{"title":"Fusene chains revisited: how kinky they are and why it matters","authors":"Tomislav Došlić","doi":"10.1007/s10910-024-01620-w","DOIUrl":"10.1007/s10910-024-01620-w","url":null,"abstract":"<div><p>We refine the enumeration of fusene chains of a given length with respect to the number of turns by constructing bijections between such chains and ternary words. Explicit formulas thus obtained are then used to compute the expected values for the whole class of bond-additive degree-based topological indices over all such chains of a given length. The results are also applicable to several other classes of chemically interesting polycyclic chains, such as, e.g., phenylene and spiro chains.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 7","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888201","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 innovative Vieta–Fibonacci wavelet collocation method for the numerical solution of three-component Brusselator reaction diffusion system of fractional order","authors":"Manpal Singh, S. Das, Rajeev","doi":"10.1007/s10910-024-01621-9","DOIUrl":"10.1007/s10910-024-01621-9","url":null,"abstract":"<div><p>The research article presents a novel approach for the numerical solution of three-component time fractional order Brusselator reaction-diffusion system using the innovative Vieta–Fibonacci wavelet and collocation method. The proposed method involves the derivation of operational matrices for both integer and fractional order derivatives, enable the accurate and efficient computation of the system. The existence, uniqueness of solution and Ulam–Hyers stability of the model are rigorously discussed. Furthermore, a comprehensive convergence analysis of the Vieta–Fibonacci wavelet method is presented, which demonstrates its effectiveness in approximating the fractional derivative of the Brusselator system. The numerical experiments showcase the superior performance of the method in terms of accuracy and computational efficiency. The application of the Vieta–Fibonacci wavelet method to the three-component fractional order Brusselator reaction-diffusion system marks a significant advancement in the field of computational mathematics. The successful implementation of the Vieta–Fibonacci wavelet method signifies a significant advancement in solving fractional-order reaction-diffusion problems.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 7","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888235","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 representations of AB-type copolymer complexes: analysis of 1H NMR chemical shift patterns in terms of a Smith–Cantor set","authors":"Howard M. Colquhoun, Ricardo Grau-Crespo","doi":"10.1007/s10910-024-01614-8","DOIUrl":"10.1007/s10910-024-01614-8","url":null,"abstract":"<div><p>When considering the possibility of storing information in the sequence of monomer residues within an AB-type copolymer chain, it is constructive to model that sequence as a string of ones and zeros. The intramolecular environment around any given digit (say a “<b>1</b>”) can then be represented by another string of integers—a <i>code</i>—obtained by summing pairs of digits at equivalent positions, in both directions, from that digit. The code can include only integers 0, 1 and 2, and can represent a number in any base <i>b</i> higher than 2. In base <i>b</i> = 3 the resulting set of codes includes <i>all</i> numbers (because only digits 0, 1 and 2 occur in ternary expansions), but in any base <i>b</i> > 3 the codes define a limited set of numbers comprising a fractal we term a Smith–Cantor set. The <sup>1</sup>H NMR spectrum of a random, AB-type co(polyester-imide) shows, on complexation with pyrene, a pattern of complexation shifts approximating very closely to the Smith–Cantor set for which <i>b</i> = 4. Other co(polyimide) complexes show a <sup>1</sup>H NMR pattern corresponding to a specific <i>sub</i>-set of this fractal. The sub-set arises from a “stop-at-zero” limitation, whereby digits in the initial string are set to zero for code-generating purposes if they occur beyond a zero, as viewed from the central “<b>1</b>”. The limitation arises in copolymers where pyrene binds by intercalation between <i>pairs</i> of adjacent diimide residues. This numerical approach provides a complete, unifying theory to account for the emergence of fractal character in the <sup>1</sup>H NMR spectra of AB-type copolymer complexes.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 7","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-024-01614-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838277","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":"Family of phase fitted 3-step second-order BDF methods for solving periodic and orbital quantum chemistry problems","authors":"Hosein Saadat, Sanaz Hami Hassan Kiyadeh, Ramin Goudarzi Karim, Ali Safaie","doi":"10.1007/s10910-024-01619-3","DOIUrl":"10.1007/s10910-024-01619-3","url":null,"abstract":"<div><p>In this paper, we introduce a novel series of second-order Backward Differentiation Formulas (BDFs) specifically designed to address phase-lag and its first derivative in the numerical resolution of Initial Value Problems (IVPs) with orbital solutions. Our methodology commences with an in-depth analysis of phase-lag phenomena associated with second-order BDFs. Following this, we construct a suite of equations by embedding algebraic functions into the operational framework of the 3-step second-order BDF (SOBDF) method. Additionally, we elaborate on equations that precisely describe the phase-lag and its derivatives, with a concentrated focus on the 3-step SOBDF method. The culmination of this work is the presentation of six distinct methods, each methodically crafted to negate both the real and imaginary elements of phase-lag and its derivatives in numerical computations. The study advances with a meticulous examination of the local truncation error and the stability regions pertinent to the six phase-fitted methods introduced. Furthermore, we scrutinize their computational performance by deploying these methods across a spectrum of initial value problems, offering valuable insights into their effectiveness in varying contexts.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838555","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":"Evaluation of smooth reaction rate of noisy experimental data using Legendre series expansion","authors":"Alireza Aghili, Amir Hossein Shabani","doi":"10.1007/s10910-024-01618-4","DOIUrl":"10.1007/s10910-024-01618-4","url":null,"abstract":"<div><p>The accurate calculation of reaction rates from experimental data is crucial for understanding and characterizing chemical processes. However, the presence of noise in experimental data can introduce errors in rate calculations. In this study, we introduced a novel approach that utilizes the Legendre series expansion method to directly derive smooth reaction rates from noisy experimental data, eliminating the need for numerical differentiation methods. This approach proves to be highly effective in handling noisy thermogravimetric analysis (TGA) data obtained from the thermal decomposition of specific polymers. We demonstrated the robustness and reliability of this method and provided Gnu Octave codes as a free alternative to MATLAB, making the implementation more accessible. Furthermore, the smooth reaction rates obtained were used to evaluate the activation energy using the Friedman isoconversional method. The results showed excellent agreement with those obtained using the Vyazovkin integral method. Additionally, the proposed method can be applied to obtain smooth derivative thermogravimetric (DTG) curves using noisy TGA data set.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 7","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140810685","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":"Endotactic and strongly endotactic networks with infinitely many positive steady states","authors":"Samay Kothari, Abhishek Deshpande","doi":"10.1007/s10910-024-01617-5","DOIUrl":"10.1007/s10910-024-01617-5","url":null,"abstract":"<div><p>The dynamics exhibited by reaction networks is often a manifestation of their steady states. We show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess a family of infinitely many positive steady states. In addition, we prove for some of these systems that there exist no weakly reversible mass-action systems that are dynamically equivalent to mass-action systems generated by these networks. This extends a result by Boros, Craciun and Yu [1], who proved the existence of weakly reversible dynamical systems with infinitely many steady states.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804723","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}
Ana Granados, Ana Portilla, Yamilet Quintana, Eva Tourís
{"title":"New bounds for variable topological indices and applications","authors":"Ana Granados, Ana Portilla, Yamilet Quintana, Eva Tourís","doi":"10.1007/s10910-024-01593-w","DOIUrl":"10.1007/s10910-024-01593-w","url":null,"abstract":"<div><p>One of the most important information related to molecular graphs is given by the determination (when possible) of upper and lower bounds for their corresponding topological indices. Such bounds allow to establish the approximate range of the topological indices in terms of molecular structural parameters. The purpose of this paper is to provide new inequalities relating several classes of variable topological indices including the first and second general Zagreb indices, the general sum-connectivity index, and the variable inverse sum deg index. Also, upper and lower bounds on the inverse degree in terms of the first general Zagreb are found. Moreover, the characterization of extremal graphs with respect to many of these inequalities is obtained. Finally, some applications are given.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-024-01593-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140669720","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":"Relationship between Lennard-Jones potential and physico-chemical parameters","authors":"Yosra Ben Torkia, Abdelmottaleb Ben Lamine","doi":"10.1007/s10910-024-01598-5","DOIUrl":"10.1007/s10910-024-01598-5","url":null,"abstract":"<div><p>We developed in this paper the used methodology to describe the Lennard-Jones potential of two atoms in rare gas. In this treatment we supposed that one atom could be described by a harmonic oscillator. The interaction potential is developed at short and long ranges. The results showed that the obtained physico-chemical parameters such as the oscillator frequency, the atom mass, and the atom charge well reproduce the Lennard-Jones potential. Then the potential well depth and the effective equilibrium diameter are expressed in function of the oscillator frequency, the atom mass and charge.</p><h3>Graphical abstract</h3>\u0000<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565254","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":"Cross section sensitivity to perturbation strengths in distorted waves for double electron capture by alpha particles from helium targets","authors":"Dževad Belkić","doi":"10.1007/s10910-024-01599-4","DOIUrl":"10.1007/s10910-024-01599-4","url":null,"abstract":"<div><p>Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second-order methods. The perturbation strength is parametrized by the Sommerfeld factor (the quotient of the nuclear charge and the relative velocity of the colliding particles). At each fixed impact energy, the sought sensitivity is monitored by gradually modifying the nuclear charges in the Sommerfeld factors. These factors reside in the Coulomb distortions of the unperturbed channels states. The focus is on the electronic distortions through the eikonal Coulomb logarithmic phases and the full Coulomb waves. The logarithmic phases are the constituents of the compound phases for the net charges of the two heavy scattering aggregates in relative motions. A striking perturbation strength sensitivity of the obtained total cross sections is recorded.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-024-01599-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565419","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":"An integral discretization scheme on a graded mesh for a fractional differential equation with integral boundary conditions","authors":"Zhongdi Cen, Jian Huang, Aimin Xu","doi":"10.1007/s10910-024-01596-7","DOIUrl":"10.1007/s10910-024-01596-7","url":null,"abstract":"<div><p>In this paper, a fractional differential equation with integral conditions is studied. The fractional differential equation is transformed into an integral equation with two initial values, where the initial values needs to ensure that the exact solution satisfies the integral boundary conditions. A graded mesh based on a priori information of the exact solution is constructed and the linear interpolation is used to approximate the functions in the fractional integral. The rigorous analysis about the convergence of the discretization scheme is derived by using the truncation error estimate techniques and the generalized Grönwall inequality. A quasi-Newton method is used to determine the initial values so that the numerical solution satisfies two integral boundary conditions within a prescribed precision. It is shown that the scheme is second-order convergent, which improves the results on the uniform mesh.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565407","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}