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Numerical solution to loaded difference scheme for time-fractional diffusion equation with temporal loads 带时间负荷的时间分数扩散方程的加载差分方案数值解法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-31 DOI: 10.1007/s10910-024-01658-w
Shweta Kumari, Mani Mehra
{"title":"Numerical solution to loaded difference scheme for time-fractional diffusion equation with temporal loads","authors":"Shweta Kumari, Mani Mehra","doi":"10.1007/s10910-024-01658-w","DOIUrl":"https://doi.org/10.1007/s10910-024-01658-w","url":null,"abstract":"<p>This paper investigates the temporally loaded time-fractional diffusion equation with initial and Dirichlet-type boundary conditions. To begin with, a solution form is established using the method of eigenfunction expansions, and its existence and uniqueness are examined along with some apriori estimates. Thereafter, a finite difference approximation is performed using the so-called <i>L</i>1 method for the Caputo fractional derivative, resulting in a loaded difference scheme. The superposition property of systems of linear algebraic equations is applied to solve the loaded difference scheme by appointing an appropriate solution representation. The unique solvability of the proposed scheme is set up. The stability and convergence of the proposed difference scheme are analysed by the discrete energy method with an order of accuracy <span>(mathcal {O}(tau ^{2-alpha }+h^2))</span>. Numerical results via two test problems are presented to validate the theoretical findings of the proposed scheme by observing the errors.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863807","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}
引用次数: 0
On properties of the first inverse Nirmala index 论第一逆尼玛拉指数的性质
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-29 DOI: 10.1007/s10910-024-01665-x
Boris Furtula, Mert Sinan Oz
{"title":"On properties of the first inverse Nirmala index","authors":"Boris Furtula, Mert Sinan Oz","doi":"10.1007/s10910-024-01665-x","DOIUrl":"https://doi.org/10.1007/s10910-024-01665-x","url":null,"abstract":"<p>The first inverse Nirmala index is a novel degree-based topological descriptor that was introduced in 2021. Preliminary QSPR investigations suggest that this index deserves further consideration because of its unusually good predictive potential. This paper investigates the relations between this index with some elementary graph quantities and some related degree-based topological index. Further, the computational analysis will reveal extremal graphs among trees, molecular trees, all connected graphs, and their molecular counterparts.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863808","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}
引用次数: 0
Q-rényi’s divergence as a possible chemical similarity criterion Q-rényi 分歧作为一种可能的化学相似性标准
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-24 DOI: 10.1007/s10910-024-01663-z
L. Flores-Gómez, N. Flores-Gallegos
{"title":"Q-rényi’s divergence as a possible chemical similarity criterion","authors":"L. Flores-Gómez, N. Flores-Gallegos","doi":"10.1007/s10910-024-01663-z","DOIUrl":"https://doi.org/10.1007/s10910-024-01663-z","url":null,"abstract":"<p>In this work, we introduce the <i>q</i>-Rényi’s divergence, which results from the conjunction of Rényi’s divergence and Jackson’s integral. The resultant equation can be employed as a measure of chemical similarity, which consists of comparing two or more chemical species with a set of molecules that have been characterized to find two or more molecules that could have similar chemical or physical properties. To carry out our study, we applied <i>q</i>-Rényi’s divergence using a set of Tetrodotoxin variants and a set of 1641 organic molecules. Our results suggest that <i>q</i>-Rényi’s divergence could be a valuable tool to complement chemical similarity studies.\u0000</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775873","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}
引用次数: 0
Numerical solution of one- and two-dimensional Hyperbolic Telegraph equation via Cubic–Quartic Hyperbolic B-Spline DQM: a statistical validity 通过三次四次双曲 B-样条 DQM 计算一维和二维双曲 Telegraph 方程的数值解法：统计有效性
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-24 DOI: 10.1007/s10910-024-01652-2
Mamta Kapoor
{"title":"Numerical solution of one- and two-dimensional Hyperbolic Telegraph equation via Cubic–Quartic Hyperbolic B-Spline DQM: a statistical validity","authors":"Mamta Kapoor","doi":"10.1007/s10910-024-01652-2","DOIUrl":"https://doi.org/10.1007/s10910-024-01652-2","url":null,"abstract":"<p>In present research work, numerical approx. of one- and two-dimensional Hyperbolic Telegraph equations is fetched with aid of Modified Cubic and Quartic Hyperbolic B-spline Differential Quadrature Methods. Modified cubic B-spline is used in Differential Quadrature Method to find weighting coefficients for Method I. Modified Quartic Hyperbolic B-spline is utilized to attain weighting coefficients for Method II. After spatial discretization partial differential equations got reduced in the system of ODEs, which later on tackled with SSPRK43 regime. Total ten Examples are discussed to check the efficacy and robustness of the implemented method. For comparison of results, error norms are evaluated. Graphical presentation of the results is also provided. It got noticed that, in most of the cases, exact solutions and present numerical solutions were compatible. The present scheme is easy to implement and it is a better approach to solve some complex natured partial differential equations. The cubic Hyperbolic B-spline has produced much better errors than the Quartic Hyperbolic B-spline. The statistical validation of the parameters is also provided via generating the correlation matrix heatmap.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785678","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}
引用次数: 0
Positive equilibria of power law kinetic systems with kinetics-based decompositions 幂律动力学系统的正平衡与基于动力学的分解
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-21 DOI: 10.1007/s10910-024-01657-x
Jaysie Mher G. Tiongson, Dylan Antonio S. J. Talabis, Lauro L. Fontanil
{"title":"Positive equilibria of power law kinetic systems with kinetics-based decompositions","authors":"Jaysie Mher G. Tiongson, Dylan Antonio S. J. Talabis, Lauro L. Fontanil","doi":"10.1007/s10910-024-01657-x","DOIUrl":"https://doi.org/10.1007/s10910-024-01657-x","url":null,"abstract":"<p>The goal of this paper is to characterize the existence of positive equilibria of power law systems through their kinetics-based decompositions. To achieve this, we consider subclasses of power law systems: PL-RDK and PL-TIK systems. PL-RDK systems are those in which the kinetic order vectors are reactant-determined, that is, branching reactions have identical vectors. PL-TIK systems are characterized by having linearly independent kinetic order vectors per linkage class. We first introduced the notion of Zero Kinetic Deficiency Decomposition of cycle terminal power law systems. Then, by considering non-cycle terminal power law systems, we extend this by introducing the notion of PL-TIK decomposition. Through these novel decomposition classes, we showed that PL-RDK systems with weakly reversible decompositions admit positive equilibria. Moreover, to ensure the existence of PL-TIK decomposition, we developed an algorithm in which any power law system can generate a PL-TIK decomposition. Lastly, we applied the algorithm to Schmitz’ Global Carbon Cycle Model.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740116","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}
引用次数: 0
Normalizing the hydrogenic polar solutions $$Theta _{ell m}(theta )$$ without Associated Legendre polynomials 对氢极解进行归一化处理 $$heta _{ell m}(theta )$$ 无需关联 Legendre 多项式
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-19 DOI: 10.1007/s10910-024-01649-x
Gregory L. Bason, B. Cameron Reed
{"title":"Normalizing the hydrogenic polar solutions $$Theta _{ell m}(theta )$$ without Associated Legendre polynomials","authors":"Gregory L. Bason, B. Cameron Reed","doi":"10.1007/s10910-024-01649-x","DOIUrl":"https://doi.org/10.1007/s10910-024-01649-x","url":null,"abstract":"<p>The normalization of the polar functions <span>(Theta _{ell , m} (theta ))</span> for the solution of Schrödinger’s equation for the Coulomb potential usually proceeds by appealing to the properties of Associated Legendre polynomials. We show how to achieve the normalization directly from the overall form of the solution and the recursion relation for its series part. When combined with a previous such normalization for the radial part of the solution, the entire hydrogen atom solution can be normalized without having to invoke any properties of special functions.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740118","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}
引用次数: 0
Entropy of hexagonal ice monolayer and of other three-coordinated systems 六角冰单层及其他三配位体系的熵
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-17 DOI: 10.1007/s10910-024-01656-y
Mikhail V. Kirov
{"title":"Entropy of hexagonal ice monolayer and of other three-coordinated systems","authors":"Mikhail V. Kirov","doi":"10.1007/s10910-024-01656-y","DOIUrl":"https://doi.org/10.1007/s10910-024-01656-y","url":null,"abstract":"<p>To calculate the entropy of three-coordinated ice-like systems, a simple and convenient approximate method of local conditional transfer matrices using 2 × 2 matrices is presented. The exponential rate of convergence of the method has been established, which makes it possible to obtain almost exact values ​​of the entropy of infinite systems. The qualitatively higher rate of convergence for three-coordinated systems compared to four-coordinated systems is due to less rigid topological restrictions on the direction of hydrogen (H-) bonds in each lattice site, which results in a significantly weaker the system’s total correlations. Along with the ice hexagonal monolayer, other three-coordinated lattices obtained by decorating a hexagonal monolayer, a square lattice, and a kagome lattice were analyzed. It is shown that approximate cluster methods for estimating the entropy of infinite three-coordinated systems are also quite accurate. The importance of the proposed method of local conditional transfer matrices for ice nanostructures is noted, for which the method is exact.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721657","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}
引用次数: 0
Stability and computational results for chemical kinetics reactions in enzyme 酶中化学动力学反应的稳定性和计算结果
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-17 DOI: 10.1007/s10910-024-01660-2
M. Sivashankar, S. Sabarinathan, Hasib Khan, Jehad Alzabut, J. F. Gómez-Aguilar
{"title":"Stability and computational results for chemical kinetics reactions in enzyme","authors":"M. Sivashankar, S. Sabarinathan, Hasib Khan, Jehad Alzabut, J. F. Gómez-Aguilar","doi":"10.1007/s10910-024-01660-2","DOIUrl":"https://doi.org/10.1007/s10910-024-01660-2","url":null,"abstract":"<p>Kinetic chemical reactions find applications across various fields. In industrial processes, they drive the production of essential materials like fertilizers and pharmaceuticals. In environmental science, they are crucial to understanding pollution dynamics. Additionally, in biochemistry, they underpin vital cellular processes, offering insights into disease mechanisms and drug development. In this work, we present a new advancement of a dynamical system for kinetically controlled chemical reactions and the dependency of its solution on the initial conditions using mathematical techniques for fractional orders. By utilizing this fixed-point approach, we can derive the existence and uniqueness theorem of the proposed model. We further show that the chemical kinetics of the fractional model are stable through the Hyers-Ulam stability condition. We finally run a numerical simulation to verify our conclusions. The manuscript concludes with demonstrative examples.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740117","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}
引用次数: 0
Theorem on rates of alignment of electronegativities of atoms in the process of formation of a chemical bond in a binary molecule 关于二元分子中化学键形成过程中原子电负性排列速率的定理
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-16 DOI: 10.1007/s10910-024-01655-z
Michael Perfileev, Vladislav Lyakishev
{"title":"Theorem on rates of alignment of electronegativities of atoms in the process of formation of a chemical bond in a binary molecule","authors":"Michael Perfileev, Vladislav Lyakishev","doi":"10.1007/s10910-024-01655-z","DOIUrl":"https://doi.org/10.1007/s10910-024-01655-z","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141644020","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}
引用次数: 0
A novel hybrid variation iteration method and eigenvalues of fractional order singular eigenvalue problems 新型混合变异迭代法和分数阶奇异特征值问题的特征值
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-07-15 DOI: 10.1007/s10910-024-01651-3
Sarika Kumari, Lok Nath Kannaujiya, Narendra Kumar, Amit K. Verma, Ravi P. Agarwal
{"title":"A novel hybrid variation iteration method and eigenvalues of fractional order singular eigenvalue problems","authors":"Sarika Kumari, Lok Nath Kannaujiya, Narendra Kumar, Amit K. Verma, Ravi P. Agarwal","doi":"10.1007/s10910-024-01651-3","DOIUrl":"https://doi.org/10.1007/s10910-024-01651-3","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141646962","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}
引用次数: 0
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