the energy preservation and the accuracy of the proposed fully discrete scheme.

The unique organizational framework for polycyclic aromatic hydrocarbons developed by us has led to the discovery of number patterns for their number of isomers. Constant-isomer series are generated by repetitive circumscribing of a given set of isomers. Benzenoid, fluoranthenoid, indacenoid, and primitive coronoid constant isomer series possess twin isomer numbers with members having corresponding topologies. The concepts of strictly pericondensed, strain-free, Clar’s aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons. In a plot of TRS isomer numbers on the Formula Periodic Table for Total Resonant Sextet Benzenoids [Table PAH6(TRS)] which is a subset of Table PAH6 for ordinary benzenoids, structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids are presented. These chemical graph theoretical results belong to the branch of mathematics called number theory.

This research delves into a comprehensive investigation of a specific group of alkanes, with the primary objective of establishing meaningful associations between their inherent physical attributes and a set of graphical parameters ranging from topological indices to their associated graphical entropies. Though there are countless techniques to relate molecular structure and physical properties of chemical compounds, the pursuit has often been pricey and arduous. With a view to curb the expense and intense labour, this work focuses on attaining some of these properties using graphical interpretations and statistical interventions. Driven by this objective, we compute Sombor index, a recently developed topological tool and some of its variants for all structural isomers of alkanes with carbon range four to nine. Furthermore, our study employs multiple regression analysis to explore their connections with some physical attributes of alkanes while concurrently addressing the challenge posed by multicollinearity. We have adopted the technique of robust regression to scale down the impact of outliers in the dataset, while generating regression models. Further, the established results are justified with a 10-fold cross validation process and a comparison with the results obtained from different topological indices. The results of this research contribute a valuable insight to the fields of chemical informatics and structural analysis, offering an enhanced comprehension of the interplay between molecular structure and physical attributes within alkanes.

In this paper, we introduce one-parameter families of multistep numerical methods for solving stiff initial value problems of ordinary differential equations. These methods are adaptive versions of second derivative backward differentiation formulas and their extensions. The stability properties of the proposed schemes are better than those of the main methods which make them suitable for solving stiff problems. Numerical experiments on some problems arising from chemical reactions verify the theoretical results.