Journal of Mathematical Chemistry最新文献

{"title":"An efficient numerical algorithm for Lane–Emden–Fowler functional BVPs arising in isothermal gas spheres and heat diffusion models","authors":"Dharmendra Kumar,&nbsp;Amit K. Barnwal,&nbsp;Nikhil Sriwastav,&nbsp;Carlo Cattani,&nbsp;Higinio Ramos,&nbsp;Mehakpreet Singh","doi":"10.1007/s10910-026-01829-x","DOIUrl":"10.1007/s10910-026-01829-x","url":null,"abstract":"<div><p>Over recent decades, the Lane–Emden–Fowler equation (LEFE) has become an important model with wide-ranging applications, including astrophysical processes and heat transfer in biological systems. Since the evolution of such systems depends on past and future states, it can be effectively described using functional-type boundary value problems. This study proposes an extended LEFE model incorporating functional arguments along with informative nonlocal three-point boundary conditions. The existence and uniqueness of solutions to the resulting functional boundary value problem are established. Due to the inherent complexity of LEFE-type functional problems, obtaining accurate and efficient numerical solutions remains challenging. To address this, a polynomial-based collocation approach using Bernstein polynomials in <span>(L^{2}[0, 1])</span> space is developed. The wide applicability of the proposed method is further demonstrated through the well-known isothermal gas spheres and heat diffusion models, considered as a particular case of the proposed problem. The results confirm that the approach achieves faster convergence, higher accuracy, and improved computational efficiency compared to existing numerical schemes. A convergence analysis further supports the effectiveness of the method for solving complex functional-type differential equations.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965459","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":"Brain in vivo MRS without and with water suppression: Padé-based nonderivative, derivative, shape and parameter estimations","authors":"Dževad Belkić,&nbsp;Karen Belkić","doi":"10.1007/s10910-026-01832-2","DOIUrl":"10.1007/s10910-026-01832-2","url":null,"abstract":"<div><p>The theme of the present study is in vivo brain magnetic resonance spectroscopy for a healthy adult volunteer. The time signals encoded without and with water suppression are analyzed by the nonderivative and derivative fast Padé transform, FPT and dFPT, respectively. Both processors are applied as shape and parameter estimators. The ever existing border between shape and parameter estimators is erased by the nonparametric dFPT. This processor begins as a shape estimator and finishes as a (quantification-equipped) parameter estimator. It forces the given total shape spectrum (envelope) to collapse onto its proper components. Component lineshape reconstructions amount to quantification since isolated peaks in spectra can be parametrized by numerical integrations. The comparably good spectra are obtained for time signals without and with water suppression. Water-unsuppressed encodings beneficially offer faster scanning sequences, eliminate magnetization transfer effects, shorten repetition times and lower the radio-frequency power deposition to the patient.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01832-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927428","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":"Approximating the matrix sign function using an iterative method with application in computing the geometric mean of Hermitian positive definite matrices","authors":"Chahat Chhabra,&nbsp;Munish Kansal","doi":"10.1007/s10910-026-01833-1","DOIUrl":"10.1007/s10910-026-01833-1","url":null,"abstract":"<div><p>In this study, we propose an iterative method for approximation of matrix sign function for the matrices with no purely imaginary eigenvalues. A comprehensive convergence details of proposed scheme is provided, and its seventh order convergence is established theoretically. The asymptotic stability of the introduced algorithm is also examined and established. To demonstrate the practical significance of the matrix sign function, the proposed algorithm is applied to the evaluating geometric mean of positive definite Hermitian matrices and the electronic density matrix arising in quantum chemistry. Finally, numerical tests are performed using proposed iterative scheme and comparative results with other well known methods have been presented to assess the superiority and effectiveness of our proposed method.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927427","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":"Fractional Fokker–Planck differential equations in mathematical chemistry: a computational analysis using CSTM–MADM techniques","authors":"Sunita Kumari Nayak,&nbsp;Saumya Ranjan Jena","doi":"10.1007/s10910-026-01828-y","DOIUrl":"10.1007/s10910-026-01828-y","url":null,"abstract":"<div><p>This study employs the Conformable Sumudu Transform Method (CSTM) in conjunction with the Modified Adomian Decomposition Method (MADM) to obtain numerical solution of the fractional Fokker Planck differential equations (FFPDEs) constructed with theCaputo fractional derivative. These equations are of significant interest due to their wide-ranging applications in diffusion processes, stochastic molecular motion, and transport phenomena in complex chemical systems. The performance of the proposed scheme is quantitatively evaluated using the L_2 and L_∞, error norms, the rate of convergence (ROC), ad computational efficiency measured by CPU execution time. To demonstrate the accuracy, robustness, and applicability of the method, five representative numerical examples are presented through two-dimensional, three-dimensional, and contour visualizations. Furthermore, convergence, stability and error analysis are provided to establish the theoretical validity of the proposed approach. All numerical simulations are performed using MATLAB FORMAT LONG (R2018a) and MATHEMATICA.Finally, the proposed CSTM-MADM framework is compared with two scale and He’s’fractal derivative approaches in the non-fractional limit, as well as the results of existing methods.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927425","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":"An (varepsilon )-uniform scheme for singularly perturbed parabolic convection–diffusion problems with an interior turning point","authors":"Jyoti Rani,&nbsp;Raghvendra Pratap Singh,&nbsp;Harshita Madduri","doi":"10.1007/s10910-026-01825-1","DOIUrl":"10.1007/s10910-026-01825-1","url":null,"abstract":"<div><p>This article presents a parameter-uniform computational approach for singularly perturbed convection–diffusion problems arising in catalytic surface reactions. We compute the evolution of reactant concentration at different time levels in reactive flow systems. The interplay between convection and diffusion causes sharp variations in reactant concentration, leading to the formation of twin boundary layers. These layers are accurately resolved by combining uniform time discretization via the implicit Euler method with exponential B-spline collocation on a layer-adapted spatial mesh. The stability and convergence of the scheme are rigorously analysed, and numerical experiments demonstrate that it accurately captures reactant distributions even for very small perturbation parameters. The numerical results are compared with existing work.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01825-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926620","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 general class of reduced nonlinear kinetic models for batch electrocoagulation: global stability and parameter identifiability","authors":"José Octavio Contreras Sánchez,&nbsp;Tame González Cruz,&nbsp;Jorge Luis Morales Martínez,&nbsp;Gilberto Carreño Aguilera,&nbsp;Joel Everardo Valtierra Olivares","doi":"10.1007/s10910-026-01827-z","DOIUrl":"10.1007/s10910-026-01827-z","url":null,"abstract":"<div><p>Electrocoagulation (EC) is a physicochemical process for water and wastewater treatment, although its kinetics still present difficulties. Its mathematical description remains a challenge due to the simultaneous occurrence of phenomena such as electrochemical generation, contaminant–coagulant interaction, floc formation, and phase separation. This work presents a general class of reduced nonlinear kinetic models for EC under batch operation in a perfectly mixed reactor. The model uses two variables: the contaminant concentration in the aqueous phase, x(t), and the active coagulant concentration, y(t). Contaminant removal follows an admissible kinetics g(x,y) under mild structural conditions. Coagulant generation is derived from an effective Faradaic term, which arises from a Langmuir-type site-blocking mechanism analogous to noncompetitive enzyme inhibition kinetics. The model’s solutions are shown to be positive and bounded. A physically admissible equilibrium is found to be globally stable by means of a Lyapunov function, without restricting the analysis to a specific kinetic form. Three illustrative removal kinetics are studied: mass-action, contaminant-saturating, and combined saturation, with their relative local convergence rates compared explicitly. Numerical simulations, performance indicators, and a local sensitivity analysis are carried out to complement the qualitative results. In addition, the model’s global sensitivity is studied based on variance (Sobol’ indices) and through a Bayesian identifiability study based on synthetic data. We find that the residual coagulant concentration at equilibrium is governed by a simple algebraic invariant that is independent of the kinetics. Furthermore, the combined saturation kinetics exhibits a sloppy parameter structure. In the contaminant-saturated regime examined here, the individual parameters turn out to be practically non-identifiable from finite, noisy synthetic contaminant data, even when the coagulant concentration is also observed. Finally, the model’s behavior is contrasted qualitatively and semi-quantitatively with experimental trends reported in the electrocoagulation literature. The proposed framework provides a mechanistically grounded mathematical tool for interpreting batch electrocoagulation as a dissipative kinetic system, distinguishing those features of its dynamics that are universal to the entire class of admissible kinetics from those that depend on the specific removal mechanism assumed. The model is not calibrated against experimental data and is intended as a qualitative and analytical tool rather than a predictive one.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926457","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":"Analytical quantum corrections to the second virial coefficient in Yukawa systems","authors":"Elif Somuncu,&nbsp;A. A. Hasanov,&nbsp;Kh. T. Hasanova","doi":"10.1007/s10910-026-01826-0","DOIUrl":"10.1007/s10910-026-01826-0","url":null,"abstract":"<div><p>In this work, new analytical formulae are proposed for evaluating quantum corrections to the second virial coefficient for systems interacting via attractive and repulsive hard-core Yukawa potentials, without imposing any prior assumptions on the potential’s functional form or shape. The derived expressions provide a general and unified framework for accurately describing quantum effects in interacting particle systems. The accuracy and robustness of the proposed formulae are demonstrated through analytical consistency and comparative analysis with existing theoretical results. Furthermore, the proposed formalism is employed to calculate the thermal properties of gases governed by hard-core Yukawa interactions, including temperature-dependent thermodynamic quantities. The results demonstrate the applicability and effectiveness of the present approach for modeling the thermodynamic behavior of real and model gases over a broad range of interaction parameters.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926458","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":"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}