Journal of Mathematical Chemistry最新文献

{"title":"Contrasting aromaticity and electronic properties of zigzag fibonapolyacene versus linear polyacene nanobelts through delta, characteristic and matching polynomials","authors":"Krishnan Balasubramanian","doi":"10.1007/s10910-026-01821-5","DOIUrl":"10.1007/s10910-026-01821-5","url":null,"abstract":"<div><p>Topological dependence of aromaticity and electronic features are juxtaposed by considering delta, matching and characteristic polynomials as well as geometry-dependent structural descriptors for the zigzag Fibonapolyacenes versus linear polyacenes containing up to 1000 rings. The coefficients of the characteristic polynomials of the zigzag Fibonapolyacenes exhibit novel mathematical sequences mapping into the Fibonacci spirals. It is shown that the delta polynomials provide significant new insights for comparing the aromaticity of the zigzag Fibonapolyacenes versus linear polyacenes. A number of electronic and geometrical parameters such as the HOMO–LUMO gaps, delta aromaticity, Mostar and Sombor indices are computed and compared. We show that the Dewar, Kekulé and constant counts of their polynomials exhibit interesting combinatorial properties. The computed results exhibit strong peripheral topological dependence on the properties of the two structures relative to the aromaticity and HOMO–LUMO gaps. The zigzag Fibonapolyacenes exhibit dramatically enhanced HOMO–LUMO gaps, aromaticity, and other properties while the linear polyacenes undergo a transition from the closed-shell singlet states to open-shell triplet states as the chain grows. The graph energy, HOMO–LUMO gap, constant spectral coefficient and Kekulé count of Fibonakilocene are computed as 5751.5511486, 0.763948, −  1.2949740230119973208828935650712 × 10⁴¹⁸ and 1.13796925398360272257523782552224 × 10²⁰⁹, respectively. The computational trends are in accord with the recent surface synthesis of long-chain polyacenes by employing scanning tunneling microscopy and spectroscopy. The present computational techniques and results for up to Fibonakilocene pave the way for the exploration of large aromatic belts and Fibonananomaterials from the standpoints of topological electronics, spintronics and aromaticity.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving the periodic field Fokker-Planck equation with a hybrid Fourier-generalized Hermite pseudospectral method","authors":"Yajin Zhang,&nbsp;Tian-jun Wang","doi":"10.1007/s10910-026-01822-4","DOIUrl":"10.1007/s10910-026-01822-4","url":null,"abstract":"<div><p>This paper presents a mixed Fourier-generalized Hermite pseudospectral method for the Fokker-Planck equation with periodic boundary conditions, encompassing both semi-discrete and fully discrete schemes. We first establish essential approximation results for the mixed Fourier-generalized Hermite interpolation, providing the mathematical foundation forsubsequent numerical analysis. Crucially, we introduce a non-standard projection operator that offers tighter error estimates than the standard interpolation operator. Based on this operator, we provide a rigorous convergence analysis of the proposed method. Finally, numerical experiments validate the theoretical findings and demonstrate the high efficiency of our approach.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interactive spatiotemporal dynamics of calcium, (text {IP}_{text {3}}), buffer, and calcium-bound buffer in neurons","authors":"Shashi Raj Solanki,&nbsp;Kamal Raj Pardasani","doi":"10.1007/s10910-026-01824-2","DOIUrl":"10.1007/s10910-026-01824-2","url":null,"abstract":"<div><p>Modeling serves as an effective tool for analyzing the spatiotemporal dynamics of calcium (<span>(text {Ca}^{text {2+}})</span>) signaling in neurons, which is a complex system involving numerous components and interactions. The interplay among the elements responsible for intracellular <span>(text {Ca}^{text {2+}})</span> distribution is highly intricate due to the diversity of structural and molecular factors involved. Nevertheless, this complexity allows for tightly regulated spatial and temporal control of signals conveyed by calcium ions. Previous studies have typically used simplified mechanisms that considered the dynamic interaction of <span>(text {Ca}^{text {2+}})</span> with either <span>(text {IP}_text {3})</span> (Inositol 1,4,5-trisphosphate) or buffer-without including the combined dynamics among <span>(text {Ca}^{text {2+}})</span>, <span>(text {IP}_text {3})</span>, buffer, and <span>(text {Ca}^{text {2+}})</span>-bound buffer. The current model addresses this limitation by incorporating all four signaling molecules: <span>(text {Ca}^{text {2+}})</span>, <span>(text {IP}_text {3})</span>, buffer, and <span>(text {Ca}^{text {2+}})</span>-bound buffer. The model is solved using the finite element method (FEM), with Gaussian quadrature employed to enhance numerical integration. This combination improves both accuracy and efficiency while reducing the computational cost of the integration process. The Crank–Nicolson method (CNM) is used to handle time discretization. Gaussian quadrature is particularly advantageous in FEM applications, as it strategically places sampling points to maximize accuracy for a given number of evaluations. The results provide new insight into the factors that cooperatively control neuronal calcium homeostasis, highlighting them as key therapeutic targets against neurodegenerative diseases.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical solution of fractal-fractional Lane–Emden equations using shifted legendre polynomials and operational matrices","authors":"A. M. Shloof,&nbsp;Mohamed I. Nouh,&nbsp;Emad A. B. Abdel-Salam,&nbsp;Abaker A. Hassaballa","doi":"10.1007/s10910-026-01819-z","DOIUrl":"10.1007/s10910-026-01819-z","url":null,"abstract":"<div><p>This study presents a novel and efficient computational framework for numerically solving fractal-fractional Lane-Emden (FFLE) equations using the new generalized Caputo fractal-fractional derivative (NGCFFD). Lane-Emden equations arise naturally in modeling astrophysical phenomena such as stellar structure, polytropic gas spheres, and isothermal gas clouds, as well as in chemical kinetics, thermoelectric processes, and various branches of applied mathematics. The proposed technique employs shifted Legendre polynomials (SLPs) to construct an operational matrix that systematically transforms these complex fractal-fractional differential equations (FFDEs) into tractable systems of algebraic equations, applicable to both linear and nonlinear multi-order FFDEs. Six representative FFLE equations are investigated across twelve computational models with varying fractal-fractional parameters (<span>(upgamma )</span>, <span>(upbeta )</span>, <span>(uprho )</span>), and the results are rigorously compared against conformable fractional (CF) and modified Riemann–Liouville (mRL) solutions available in the literature. The proposed fractal-fractional models consistently outperform the corresponding standard Caputo models. An error estimation theorem and a convergence analysis confirm that the series solutions converge to the exact solutions in the Hilbert space <span>({L}^{2})</span>[0,1]. We think this is the first study to report a numerical solution of fractal-fractional Lane-Emden equations, establishing the fractal order parameter β as an essential, rather than merely supplementary, modeling component for certain classes of singular nonlinear problems.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Strictly localized orbitals from spatial partitioning with the discontinuous Galerkin method","authors":"César Feniou,&nbsp;Julien Toulouse","doi":"10.1007/s10910-026-01823-3","DOIUrl":"10.1007/s10910-026-01823-3","url":null,"abstract":"<div><p>We present a rigorous electronic-structure theory of strictly localized orbitals associated with a spatial partition of the one-electron Hilbert space that remains well defined in the complete basis-set limit. Each strictly localized orbital is supported on a spatial domain and may be discontinuous at domain interfaces. Using the interior-penalty discontinuous Galerkin method, these strictly localized orbitals can be employed in variational electronic-structure calculations despite their discontinuities at domain interfaces. As a proof of concept, we present numerical illustrations on one-dimensional diatomic model systems. They show that variational calculations can be carried out in a basis of strictly localized orbitals while maintaining good agreement with conventional calculations. Moreover, these strictly localized orbitals naturally lead to chemically intuitive representations of many-electron wave functions in the spirit of valence-bond theory.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A general informatic tool for treating solution equilibria in supramolecular chemistry","authors":"Riccardo Salvio","doi":"10.1007/s10910-026-01818-0","DOIUrl":"10.1007/s10910-026-01818-0","url":null,"abstract":"<div><p>This work presents a versatile, open-source computational framework for the quantitative analysis of equilibria in solution, with particular emphasis on problems commonly encountered in supramolecular chemistry. The approach is based on a general numerical treatment of complex equilibrium systems, overcoming the limitations of analytical solutions that are restricted to only the simplest cases. The framework is implemented through a series of MATLAB scripts that are fully transparent, easily modifiable, and freely available, thereby avoiding the “black box” character of many commercial programs and enabling users to adapt the workflow to their specific experimental systems. The capabilities and performance of the tool are illustrated through its application to a range of representative datasets, including real experimental data acquired in the course of our own research activities. We demonstrate its utility for the analysis of host–guest complexation and acid–base titrations in which complexation phenomena are involved, thereby illustrating its reliability and broad applicability to recurring problems in supramolecular chemistry. At the same time, the methodology retains general validity for the treatment of almost any equilibrium process occurring in solution. By providing detailed documentation of the underlying mathematical and computational procedures, as well as complete access to the original scripts, this work promotes reproducibility and offers a flexible platform that can be readily employed to test mechanistic hypotheses and readily extended to address new and more elaborate systems.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01818-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A binomial approach to the stochastic kinetics of simple chemical reactions","authors":"Gábor Lente","doi":"10.1007/s10910-026-01820-6","DOIUrl":"10.1007/s10910-026-01820-6","url":null,"abstract":"<div><p>An approximate solution method is proposed to find the time dependence of the individual state probabilities in the master equation of the continuous time discrete state (CDS) stochastic kinetic approach. In systems where giving the number of a single type of molecule is enough to identify a state, this molecule number is assumed to show a binomial distribution whose expectation is the same as the solution of the corresponding deterministic rate equation. The approximation method is tested in ten different systems. In the first order reaction, it gives the exact solution of the stochastic master equation. In other systems, comparisons of expectations, standard deviations and distributions at selected reaction times with the exact ones at low initial molecule numbers show that the method gives reasonable results, whose precision is improved with an increase of initial molecule numbers. For the zeroth order process, a closed from for the exact solution of the master equation is also reported.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01820-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The unique equilibrium’s global exponential asymptotic stability of the irreversible Michaelis–Menten mechanism of enzyme kinetics","authors":"Benjamin Wacker","doi":"10.1007/s10910-026-01817-1","DOIUrl":"10.1007/s10910-026-01817-1","url":null,"abstract":"<div><p>In this work, we investigate the dynamical system of irreversible Michaelis–Menten kinetics in enzyme kinetics. We first summarize some important theoretical results such as non-negativity, boundedness or conservation laws for solutions of the time-continuous dynamical system. As our main contribution regarding this time-continuous setting, we demonstrate that the unique equilibrium state is globally exponentially asymptotically stable by providing a suitable Lyapunov-function. Based on the implicit Eulerian time-stepping method, we propose an explicit reformulation of this time-discretization for the numerical simulation. Our main result for the time-discrete dynamical system is that the unique equilibrium state of the time-discretization is globally exponentially asymptotically stable as well. Conclusively, we illustrate our theoretical findings by numerical experiments.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01817-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"High-order multi-structures-preserving exponential integrators for the derivative nonlinear Schrödinger equation","authors":"Liping Wu,&nbsp;Li Yang,&nbsp;Chaolong Jiang","doi":"10.1007/s10910-026-01816-2","DOIUrl":"10.1007/s10910-026-01816-2","url":null,"abstract":"<div><p>This paper presents a novel class of high-order mass-, energy- and momentum-preserving exponential integrators for solving the derivative nonlinear Schrödinger equation. Firstly, we reformulate the original system into an exponential supplementary variable system based on the idea of the exponential supplementary variable approach, and then the reformulated system is discretized by using the standard Fourier pseudo-spectral method in space and the high-order prediction-correction Lawson Runge–Kutta method in time, respectively. The proposed method is highly efficient, temporally high-order accurate, and simultaneously preserves the mass, energy and momentum in the discrete setting. Finally, numerical experiments validate the accuracy and energy-preserving properties.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal error estimates of the mass-preserving Galerkin finite element method for coupled nonlinear Schrödinger equations","authors":"Lili Li,&nbsp;Wanqiu Yuan","doi":"10.1007/s10910-026-01814-4","DOIUrl":"10.1007/s10910-026-01814-4","url":null,"abstract":"<div><p>In this paper, a linearized mass-preserving Galerkin finite element method is proposed to solve the multi-dimensional coupled nonlinear Schrödinger equations. The proof of an unconditional convergence is given without any time step restrictions. Our main idea is to obtain the boundedness of the numerical approximation in certain norms, where the Sobolev embedding theorem and the inverse inequality have been used. Numerical examples are given to demonstrate our theoretical results.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148519436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}