In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic. Global dynamics of the co-existing equilibrium point has been discussed with the help of the geometric approach. Furthermore, it is established that the proposed system undergoes through a Hopf bifurcation with respect to some important parameters. Finally, some numerical simulations have been done to test our theoretical results.
{"title":"Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey","authors":"P. Panja, Soovoojeet Jana, S. Mondal","doi":"10.3934/naco.2020033","DOIUrl":"https://doi.org/10.3934/naco.2020033","url":null,"abstract":"In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic. Global dynamics of the co-existing equilibrium point has been discussed with the help of the geometric approach. Furthermore, it is established that the proposed system undergoes through a Hopf bifurcation with respect to some important parameters. Finally, some numerical simulations have been done to test our theoretical results.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"45 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84282543","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}
The current work aims at finding the approximate solution to solve the nonlinear fractional type Volterra integro-differential equation begin{document}$ begin{equation*} sumlimits_{k = 1}^{m}F_{k}(x)D^{(kalpha )}y(x)+lambda int_{0}^{x}K(x, t)D^{(alpha )}y(t)dt = g(x)y^{2}(x)+h(x)y(x)+P(x). end{equation*} $end{document} In order to solve the aforementioned equation, the researchers relied on the Bernstein polynomials besides the fractional Caputo derivatives through applying the collocation method. So, the equation becomes nonlinear system of equations. By solving the former nonlinear system equation, we get the approximate solution in form of Bernstein's fractional series. Besides, we will present some examples with the estimate of the error.
The current work aims at finding the approximate solution to solve the nonlinear fractional type Volterra integro-differential equation begin{document}$ begin{equation*} sumlimits_{k = 1}^{m}F_{k}(x)D^{(kalpha )}y(x)+lambda int_{0}^{x}K(x, t)D^{(alpha )}y(t)dt = g(x)y^{2}(x)+h(x)y(x)+P(x). end{equation*} $end{document} In order to solve the aforementioned equation, the researchers relied on the Bernstein polynomials besides the fractional Caputo derivatives through applying the collocation method. So, the equation becomes nonlinear system of equations. By solving the former nonlinear system equation, we get the approximate solution in form of Bernstein's fractional series. Besides, we will present some examples with the estimate of the error.
{"title":"Application of the bernstein polynomials for solving the nonlinear fractional type Volterra integro-differential equation with caputo fractional derivatives","authors":"Miloud Moussai","doi":"10.3934/NACO.2021021","DOIUrl":"https://doi.org/10.3934/NACO.2021021","url":null,"abstract":"The current work aims at finding the approximate solution to solve the nonlinear fractional type Volterra integro-differential equation begin{document}$ begin{equation*} sumlimits_{k = 1}^{m}F_{k}(x)D^{(kalpha )}y(x)+lambda int_{0}^{x}K(x, t)D^{(alpha )}y(t)dt = g(x)y^{2}(x)+h(x)y(x)+P(x). end{equation*} $end{document} In order to solve the aforementioned equation, the researchers relied on the Bernstein polynomials besides the fractional Caputo derivatives through applying the collocation method. So, the equation becomes nonlinear system of equations. By solving the former nonlinear system equation, we get the approximate solution in form of Bernstein's fractional series. Besides, we will present some examples with the estimate of the error.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"24 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78215987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we define a new class of functions on Riemannian manifolds, called geodesic begin{document}$ mathcal{E} $end{document}-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local begin{document}$ mathcal{E} $end{document}-invex set.
In this article, we define a new class of functions on Riemannian manifolds, called geodesic begin{document}$ mathcal{E} $end{document}-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local begin{document}$ mathcal{E} $end{document}-invex set.
{"title":"Geodesic $ mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems","authors":"Akhlad Iqbal, P. Kumar","doi":"10.3934/naco.2021040","DOIUrl":"https://doi.org/10.3934/naco.2021040","url":null,"abstract":"<p style='text-indent:20px;'>In this article, we define a new class of functions on Riemannian manifolds, called geodesic <inline-formula><tex-math id=\"M2\">begin{document}$ mathcal{E} $end{document}</tex-math></inline-formula>-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local <inline-formula><tex-math id=\"M3\">begin{document}$ mathcal{E} $end{document}</tex-math></inline-formula>-invex set.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"89 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79765985","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}
This paper discusses exact (approximate) controllability and exact (approximate) observability of stochastic implicit systems in Banach spaces. Firstly, we introduce the stochastic GE-evolution operator in Banach space and discuss existence and uniqueness of the mild solution to stochastic implicit systems by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact (approximate) controllability and exact (approximate) observability of the systems considered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.
{"title":"Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator","authors":"Zhao-qiang Ge","doi":"10.3934/NACO.2021009","DOIUrl":"https://doi.org/10.3934/NACO.2021009","url":null,"abstract":"This paper discusses exact (approximate) controllability and exact (approximate) observability of stochastic implicit systems in Banach spaces. Firstly, we introduce the stochastic GE-evolution operator in Banach space and discuss existence and uniqueness of the mild solution to stochastic implicit systems by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact (approximate) controllability and exact (approximate) observability of the systems considered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"50 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79128356","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}
The aim of this work is to apply the results of R. Gabasov et al. [ 4 , 14 ] to an extended class of optimal control problems in the Bolza form, with intermediate phase constraints and multivariate control. In this paper, the developed iterative numerical method avoids the discretization of the dynamical system. Indeed, by using a piecewise constant control, the problem is reduced for each iteration to a linear programming problem, this auxiliary task allows to improve the value of the quality criterion. The process is repeated until the optimal or the suboptimal control is obtained. As an application, we use this method to solve an extension of the deterministic optimal cash management model of S.P. Sethi [ 31 , 32 ]. In this extension, we assume that the bank overdrafts and short selling of stock are allowed, but within the authorized time limit. The results of the numerical example show that the optimal decision for the firm depends closely on the intermediate moment, the optimal decision for the firm is to purchase until a certain date the stocks at their authorized maximum value in order to take advantage of the returns derived from stock. After that, it sales the stocks at their authorized maximum value in order to satisfy the constraint at the intermediate moment.
{"title":"Optimal control of a dynamical system with intermediate phase constraints and applications in cash management","authors":"Mourad Azi, Mohand Ouamer Bibi","doi":"10.3934/NACO.2021005","DOIUrl":"https://doi.org/10.3934/NACO.2021005","url":null,"abstract":"The aim of this work is to apply the results of R. Gabasov et al. [ 4 , 14 ] to an extended class of optimal control problems in the Bolza form, with intermediate phase constraints and multivariate control. In this paper, the developed iterative numerical method avoids the discretization of the dynamical system. Indeed, by using a piecewise constant control, the problem is reduced for each iteration to a linear programming problem, this auxiliary task allows to improve the value of the quality criterion. The process is repeated until the optimal or the suboptimal control is obtained. As an application, we use this method to solve an extension of the deterministic optimal cash management model of S.P. Sethi [ 31 , 32 ]. In this extension, we assume that the bank overdrafts and short selling of stock are allowed, but within the authorized time limit. The results of the numerical example show that the optimal decision for the firm depends closely on the intermediate moment, the optimal decision for the firm is to purchase until a certain date the stocks at their authorized maximum value in order to take advantage of the returns derived from stock. After that, it sales the stocks at their authorized maximum value in order to satisfy the constraint at the intermediate moment.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"17 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82189027","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}
The present manuscript deals with a 3-D food chain ecological model incorporating three species phytoplankton, zooplankton, and fish. To make the model more realistic, we include predation delay in the fish population due to the vertical migration of zooplankton species. We have assumed that additional food is available for both the predator population, viz., zooplankton, and fish. The main motive of the present study is to analyze the impact of available additional food and predation delay on the plankton-fish dynamics. The positivity and boundedness (with and without delay) are proved to make the system biologically valid. The steady states are determined to discuss the stability behavior of non-delayed dynamics under certain conditions. Considering available additional food as a control parameter, we have estimated ranges of alternative food for maintaining the sustainability and stability of the plankton-fish ecosystem. The Hopf-bifurcation analysis is carried out by considering time delay as a bifurcation parameter. The predation delay includes complexity in the system dynamics as it passes through its critical value. The direction of Hopf-bifurcation and stability of bifurcating periodic orbits are also determined using the centre manifold theorem. Numerical simulation is executed to validate theoretical results.
{"title":"Dynamical complexity in a delayed Plankton-Fish model with alternative food for predators","authors":"R. Kaur, Amit Sharma, A. Sharma","doi":"10.3934/naco.2021036","DOIUrl":"https://doi.org/10.3934/naco.2021036","url":null,"abstract":"The present manuscript deals with a 3-D food chain ecological model incorporating three species phytoplankton, zooplankton, and fish. To make the model more realistic, we include predation delay in the fish population due to the vertical migration of zooplankton species. We have assumed that additional food is available for both the predator population, viz., zooplankton, and fish. The main motive of the present study is to analyze the impact of available additional food and predation delay on the plankton-fish dynamics. The positivity and boundedness (with and without delay) are proved to make the system biologically valid. The steady states are determined to discuss the stability behavior of non-delayed dynamics under certain conditions. Considering available additional food as a control parameter, we have estimated ranges of alternative food for maintaining the sustainability and stability of the plankton-fish ecosystem. The Hopf-bifurcation analysis is carried out by considering time delay as a bifurcation parameter. The predation delay includes complexity in the system dynamics as it passes through its critical value. The direction of Hopf-bifurcation and stability of bifurcating periodic orbits are also determined using the centre manifold theorem. Numerical simulation is executed to validate theoretical results.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87020706","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}
In this paper, we introduce and study a modified extragradient algorithm for approximating solutions of a certain class of split pseudo-monotone variational inequality problem in real Hilbert spaces. Using our proposed algorithm, we established a strong convergent result for approximating solutions of the aforementioned problem. Our strong convergent result is obtained without prior knowledge of the Lipschitz constant of the pseudo-monotone operator used in this paper, and with minimized number of projections per iteration compared to other results on split variational inequality problem in the literature. Furthermore, numerical examples are given to show the performance and advantage of our method as well as comparing it with related methods in the literature.
{"title":"A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem","authors":"G. Ogwo, C. Izuchukwu, O. Mewomo","doi":"10.3934/NACO.2021011","DOIUrl":"https://doi.org/10.3934/NACO.2021011","url":null,"abstract":"In this paper, we introduce and study a modified extragradient algorithm for approximating solutions of a certain class of split pseudo-monotone variational inequality problem in real Hilbert spaces. Using our proposed algorithm, we established a strong convergent result for approximating solutions of the aforementioned problem. Our strong convergent result is obtained without prior knowledge of the Lipschitz constant of the pseudo-monotone operator used in this paper, and with minimized number of projections per iteration compared to other results on split variational inequality problem in the literature. Furthermore, numerical examples are given to show the performance and advantage of our method as well as comparing it with related methods in the literature.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"52 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81110145","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}
In this paper, we study excess demand equilibrium problems in Euclidean spaces. Applying the Glicksberg's fixed point theorem, sufficient conditions for the existence of solutions for the reference problems are established. We introduce a concept of well-posedness, say Levitin–Polyak well-posedness in the sense of Painlevé–Kuratowski, and investigate sufficient conditions for such kind of well-posedness.
{"title":"Existence and well-posedness for excess demand equilibrium problems","authors":"L. Q. Anh, Pham Thanh Duoc, T. Q. Duy","doi":"10.3934/naco.2021043","DOIUrl":"https://doi.org/10.3934/naco.2021043","url":null,"abstract":"In this paper, we study excess demand equilibrium problems in Euclidean spaces. Applying the Glicksberg's fixed point theorem, sufficient conditions for the existence of solutions for the reference problems are established. We introduce a concept of well-posedness, say Levitin–Polyak well-posedness in the sense of Painlevé–Kuratowski, and investigate sufficient conditions for such kind of well-posedness.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"23 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89002903","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}
An efficiently preconditioned Newton-like method for the computation of the eigenpairs of large and sparse nonsymmetric matrices is proposed. A sequence of preconditioners based on the Broyden-type rank-one update formula are constructed for the solution of the linearized Newton system. The properties of the preconditioned matrix are investigated. Numerical results are given which reveal that the new proposed algorithms are efficient.
{"title":"Preconditioned inexact Newton-like method for large nonsymmetric eigenvalue problems","authors":"Hongyi Miao, Li Wang","doi":"10.3934/NACO.2021012","DOIUrl":"https://doi.org/10.3934/NACO.2021012","url":null,"abstract":"An efficiently preconditioned Newton-like method for the computation of the eigenpairs of large and sparse nonsymmetric matrices is proposed. A sequence of preconditioners based on the Broyden-type rank-one update formula are constructed for the solution of the linearized Newton system. The properties of the preconditioned matrix are investigated. Numerical results are given which reveal that the new proposed algorithms are efficient.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"15 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87180163","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}
In a grid network, the nodes could be traversed either horizontally or vertically. The constrained shortest Hamiltonian path goes over the nodes between a source node and a destination node, and it is constrained to traverse some nodes at least once while others could be traversed several times. There are various applications of the problem, especially in routing problems. It is an NP-complete problem, and the well-known Bellman-Held-Karp algorithm could solve the shortest Hamiltonian circuit problem within begin{document}$ {rm O(}{{rm 2}}^{{rm n}}{{rm n}}^{{rm 2}}{rm )} $end{document} time complexity; however, the shortest Hamiltonian path problem is more complicated. So, a metaheuristic algorithm based on ant colony optimization is applied to obtain the optimal solution. The proposed method applies the rooted shortest path tree structure since in the optimal solution the paths between the restricted nodes are the shortest paths. Then, the shortest path tree is obtained by at most begin{document}$ {rm O(}{{rm n}}^{{rm 3}}{rm )} $end{document} time complexity at any iteration and the ants begin to improve the solution and the optimal solution is constructed in a reasonable time. The algorithm is verified by some numerical examples and the ant colony parameters are tuned by design of experiment method, and the optimal setting for different size of networks are determined.
In a grid network, the nodes could be traversed either horizontally or vertically. The constrained shortest Hamiltonian path goes over the nodes between a source node and a destination node, and it is constrained to traverse some nodes at least once while others could be traversed several times. There are various applications of the problem, especially in routing problems. It is an NP-complete problem, and the well-known Bellman-Held-Karp algorithm could solve the shortest Hamiltonian circuit problem within begin{document}$ {rm O(}{{rm 2}}^{{rm n}}{{rm n}}^{{rm 2}}{rm )} $end{document} time complexity; however, the shortest Hamiltonian path problem is more complicated. So, a metaheuristic algorithm based on ant colony optimization is applied to obtain the optimal solution. The proposed method applies the rooted shortest path tree structure since in the optimal solution the paths between the restricted nodes are the shortest paths. Then, the shortest path tree is obtained by at most begin{document}$ {rm O(}{{rm n}}^{{rm 3}}{rm )} $end{document} time complexity at any iteration and the ants begin to improve the solution and the optimal solution is constructed in a reasonable time. The algorithm is verified by some numerical examples and the ant colony parameters are tuned by design of experiment method, and the optimal setting for different size of networks are determined.
{"title":"Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks","authors":"M. Abdolhosseinzadeh, Mir Mohammad Alipour","doi":"10.3934/naco.2020028","DOIUrl":"https://doi.org/10.3934/naco.2020028","url":null,"abstract":"In a grid network, the nodes could be traversed either horizontally or vertically. The constrained shortest Hamiltonian path goes over the nodes between a source node and a destination node, and it is constrained to traverse some nodes at least once while others could be traversed several times. There are various applications of the problem, especially in routing problems. It is an NP-complete problem, and the well-known Bellman-Held-Karp algorithm could solve the shortest Hamiltonian circuit problem within begin{document}$ {rm O(}{{rm 2}}^{{rm n}}{{rm n}}^{{rm 2}}{rm )} $end{document} time complexity; however, the shortest Hamiltonian path problem is more complicated. So, a metaheuristic algorithm based on ant colony optimization is applied to obtain the optimal solution. The proposed method applies the rooted shortest path tree structure since in the optimal solution the paths between the restricted nodes are the shortest paths. Then, the shortest path tree is obtained by at most begin{document}$ {rm O(}{{rm n}}^{{rm 3}}{rm )} $end{document} time complexity at any iteration and the ants begin to improve the solution and the optimal solution is constructed in a reasonable time. The algorithm is verified by some numerical examples and the ant colony parameters are tuned by design of experiment method, and the optimal setting for different size of networks are determined.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77499744","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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