Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,na...Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.展开更多
Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as ...Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2 and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.展开更多
Bond connectivity topological index S i based on chemical bonds was defined by using a matrix method.And S i is formed by atomic parameters such as the number of valence electrons,the number of the highest main quan...Bond connectivity topological index S i based on chemical bonds was defined by using a matrix method.And S i is formed by atomic parameters such as the number of valence electrons,the number of the highest main quantum of atoms and the bonding electrons and bond parameters such as the length of bonds,the electronegativity difference of bonding atoms.The molecular bond connectivity topological index S is composed of S i.The thermodynamic properties of saturated hydrocarbons,unsaturated hydrocarbons,oxygen organic,methane halide and transitional element compounds and the molecular bond connectivity topological index S have an optimal correlative relationship.展开更多
Topological method was applied firstly to calculate the topological connectivity index of minerals (TCIM). The reciprocal of effective atomic refractivity of metal element in minerals was chosen as its valence. The re...Topological method was applied firstly to calculate the topological connectivity index of minerals (TCIM). The reciprocal of effective atomic refractivity of metal element in minerals was chosen as its valence. The reasonability of TCIM as an activity criterion was tested through comparison of TCIM with two kinds of electronegativity parameter, i.e. ionic percentage and energy criteria of Yang’s electronegativity, solubility product, energy criterion according to the generalized perturbation theory and adsorption of flotation reagents on the surface of minerals. The results indicated that TCIM is an effective structural parameter of minerals to study the structure activity relationship. In addition, different mineral is of different TCIM value, so TCIM brings about convenience in comparison of flotation activity for minerals.展开更多
Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and...Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and A(t), B(t), C(t), D(t) were developed on the basis of molecular topology and autocorrelation function in mathematics. The first group were obtained from Van der Waals volume, electronegativity and topological vertex degree;and the second group were obtained from the different combination of topological vertex degree.Corresponding softwares of ATIJP and ATITP have been developed for calculating these two new groups of indexes. Better results have been obtained from the application of these indexes in QSAR study.展开更多
A novel topological index derived from eccentric connectivity index has been proposed. The new topological index and eccentric connectivity index were correlated with eight physical properties such as the boiling poin...A novel topological index derived from eccentric connectivity index has been proposed. The new topological index and eccentric connectivity index were correlated with eight physical properties such as the boiling point, critical temperature, critical pressure, critical volume, evaporation heat, density, heat capacity, surface tension, and three thermodynamic properties such as standard enthalpy, standard entropy and standard formation free energy of alkanes. A series of empiric equations for calculating the properties were obtained. Correlation coefficients of nine properties were more than 0.99. Regression analysis and calculation results indicated that the topological indices were well correlated with the physico-chemical properties of alkanes, and the novel topological index was far superior to eccentric connectivity index in the correlation.展开更多
Based on the distance matrix and adjacent matrix of molecular structure, a novel topological index is proposed. A set of topological parameters is built to reflect the magnitude, shape and other structure information ...Based on the distance matrix and adjacent matrix of molecular structure, a novel topological index is proposed. A set of topological parameters is built to reflect the magnitude, shape and other structure information of the substance. The interdependency between new topological index and conductivity for alkylimidazolium cations was analyzed and a quantitative relationship to describe this interdependency was obtained using the linear analyzing method. The analysis results show that the proposed topological index is quite satisfied with higher precision of the prediction. From the molecular structure of ionic liquid, the value of conductivity can be predicted correctly. This method can be also used to predict other physical properties of the ionic liquid.展开更多
This paper proposed a topological index S which combined the graph feature and chemical surroundings. It can reflect the essential properties of chemical compounds better. The capacity of distinguishing structural iso...This paper proposed a topological index S which combined the graph feature and chemical surroundings. It can reflect the essential properties of chemical compounds better. The capacity of distinguishing structural isomers of saturated hydrocarbons is high.展开更多
Edge-adjacency index and information topological index for 82 molecules of alkanes have been constructed and calculated. The topological indices were used to correlate with seven physical properties of the alkanes. So...Edge-adjacency index and information topological index for 82 molecules of alkanes have been constructed and calculated. The topological indices were used to correlate with seven physical properties of the alkanes. Some empirical equations were obtained through regression. The regression and calculation results show a good agreement of the topological indices and the properties.展开更多
The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecu...The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded cases of the adjacent atoms respectively. The standard formation enthalpies of ABn(g) molecules were correlated with F’* (A = C, Al, Si, Ti, Zr, B = F, Cl, Br, I, H, n=1 -4) and these correlation coefficients are all more than 0.96. Some molecules (e.g CH4, SiH4,etc. )can be preferably handled by F* but can not be dealt with by other topological indices. By contrast to traditional hydrogen suppressed graph, the contribution of hydrogen atoms to structures and properties of molecules is considered.展开更多
The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of str...The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of structural topology optimization are also discussed.Furthermore,two structural topology optimization models,optimizing a performance index under the limitation of an economic index,represented by the minimum compliance with a volume constraint(MCVC)model,and optimizing an economic index under the limitation of a performance index,represented by the minimum weight with a displacement constraint(MWDC)model,are presented.Based on a comparison of numerical example results,the conclusions can be summarized as follows:(1)under the same external loading and displacement performance conditions,the results of the MWDC model are almost equal to those of the MCVC model;(2)the MWDC model overcomes the difficulties and shortcomings of the MCVC model;this makes the MWDC model more feasible in model construction;(3)constructing a model of minimizing an economic index under the limitations of performance indexes is better at meeting the needs of practical engineering problems and completely satisfies safety and economic requirements in mechanical engineering,which have remained unchanged since the early days of mechanical engineering.展开更多
A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The struc...A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.There are various uses of graph theory in the field of basic science.The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points.In this paper we study the topological descriptor of a newly design hexagon star network.More preciously,we have computed variation of the Randic0 R0,fourth Zagreb M4,fifth Zagreb M5,geometric-arithmetic GA;atom-bond connectivity ABC;harmonic H;symmetric division degree SDD;first redefined Zagreb,second redefined Zagreb,third redefined Zagreb,augmented Zagreb AZI,Albertson A;Irregularity measures,Reformulated Zagreb,and forgotten topological descriptors for hexagon star network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.We also gave the numerical and graphical representations comparisons of our different results.展开更多
A numerical parameter mathematically derived from the graph structure is a topological index.The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model ...A numerical parameter mathematically derived from the graph structure is a topological index.The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model between the chemical structures of various chemicals compounds.Here,we investigate some old degree-based topological indices like Randic index,sum connectivity index,ABC index,GA index,1st and 2nd Zagreb indices,modified second Zagreb index,redefined version of 1st,2nd and 3rd Zagreb indices,hyper and augmented Zagreb indices,forgotten index and symmetric division degree index,and some new degree-based indices like SK index,SK1 index,SK2 index,and AG1 index of triangular chandelier-lattice(TCL).The results are generalized by using edge partition and closed formulas for topological indices of triangular chandelier-lattice are analysed.展开更多
The introduction of graph-theoretical structure descriptors represents an important step forward in the research of predictive models in chemistry and falls within the lines of the increasing use of mathematical and c...The introduction of graph-theoretical structure descriptors represents an important step forward in the research of predictive models in chemistry and falls within the lines of the increasing use of mathematical and computational methods in contemporary chemistry.The basis for these models is the study of the quantitative structure-property and structure-activity relationship.In this paper,we investigate Great rhom-bitrihexagonal which is a kind of dodecagon honeycomb net-work covered by quadrangle and hexagon.Many topological indexes of Great rhom-bitrihexagonal have being investigated,such as sum-connectivity index,atom-bond connectivity index,geometric-arithmetic index,fifth,harmonic index,Randićconnectivity index,first Zagreb index,second Zagreb index and the corresponding Zagreb polynomials,modified Zagreb index,fourth atom-bond connectivity index,augmented Zagreb index,hyper-Zagreb index,Sankruti index,forgotten topological index,first multiple Zagreb index,second multiple Zagreb index,as well as derived geometric-arithmetic index,Narumi-Katayama index and modified Narumi-Katayama index.展开更多
Serious games have recently enticed many researchers due to their wide range of capabilities.A serious game is a mean of gaming for a serious job such as healthcare,education,and entertainment purposes.With the advanc...Serious games have recently enticed many researchers due to their wide range of capabilities.A serious game is a mean of gaming for a serious job such as healthcare,education,and entertainment purposes.With the advancement in the Internet of Things,new research directions are paving the way in serious games.However,the internet connectivity of players in Internetof-things-enabled serious games is a matter of concern and has been worth investigating.Different studies on topologies,frameworks,and architecture of communication technologies are conducted to integrate them with serious games on machine and network levels.However,the Internet of things,whose core requirement is the provision of connectivity on the application layer,has different challenges for more dynamic applications such as serious games.The performance of Internet-of-things-enabled serious games depends on the type of infrastructure(wired,wireless)network and Mobile Ad-hoc Network(MANET)and is subtly different from one type of network to another.This paper investigates the connectivity challenges in the Internet-of-thingsenabled serious games using the mentioned infrastructure and identifies the core requirements for these games.It also aims to evaluate various parameters such as reliability,scalability,response time,to name a few,with varying infrastructure and network types.Results highlight the preliminary infrastructure finding and highlight the core setup for which the games are deployed.Moreover,this work will be a steppingstone for architecting the connectivity in serious games in a typical smart space with many infrastructures such as wired networks,wireless networks,and MANET.展开更多
文摘Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.
文摘Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2 and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.
文摘Bond connectivity topological index S i based on chemical bonds was defined by using a matrix method.And S i is formed by atomic parameters such as the number of valence electrons,the number of the highest main quantum of atoms and the bonding electrons and bond parameters such as the length of bonds,the electronegativity difference of bonding atoms.The molecular bond connectivity topological index S is composed of S i.The thermodynamic properties of saturated hydrocarbons,unsaturated hydrocarbons,oxygen organic,methane halide and transitional element compounds and the molecular bond connectivity topological index S have an optimal correlative relationship.
文摘Topological method was applied firstly to calculate the topological connectivity index of minerals (TCIM). The reciprocal of effective atomic refractivity of metal element in minerals was chosen as its valence. The reasonability of TCIM as an activity criterion was tested through comparison of TCIM with two kinds of electronegativity parameter, i.e. ionic percentage and energy criteria of Yang’s electronegativity, solubility product, energy criterion according to the generalized perturbation theory and adsorption of flotation reagents on the surface of minerals. The results indicated that TCIM is an effective structural parameter of minerals to study the structure activity relationship. In addition, different mineral is of different TCIM value, so TCIM brings about convenience in comparison of flotation activity for minerals.
文摘Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and A(t), B(t), C(t), D(t) were developed on the basis of molecular topology and autocorrelation function in mathematics. The first group were obtained from Van der Waals volume, electronegativity and topological vertex degree;and the second group were obtained from the different combination of topological vertex degree.Corresponding softwares of ATIJP and ATITP have been developed for calculating these two new groups of indexes. Better results have been obtained from the application of these indexes in QSAR study.
基金Supported by the Natural Science Fund of Hubei Educational Committee (99A088)
文摘A novel topological index derived from eccentric connectivity index has been proposed. The new topological index and eccentric connectivity index were correlated with eight physical properties such as the boiling point, critical temperature, critical pressure, critical volume, evaporation heat, density, heat capacity, surface tension, and three thermodynamic properties such as standard enthalpy, standard entropy and standard formation free energy of alkanes. A series of empiric equations for calculating the properties were obtained. Correlation coefficients of nine properties were more than 0.99. Regression analysis and calculation results indicated that the topological indices were well correlated with the physico-chemical properties of alkanes, and the novel topological index was far superior to eccentric connectivity index in the correlation.
文摘Based on the distance matrix and adjacent matrix of molecular structure, a novel topological index is proposed. A set of topological parameters is built to reflect the magnitude, shape and other structure information of the substance. The interdependency between new topological index and conductivity for alkylimidazolium cations was analyzed and a quantitative relationship to describe this interdependency was obtained using the linear analyzing method. The analysis results show that the proposed topological index is quite satisfied with higher precision of the prediction. From the molecular structure of ionic liquid, the value of conductivity can be predicted correctly. This method can be also used to predict other physical properties of the ionic liquid.
文摘This paper proposed a topological index S which combined the graph feature and chemical surroundings. It can reflect the essential properties of chemical compounds better. The capacity of distinguishing structural isomers of saturated hydrocarbons is high.
文摘Edge-adjacency index and information topological index for 82 molecules of alkanes have been constructed and calculated. The topological indices were used to correlate with seven physical properties of the alkanes. Some empirical equations were obtained through regression. The regression and calculation results show a good agreement of the topological indices and the properties.
基金Funded by the Nature Science Foundation of China (No. 29773033)
文摘The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded cases of the adjacent atoms respectively. The standard formation enthalpies of ABn(g) molecules were correlated with F’* (A = C, Al, Si, Ti, Zr, B = F, Cl, Br, I, H, n=1 -4) and these correlation coefficients are all more than 0.96. Some molecules (e.g CH4, SiH4,etc. )can be preferably handled by F* but can not be dealt with by other topological indices. By contrast to traditional hydrogen suppressed graph, the contribution of hydrogen atoms to structures and properties of molecules is considered.
基金supported by the National Natural Science Foundation of China(Grant 11172013)
文摘The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of structural topology optimization are also discussed.Furthermore,two structural topology optimization models,optimizing a performance index under the limitation of an economic index,represented by the minimum compliance with a volume constraint(MCVC)model,and optimizing an economic index under the limitation of a performance index,represented by the minimum weight with a displacement constraint(MWDC)model,are presented.Based on a comparison of numerical example results,the conclusions can be summarized as follows:(1)under the same external loading and displacement performance conditions,the results of the MWDC model are almost equal to those of the MCVC model;(2)the MWDC model overcomes the difficulties and shortcomings of the MCVC model;this makes the MWDC model more feasible in model construction;(3)constructing a model of minimizing an economic index under the limitations of performance indexes is better at meeting the needs of practical engineering problems and completely satisfies safety and economic requirements in mechanical engineering,which have remained unchanged since the early days of mechanical engineering.
文摘A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.There are various uses of graph theory in the field of basic science.The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points.In this paper we study the topological descriptor of a newly design hexagon star network.More preciously,we have computed variation of the Randic0 R0,fourth Zagreb M4,fifth Zagreb M5,geometric-arithmetic GA;atom-bond connectivity ABC;harmonic H;symmetric division degree SDD;first redefined Zagreb,second redefined Zagreb,third redefined Zagreb,augmented Zagreb AZI,Albertson A;Irregularity measures,Reformulated Zagreb,and forgotten topological descriptors for hexagon star network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.We also gave the numerical and graphical representations comparisons of our different results.
文摘A numerical parameter mathematically derived from the graph structure is a topological index.The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model between the chemical structures of various chemicals compounds.Here,we investigate some old degree-based topological indices like Randic index,sum connectivity index,ABC index,GA index,1st and 2nd Zagreb indices,modified second Zagreb index,redefined version of 1st,2nd and 3rd Zagreb indices,hyper and augmented Zagreb indices,forgotten index and symmetric division degree index,and some new degree-based indices like SK index,SK1 index,SK2 index,and AG1 index of triangular chandelier-lattice(TCL).The results are generalized by using edge partition and closed formulas for topological indices of triangular chandelier-lattice are analysed.
文摘The introduction of graph-theoretical structure descriptors represents an important step forward in the research of predictive models in chemistry and falls within the lines of the increasing use of mathematical and computational methods in contemporary chemistry.The basis for these models is the study of the quantitative structure-property and structure-activity relationship.In this paper,we investigate Great rhom-bitrihexagonal which is a kind of dodecagon honeycomb net-work covered by quadrangle and hexagon.Many topological indexes of Great rhom-bitrihexagonal have being investigated,such as sum-connectivity index,atom-bond connectivity index,geometric-arithmetic index,fifth,harmonic index,Randićconnectivity index,first Zagreb index,second Zagreb index and the corresponding Zagreb polynomials,modified Zagreb index,fourth atom-bond connectivity index,augmented Zagreb index,hyper-Zagreb index,Sankruti index,forgotten topological index,first multiple Zagreb index,second multiple Zagreb index,as well as derived geometric-arithmetic index,Narumi-Katayama index and modified Narumi-Katayama index.
基金This research is supported by the Ministry of Culture,Sports and Tourism and Korea Creative Content Agency(Project Number:R2020040243)by the National Research Foundation of Korea(NRF)Grant funded by the Korean government under Grant NRF-2021R1I1A1A01045177.
文摘Serious games have recently enticed many researchers due to their wide range of capabilities.A serious game is a mean of gaming for a serious job such as healthcare,education,and entertainment purposes.With the advancement in the Internet of Things,new research directions are paving the way in serious games.However,the internet connectivity of players in Internetof-things-enabled serious games is a matter of concern and has been worth investigating.Different studies on topologies,frameworks,and architecture of communication technologies are conducted to integrate them with serious games on machine and network levels.However,the Internet of things,whose core requirement is the provision of connectivity on the application layer,has different challenges for more dynamic applications such as serious games.The performance of Internet-of-things-enabled serious games depends on the type of infrastructure(wired,wireless)network and Mobile Ad-hoc Network(MANET)and is subtly different from one type of network to another.This paper investigates the connectivity challenges in the Internet-of-thingsenabled serious games using the mentioned infrastructure and identifies the core requirements for these games.It also aims to evaluate various parameters such as reliability,scalability,response time,to name a few,with varying infrastructure and network types.Results highlight the preliminary infrastructure finding and highlight the core setup for which the games are deployed.Moreover,this work will be a steppingstone for architecting the connectivity in serious games in a typical smart space with many infrastructures such as wired networks,wireless networks,and MANET.