Pub Date : 2023-01-01DOI: 10.46793/match.90-1.019a
Carlos Andreu-Vilarroig, J. Cortés, A. Navarro‐Quiles, Sorina‐Madalina Sferle
The general adsorption kinetic model, also called pseudo- order (PNO) equation, is revisited using random differential equations. We provide a full probabilistic solution of the model, which is a stochastic process, by computing its first probability density function under very general hypotheses on its parameters, that are treated as absolutely continuous random variables with an arbitrary joint probability density function. The analysis is based on the so called Random Variable Transformation technique. From the first probability density function, we compute relevant information of the PNO model, such that, the mean, the variance and confidence interval. We also provide explicit expressions for the probability density functions of other significant quantities as the time required to reach a specific level of absorbed substance or the rate coefficient of the chemical reaction. All the theoretical findings are illustrated by means of real data. The application includes a thorough discussion about two important uncertainty quantification inverse methods, namely, the Random Least Mean Square and the Bayesian technique, to assign appropriate probability density functions to all the PNO model parameters so that the solution captures data uncertainties.
{"title":"Statistical Analysis of a General Adsorption Kinetic Model with Randomness in Its Formulation. An Application to Real Data","authors":"Carlos Andreu-Vilarroig, J. Cortés, A. Navarro‐Quiles, Sorina‐Madalina Sferle","doi":"10.46793/match.90-1.019a","DOIUrl":"https://doi.org/10.46793/match.90-1.019a","url":null,"abstract":"The general adsorption kinetic model, also called pseudo- order (PNO) equation, is revisited using random differential equations. We provide a full probabilistic solution of the model, which is a stochastic process, by computing its first probability density function under very general hypotheses on its parameters, that are treated as absolutely continuous random variables with an arbitrary joint probability density function. The analysis is based on the so called Random Variable Transformation technique. From the first probability density function, we compute relevant information of the PNO model, such that, the mean, the variance and confidence interval. We also provide explicit expressions for the probability density functions of other significant quantities as the time required to reach a specific level of absorbed substance or the rate coefficient of the chemical reaction. All the theoretical findings are illustrated by means of real data. The application includes a thorough discussion about two important uncertainty quantification inverse methods, namely, the Random Least Mean Square and the Bayesian technique, to assign appropriate probability density functions to all the PNO model parameters so that the solution captures data uncertainties.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79084073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.89-3.665j
S. Joseph
We define a general unary graph operation and give several applications of these operation in this paper. The adjacency matrix and the complete spectrum of the derived graphs are determined. Different methods for generating sequences of orderenergetic graphs from known orderenergetic graphs are described. Several methods are described for generating orderenergetic graphs from non-orderenergetic graphs. Methods for generating new families of integral graphs using this new operation are also discussed. It is also possible to generate infinite sequences of pair of equienergetic and non-cospectral graphs using this graph operation.
{"title":"Several Methods for Generating Families of Orderenergetic, Integral and Equienergetic Graphs","authors":"S. Joseph","doi":"10.46793/match.89-3.665j","DOIUrl":"https://doi.org/10.46793/match.89-3.665j","url":null,"abstract":"We define a general unary graph operation and give several applications of these operation in this paper. The adjacency matrix and the complete spectrum of the derived graphs are determined. Different methods for generating sequences of orderenergetic graphs from known orderenergetic graphs are described. Several methods are described for generating orderenergetic graphs from non-orderenergetic graphs. Methods for generating new families of integral graphs using this new operation are also discussed. It is also possible to generate infinite sequences of pair of equienergetic and non-cospectral graphs using this graph operation.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83552826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.90-1.075g
Marcos González Laffitte, Nora Beier, Nico Domschke, Peter F. Stadler
The computation of reliable, chemically correct atom maps from educt/product pairs has turned out to be a difficult problem in cheminformatics because the chemically correct solution is not necessarily an optimal solution for combinatorial formulations such as maximum common subgraph problems. As a consequence, competing models have been devised and compared in extensive benchmarking studies. Due to isomorphisms among products and educts it is not immediately obvious, however, when two atom maps for a given educt/product pairs are the same. We formalize here the equivalence of atom maps and show that equivalence of atom maps is in turn equivalent to the isomorphism of labeled auxiliary graphs. In particular, we demonstrate that Fujita's Imaginary Transition State can be used for this purpose. Numerical experiments show that practical feasibility. Generalizations to the equivalence of subgraph matches, double pushout graph transformation rules, and mechanisms of multi-step reactions are discussed briefly.
{"title":"Comparison of Atom Maps","authors":"Marcos González Laffitte, Nora Beier, Nico Domschke, Peter F. Stadler","doi":"10.46793/match.90-1.075g","DOIUrl":"https://doi.org/10.46793/match.90-1.075g","url":null,"abstract":"The computation of reliable, chemically correct atom maps from educt/product pairs has turned out to be a difficult problem in cheminformatics because the chemically correct solution is not necessarily an optimal solution for combinatorial formulations such as maximum common subgraph problems. As a consequence, competing models have been devised and compared in extensive benchmarking studies. Due to isomorphisms among products and educts it is not immediately obvious, however, when two atom maps for a given educt/product pairs are the same. We formalize here the equivalence of atom maps and show that equivalence of atom maps is in turn equivalent to the isomorphism of labeled auxiliary graphs. In particular, we demonstrate that Fujita's Imaginary Transition State can be used for this purpose. Numerical experiments show that practical feasibility. Generalizations to the equivalence of subgraph matches, double pushout graph transformation rules, and mechanisms of multi-step reactions are discussed briefly.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87021968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.90-1.151d
Qamar Din, Umer Saeed
Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.
{"title":"Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System","authors":"Qamar Din, Umer Saeed","doi":"10.46793/match.90-1.151d","DOIUrl":"https://doi.org/10.46793/match.90-1.151d","url":null,"abstract":"Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84250089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.90-1.005a
A. Ashrafi, A. Bretto, A. Faisant
In this article we build a linear representation starting from a multigraph; this allows us to give an algebraic view of the multigraph we are studying. We show that two isomorphic multigraphs give equivalent representations; conversely two equivalent representations give isomorphic multigraphs. For the clarity of the article we give at the beginning, classical results on representations, nevertheless these are specific to our graph representation.
{"title":"Linear Representation of Graphs: Applications to Molecular Graphs","authors":"A. Ashrafi, A. Bretto, A. Faisant","doi":"10.46793/match.90-1.005a","DOIUrl":"https://doi.org/10.46793/match.90-1.005a","url":null,"abstract":"In this article we build a linear representation starting from a multigraph; this allows us to give an algebraic view of the multigraph we are studying. We show that two isomorphic multigraphs give equivalent representations; conversely two equivalent representations give isomorphic multigraphs. For the clarity of the article we give at the beginning, classical results on representations, nevertheless these are specific to our graph representation.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75040494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.89-3.687g
S. K. Ghezelahmad
The matching energy of a graph G, denoted by ME(G), is def ined as the sum of absolute values of the zeros of the matching polynomial of G. In this paper, we prove that if G is a connected graph of order n with maximum degree at most 3, then ME(G) > n with only six exceptions. In particular, we show that there are only two connected graphs with maximum degree at most three, whose matching energies are equal to the number of vertices.
{"title":"Matching Energy of Graphs with Maximum Degree at Most 3","authors":"S. K. Ghezelahmad","doi":"10.46793/match.89-3.687g","DOIUrl":"https://doi.org/10.46793/match.89-3.687g","url":null,"abstract":"The matching energy of a graph G, denoted by ME(G), is def ined as the sum of absolute values of the zeros of the matching polynomial of G. In this paper, we prove that if G is a connected graph of order n with maximum degree at most 3, then ME(G) > n with only six exceptions. In particular, we show that there are only two connected graphs with maximum degree at most three, whose matching energies are equal to the number of vertices.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76309786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.89-3.699g
W. Gao
{"title":"Chemical Trees with Maximal VDB Topological Indices","authors":"W. Gao","doi":"10.46793/match.89-3.699g","DOIUrl":"https://doi.org/10.46793/match.89-3.699g","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82782599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.90-1.103l
Yizhong Liu
Recently, establishing proper dynamical models to describe the relationship among different chemical substances has become a vital theme in chemistry. In this present article, we set up a new fractional-order delayed glycolytic oscillator model. Utilizing the contraction mapping theorem, we explore the existence and uniqueness of the solution to the involved fractional glycolytic oscillator model with delay. By virtue of some suitable analytical skills, we discuss the non-negativeness of the solution to the established fractional glycolytic oscillator system. Taking advantage of a suitable function, we investigate the boundedness of the fractional glycolytic oscillator system. Exploiting the stability and bifurcation theory of fractional dynamical system, we study the stability and the generation of Hopf bifurcation of the fractional glycolytic oscillator system with delay. Making use of delayed feedback controller and PDα controller, we deal with the Hopf bifurcation control of the fractional glycolytic oscillator system owing delay. Computer simulation results are displayed to support the obtained assertions. The acquired results of this article own great theoretical value in dominating the concentrations of different chemical compositions.
{"title":"Exploration and Control of Bifurcation in a Fractional-Order Delayed Glycolytic Oscillator Model","authors":"Yizhong Liu","doi":"10.46793/match.90-1.103l","DOIUrl":"https://doi.org/10.46793/match.90-1.103l","url":null,"abstract":"Recently, establishing proper dynamical models to describe the relationship among different chemical substances has become a vital theme in chemistry. In this present article, we set up a new fractional-order delayed glycolytic oscillator model. Utilizing the contraction mapping theorem, we explore the existence and uniqueness of the solution to the involved fractional glycolytic oscillator model with delay. By virtue of some suitable analytical skills, we discuss the non-negativeness of the solution to the established fractional glycolytic oscillator system. Taking advantage of a suitable function, we investigate the boundedness of the fractional glycolytic oscillator system. Exploiting the stability and bifurcation theory of fractional dynamical system, we study the stability and the generation of Hopf bifurcation of the fractional glycolytic oscillator system with delay. Making use of delayed feedback controller and PDα controller, we deal with the Hopf bifurcation control of the fractional glycolytic oscillator system owing delay. Computer simulation results are displayed to support the obtained assertions. The acquired results of this article own great theoretical value in dominating the concentrations of different chemical compositions.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79987075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.89-3.583d
K. Das, T. Vetrík
{"title":"General Gutman Index of a Graph","authors":"K. Das, T. Vetrík","doi":"10.46793/match.89-3.583d","DOIUrl":"https://doi.org/10.46793/match.89-3.583d","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80089179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.46793/match.90-1.235y
Luzhen Ye
{"title":"Further Variants of Gutman's Formulas","authors":"Luzhen Ye","doi":"10.46793/match.90-1.235y","DOIUrl":"https://doi.org/10.46793/match.90-1.235y","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81432964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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