Pub Date : 2021-04-16DOI: 10.11648/J.ACM.20211002.11
Bazuaye Frank Etin-Osa, Ezeora Jeremiah
The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.
{"title":"Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques","authors":"Bazuaye Frank Etin-Osa, Ezeora Jeremiah","doi":"10.11648/J.ACM.20211002.11","DOIUrl":"https://doi.org/10.11648/J.ACM.20211002.11","url":null,"abstract":"The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76758156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-30DOI: 10.11648/J.ACM.20211001.13
Francis Bassono, Rasmané Yaro, J. B. Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga
Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.
{"title":"About Exact Solution of Some Non Linear Partial Integro-differential Equations","authors":"Francis Bassono, Rasmané Yaro, J. B. Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga","doi":"10.11648/J.ACM.20211001.13","DOIUrl":"https://doi.org/10.11648/J.ACM.20211001.13","url":null,"abstract":"Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75425084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-12DOI: 10.11648/J.ACM.20211001.12
S. Charles, R. John, Adicka Daniel
The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t)and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.
{"title":"Numerical Solution of the Navier-Stokes Equations for Incompressible Fluid Flow by Crank-Nicolson Implicit Scheme","authors":"S. Charles, R. John, Adicka Daniel","doi":"10.11648/J.ACM.20211001.12","DOIUrl":"https://doi.org/10.11648/J.ACM.20211001.12","url":null,"abstract":"The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t)and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88978570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-10DOI: 10.11648/J.ACM.20211001.11
J. Pahade, M. Jha
Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.
{"title":"Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable","authors":"J. Pahade, M. Jha","doi":"10.11648/J.ACM.20211001.11","DOIUrl":"https://doi.org/10.11648/J.ACM.20211001.11","url":null,"abstract":"Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78234358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.11648/j.acm.20211006.15
Anwarud Din, Peijiang Liu, Ting Cui
{"title":"Stochastic Stability and Optimal Control Analysis for a Tobacco Smoking Model","authors":"Anwarud Din, Peijiang Liu, Ting Cui","doi":"10.11648/j.acm.20211006.15","DOIUrl":"https://doi.org/10.11648/j.acm.20211006.15","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83611332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: With the increasingly serious air pollution problem, PM2.5 concentration, as an effective indicator to evaluate air quality, has attracted extensive attention from all sectors of society. Accurate prediction of PM2.5 concentrations is of great significance in providing the public with early air pollution warning information to protect public health. With a decade of development, artificial intelligence technology has given birth to various prediction models with high-performance, in particular, brought new impetus to the prediction of PM2.5 concentrations. In this study, a stacking-based ensemble model with self-adaptive hyper-parameter optimization is proposed to solve the PM2.5 concentrations prediction problem. First, the raw data are preprocessed with the normalization method to reduce the influence of the different orders of magnitude of input variables on model performance. Second, the Bayesian optimization method is used to optimize the hyper-parameters of the base predictors to improve their performance. Finally, a stacking ensemble method is applied to integrate the optimized base predictors into an ensemble model for final prediction. In the experiments, two datasets from the air quality stations in different areas are tested with four metrics to evaluate the performance of the proposed model in PM2.5 concentration prediction. The experimental results show that the proposed model outperforms other baseline models in solving the PM2.5 concentrations prediction problem.
{"title":"Predicting PM2.5 Concentrations Using Stacking-based Ensemble Model","authors":"Haoyuan Zhang, Yilun Jin, Jiaxuan Shi, Shuai Zhang","doi":"10.11648/j.acm.20211006.14","DOIUrl":"https://doi.org/10.11648/j.acm.20211006.14","url":null,"abstract":": With the increasingly serious air pollution problem, PM2.5 concentration, as an effective indicator to evaluate air quality, has attracted extensive attention from all sectors of society. Accurate prediction of PM2.5 concentrations is of great significance in providing the public with early air pollution warning information to protect public health. With a decade of development, artificial intelligence technology has given birth to various prediction models with high-performance, in particular, brought new impetus to the prediction of PM2.5 concentrations. In this study, a stacking-based ensemble model with self-adaptive hyper-parameter optimization is proposed to solve the PM2.5 concentrations prediction problem. First, the raw data are preprocessed with the normalization method to reduce the influence of the different orders of magnitude of input variables on model performance. Second, the Bayesian optimization method is used to optimize the hyper-parameters of the base predictors to improve their performance. Finally, a stacking ensemble method is applied to integrate the optimized base predictors into an ensemble model for final prediction. In the experiments, two datasets from the air quality stations in different areas are tested with four metrics to evaluate the performance of the proposed model in PM2.5 concentration prediction. The experimental results show that the proposed model outperforms other baseline models in solving the PM2.5 concentrations prediction problem.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80260317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.11648/j.acm.20211004.11
Evuiroro Edirin Judith, Ojarikre Henritta Ify
{"title":"Chaos and Bifurcation of Control Feedback System Using Variational Iteration Method","authors":"Evuiroro Edirin Judith, Ojarikre Henritta Ify","doi":"10.11648/j.acm.20211004.11","DOIUrl":"https://doi.org/10.11648/j.acm.20211004.11","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80086998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.11648/j.acm.20211006.13
Bamanga Dawuda, Shafiu Jibrin, I. Abdullahi
{"title":"A Weighted Analytic Center for Second-Order Cone Constraints","authors":"Bamanga Dawuda, Shafiu Jibrin, I. Abdullahi","doi":"10.11648/j.acm.20211006.13","DOIUrl":"https://doi.org/10.11648/j.acm.20211006.13","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80490532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-04DOI: 10.11648/J.ACM.20200906.14
Ba Demba Bocar
In this paper we define the multifractional Brownian motion and we give some properties. we study the uniform Convergence of the Serie expansion. After having determined the covariance function, we give in proposition 2 another proof of almost sure uniform convergence on compact K of the series. We will finish by showing that the m.B.f is locally astymptotically self-similar, with field or fractional Brownian field with Hurst exposant H. One of the problem, for application of multifractional Brownian motion, is the regularity of the function. In the filtered white noise model the increments are no more homogeneous as in fractional Brownian field case. It is obvious when we consider the tangent field associated with a function. Still the multifractional function in the previous model is constant and it is not convient for many applications. We show the uniform convergence of the series on K. We deduce from the previous questions the almost sure uniform convergence of the series to a mBm.
{"title":"Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion","authors":"Ba Demba Bocar","doi":"10.11648/J.ACM.20200906.14","DOIUrl":"https://doi.org/10.11648/J.ACM.20200906.14","url":null,"abstract":"In this paper we define the multifractional Brownian motion and we give some properties. we study the uniform Convergence of the Serie expansion. After having determined the covariance function, we give in proposition 2 another proof of almost sure uniform convergence on compact K of the series. We will finish by showing that the m.B.f is locally astymptotically self-similar, with field or fractional Brownian field with Hurst exposant H. One of the problem, for application of multifractional Brownian motion, is the regularity of the function. In the filtered white noise model the increments are no more homogeneous as in fractional Brownian field case. It is obvious when we consider the tangent field associated with a function. Still the multifractional function in the previous model is constant and it is not convient for many applications. We show the uniform convergence of the series on K. We deduce from the previous questions the almost sure uniform convergence of the series to a mBm.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76497881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-16DOI: 10.11648/J.ACM.20200906.13
Liu Liu, Qing-bang Zhang
Based on the proximal point algorithm, which is a widely used tool for solving a variety of convex optimization problems, there are many algorithms for finding zeros of maximally monotone operators. The algorithm works by applying successively so-called "resolvent" mappings with errors associated to the original object, and is weakly convergent in Hilbert space. In order to acquiring the strong convergence of the algorithm, in this paper, we construct a hybrid Halpern type proximal point algorithm with errors for approximating the zero of a maximal monotone operator, which is a combination of modified proximal point algorithm raised by Yao and Noor and Halpern inexact proximal point algorithm raised by Zhang, respectively. Then, we prove the strong convergence of our algorithm with weaker assumptions in Hilbert space. Finally, we present a numerical example to show the convergence and the convergence speed, which is not affected but accelerated by the projection in the algorithm. Our work improved and generalized some known results.
{"title":"Strong Convergence of the Hybrid Halpern Type Proximal Point Algorithm","authors":"Liu Liu, Qing-bang Zhang","doi":"10.11648/J.ACM.20200906.13","DOIUrl":"https://doi.org/10.11648/J.ACM.20200906.13","url":null,"abstract":"Based on the proximal point algorithm, which is a widely used tool for solving a variety of convex optimization problems, there are many algorithms for finding zeros of maximally monotone operators. The algorithm works by applying successively so-called \"resolvent\" mappings with errors associated to the original object, and is weakly convergent in Hilbert space. In order to acquiring the strong convergence of the algorithm, in this paper, we construct a hybrid Halpern type proximal point algorithm with errors for approximating the zero of a maximal monotone operator, which is a combination of modified proximal point algorithm raised by Yao and Noor and Halpern inexact proximal point algorithm raised by Zhang, respectively. Then, we prove the strong convergence of our algorithm with weaker assumptions in Hilbert space. Finally, we present a numerical example to show the convergence and the convergence speed, which is not affected but accelerated by the projection in the algorithm. Our work improved and generalized some known results.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86520609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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