Pub Date : 2019-09-01DOI: 10.22052/IJMC.2017.106402.1325
Mostafa Abbaszadeh, M. Dehghan, G. Karamali
The main aim of the current paper is to propose an upwind local radial basis functions-finite difference (RBF-FD) method for solving compressible Euler equation. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equations and finite-rate chemistry is studied. The presented technique is based on the developed idea in [58]. For checking the ability of the new procedure, the compressible Euler equation is solved. This equation has been classified in category of system of advection-diffusion equations. The solutions of advection equations have some shock, thus, special numerical methods should be applied for example discontinuous Galerkin and finite volume methods. Moreover, two problems are given that show the acceptable accuracy and efficiency of the proposed scheme.
{"title":"An upwind local radial basis functions-finite difference (RBF-FD) method for solving compressible Euler equation with application in finite-rate Chemistry","authors":"Mostafa Abbaszadeh, M. Dehghan, G. Karamali","doi":"10.22052/IJMC.2017.106402.1325","DOIUrl":"https://doi.org/10.22052/IJMC.2017.106402.1325","url":null,"abstract":"The main aim of the current paper is to propose an upwind local radial basis functions-finite difference (RBF-FD) method for solving compressible Euler equation. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equations and finite-rate chemistry is studied. The presented technique is based on the developed idea in [58]. For checking the ability of the new procedure, the compressible Euler equation is solved. This equation has been classified in category of system of advection-diffusion equations. The solutions of advection equations have some shock, thus, special numerical methods should be applied for example discontinuous Galerkin and finite volume methods. Moreover, two problems are given that show the acceptable accuracy and efficiency of the proposed scheme.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82462985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.22052/IJMC.2017.82177.1280
K. Pattabiraman, T. Suganya
The topological efficiency index of a connected graph $G,$ denoted by $rho (G),$ is defined as $rho(G)=frac{2W(G)}{left|V(G)right|underline w(G)},$ where $underline w(G)=text { min }left{w_v(G):vin V(G)right}$ and $W(G)$ is the Wiener index of $G.$ In this paper, we obtain the value of topological efficiency index for some composite graphs such as tensor product, strong product, symmetric difference and disjunction of two connected graphs. Further, we have obtained the topological efficiency index for a double graph of a given graph.
{"title":"Topological Efficiency of Some Product Graphs","authors":"K. Pattabiraman, T. Suganya","doi":"10.22052/IJMC.2017.82177.1280","DOIUrl":"https://doi.org/10.22052/IJMC.2017.82177.1280","url":null,"abstract":"The topological efficiency index of a connected graph $G,$ denoted by $rho (G),$ is defined as $rho(G)=frac{2W(G)}{left|V(G)right|underline w(G)},$ where $underline w(G)=text { min }left{w_v(G):vin V(G)right}$ and $W(G)$ is the Wiener index of $G.$ In this paper, we obtain the value of topological efficiency index for some composite graphs such as tensor product, strong product, symmetric difference and disjunction of two connected graphs. Further, we have obtained the topological efficiency index for a double graph of a given graph.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89461644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-01DOI: 10.22052/IJMC.2017.81498.1279
A. Ghalavand
The Wiener index W and the edge-Wiener index W_e of G are defined as the sum of distances between all pairs of vertices in G and the sum of distances between all pairs of edges in G, respectively. In this paper, we identify the four trees, with the first through fourth greatest Wiener and edge-Wiener index among all trees of order n ≥ 10.
{"title":"Trees with the Greatest Wiener and Edge-Wiener Index","authors":"A. Ghalavand","doi":"10.22052/IJMC.2017.81498.1279","DOIUrl":"https://doi.org/10.22052/IJMC.2017.81498.1279","url":null,"abstract":"The Wiener index W and the edge-Wiener index W_e of G are defined as the sum of distances between all pairs of vertices in G and the sum of distances between all pairs of edges in G, respectively. In this paper, we identify the four trees, with the first through fourth greatest Wiener and edge-Wiener index among all trees of order n ≥ 10.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88150012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-01DOI: 10.22052/IJMC.2018.111016.1335
M. M. Khalsaraei, A. Shokri, M. Molayi
In this paper, we present a new class of hybrid methods for the numerical solution of first order ordinary differential equations (ODEs). The accuracy and stability properties of the new methods are investigated. In the final section, we apply new hybrid methods to solve two stiff chemical problems such as Roberston problem.
{"title":"The new high approximation of stiff systems of first order IVPs arising from chemical reactions by k-step L-stable hybrid methods","authors":"M. M. Khalsaraei, A. Shokri, M. Molayi","doi":"10.22052/IJMC.2018.111016.1335","DOIUrl":"https://doi.org/10.22052/IJMC.2018.111016.1335","url":null,"abstract":"In this paper, we present a new class of hybrid methods for the numerical solution of first order ordinary differential equations (ODEs). The accuracy and stability properties of the new methods are investigated. In the final section, we apply new hybrid methods to solve two stiff chemical problems such as Roberston problem.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74144845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-01DOI: 10.22052/IJMC.2018.137247.1370
Gholam Hosein Askarirobati, A. H. Borzabadi, A. Heydari
Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. This paper applies an evolutionary optimization scheme, inspired by Multi-objective Invasive Weed Optimization (MOIWO) and Non-dominated Sorting (NS) strategies, to find approximate solutions for multi-objective optimal control problems (MOCPs). The desired control function may be subjected to severe changes over a period of time. In response to deficiency, the process of dispersal has been modified in the MOIWO. This modification will increase the exploration power of the weeds and reduces the search space gradually during the iteration process. The performance of the proposed algorithm is compared with conventional Non-dominated Sorting Genetic Algorithm (NSGA-II) and Non-dominated Sorting Invasive Weed Optimization (NSIWO) algorithm.The results show that the proposed algorithm has better performance than others in terms of computing time, convergence rate and diversity of solutions on the Pareto frontier.
{"title":"Solving Multi-objective Optimal Control Problems of chemical processes using Hybrid Evolutionary Algorithm","authors":"Gholam Hosein Askarirobati, A. H. Borzabadi, A. Heydari","doi":"10.22052/IJMC.2018.137247.1370","DOIUrl":"https://doi.org/10.22052/IJMC.2018.137247.1370","url":null,"abstract":"Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. This paper applies an evolutionary optimization scheme, inspired by Multi-objective Invasive Weed Optimization (MOIWO) and Non-dominated Sorting (NS) strategies, to find approximate solutions for multi-objective optimal control problems (MOCPs). The desired control function may be subjected to severe changes over a period of time. In response to deficiency, the process of dispersal has been modified in the MOIWO. This modification will increase the exploration power of the weeds and reduces the search space gradually during the iteration process. The performance of the proposed algorithm is compared with conventional Non-dominated Sorting Genetic Algorithm (NSGA-II) and Non-dominated Sorting Invasive Weed Optimization (NSIWO) algorithm.The results show that the proposed algorithm has better performance than others in terms of computing time, convergence rate and diversity of solutions on the Pareto frontier.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78866228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-01DOI: 10.22052/IJMC.2018.114473.1339
D. Heidari, D. Mazaheri, B. Davvaz
A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt metathesis reactions, and we observe that these chemical reactions are examples of the phenomena when composition of two elements is a set of elements.
{"title":"Chemical salt reactions as algebraic hyperstructures","authors":"D. Heidari, D. Mazaheri, B. Davvaz","doi":"10.22052/IJMC.2018.114473.1339","DOIUrl":"https://doi.org/10.22052/IJMC.2018.114473.1339","url":null,"abstract":"A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt metathesis reactions, and we observe that these chemical reactions are examples of the phenomena when composition of two elements is a set of elements.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72623901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-01DOI: 10.22052/IJMC.2019.146761.1388
B. Basavanagoud, Anand P. Barangi, Praveen Jakkannavar
In this paper, we obtain M-polynomial of some graph operations and cy- cle related graphs. As an application, we compute M-polynomial of some nanostruc- tures viz., TUC4C8[p; q] nanotube, TUC4C8[p; q] nanotorus, line graph of subdivision graph of TUC4C8[p; q] nanotube and TUC4C8[p; q] nanotorus, V-tetracenic nanotube and V-tetracenic nanotorus. Further, we derive some degree based topological indices from the obtained polynomials.
{"title":"M-polynomial of some Graph Operations and Cycle Related Graphs","authors":"B. Basavanagoud, Anand P. Barangi, Praveen Jakkannavar","doi":"10.22052/IJMC.2019.146761.1388","DOIUrl":"https://doi.org/10.22052/IJMC.2019.146761.1388","url":null,"abstract":"In this paper, we obtain M-polynomial of some graph operations and cy- cle related graphs. As an application, we compute M-polynomial of some nanostruc- tures viz., TUC4C8[p; q] nanotube, TUC4C8[p; q] nanotorus, line graph of subdivision graph of TUC4C8[p; q] nanotube and TUC4C8[p; q] nanotorus, V-tetracenic nanotube and V-tetracenic nanotorus. Further, we derive some degree based topological indices from the obtained polynomials.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87217334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-03-01DOI: 10.22052/IJMC.2019.174207.1430
Beata Szefler, Raluca Pop
Aromaticity is used to describe the durability and reactivity of structures containing delocalized electrons.In this review article, the aromaticity of fullerenes patched with flowers of 6-and 8-membered ringsis discussed, optimized at the HF and DFT levels of theory, in terms of HOMA and NICS criteria. The aromatic character of these nanostructures allows for functionalization and finally for increasing their solubility in polar solvents. The overall conclusion is that several of the yet hypothetical molecular nanostructures herein described are serious candidates for new medicinal products, as a proposal for personalized medicine.
{"title":"Aromaticity of fullerenes, the way to their functionalization (Review)","authors":"Beata Szefler, Raluca Pop","doi":"10.22052/IJMC.2019.174207.1430","DOIUrl":"https://doi.org/10.22052/IJMC.2019.174207.1430","url":null,"abstract":"Aromaticity is used to describe the durability and reactivity of structures containing delocalized electrons.In this review article, the aromaticity of fullerenes patched with flowers of 6-and 8-membered ringsis discussed, optimized at the HF and DFT levels of theory, in terms of HOMA and NICS criteria. The aromatic character of these nanostructures allows for functionalization and finally for increasing their solubility in polar solvents. The overall conclusion is that several of the yet hypothetical molecular nanostructures herein described are serious candidates for new medicinal products, as a proposal for personalized medicine.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86446953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-03-01DOI: 10.22052/IJMC.2019.151000.1397
M. Ahmadi, E. Farhadi, M. Ghavanloo
Fullerenes have wide application in various fields including electronic and optic, medical science, biotechnology and have received a lot of recent chemists and mathematicians’ attention. Due to many applications of fullerenes, the study of their stability is important. In this paper, we study the effective parameters that affect the fullerene's stability and then according to these parameters, we introduce a new function to examine the stability of every fullerene. By using this function, we determine the stable isometric of each fullerene in a unique way.
{"title":"On the Stability of Fullerenes","authors":"M. Ahmadi, E. Farhadi, M. Ghavanloo","doi":"10.22052/IJMC.2019.151000.1397","DOIUrl":"https://doi.org/10.22052/IJMC.2019.151000.1397","url":null,"abstract":"Fullerenes have wide application in various fields including electronic and optic, medical science, biotechnology and have received a lot of recent chemists and mathematicians’ attention. Due to many applications of fullerenes, the study of their stability is important. In this paper, we study the effective parameters that affect the fullerene's stability and then according to these parameters, we introduce a new function to examine the stability of every fullerene. By using this function, we determine the stable isometric of each fullerene in a unique way.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73272142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-03-01DOI: 10.22052/IJMC.2018.118152.1343
F. Afshari, M. Maghasedi
A C4C8 net is a trivalent decoration made by alternating squares C4 and octagons C8. It can cover either a cylinder or a torus. In this paper, we study the adjacency spectrum of rhomboidal C4C8 tori. We also give lower and upper bounds for a chemical quantity, namely Estrada index, for a C4C8 net.
{"title":"On the Eigenvalues of Rhomboidal C4C8(R)[n; n] Nanotori","authors":"F. Afshari, M. Maghasedi","doi":"10.22052/IJMC.2018.118152.1343","DOIUrl":"https://doi.org/10.22052/IJMC.2018.118152.1343","url":null,"abstract":"A C4C8 net is a trivalent decoration made by alternating squares C4 and octagons C8. It can cover either a cylinder or a torus. In this paper, we study the adjacency spectrum of rhomboidal C4C8 tori. We also give lower and upper bounds for a chemical quantity, namely Estrada index, for a C4C8 net.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81725147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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