Pub Date : 2021-01-01DOI: 10.3844/jmssp.2021.73.81
Yongxin Jiang, Tianxiu Luand, Xiaofang Yang
Corresponding Author: Tianxiu Lu College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, P.R. China Email: lubeeltx@163.com Abstract: In this study, several kinds of distributional chaos are defined in a non-autonomous discrete system and the chaotic behavior of the mapping sequence , 1 =( , , ) n n n f f f , n ( is a set of natural numbers) is studied.
摘要:本文在非自治离散系统中定义了几种分布混沌，研究了映射序列1 =(，，)n n n f f，n(是一组自然数)的混沌行为。
{"title":"Some Kinds of Distributional Chaos for Non-Autonomous Discrete Systems","authors":"Yongxin Jiang, Tianxiu Luand, Xiaofang Yang","doi":"10.3844/jmssp.2021.73.81","DOIUrl":"https://doi.org/10.3844/jmssp.2021.73.81","url":null,"abstract":"Corresponding Author: Tianxiu Lu College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, P.R. China Email: lubeeltx@163.com Abstract: In this study, several kinds of distributional chaos are defined in a non-autonomous discrete system and the chaotic behavior of the mapping sequence , 1 =( , , ) n n n f f f , n ( is a set of natural numbers) is studied.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"137 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76614346","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 : 2021-01-01DOI: 10.3844/jmssp.2021.83.87
A. Hatemi-J, Youssef El-Khatib
Corresponding Author: Abdulnasser Hatemi-J College of Business and Economics, Department of Accounting and Finance, UAE University, United Arab Emirates Email: AHatemi@uaeu.ac.ae Abstract: The current article handles the valuation of currency options in the market that is suffering from a financial crisis. The standard formulas for this purpose do not perform accurately. European foreign currency exchange options for both the call and the put versions are dealt with. It is assumed that the value of the underlying asset is a stochastic process that follows a modified Black Scholes model with an augmented stochastic volatility to account for the impact of the crisis. Under these settings, a closed form solution is offered for the option-pricing problem on foreign currency. The underlying solution is mathematically proved. In addition, some simulation results and an application are provided. The results based on the new formula accord better with reality compared to the standard formula.
{"title":"On the Valuation of Currency Options in Stressed Markets","authors":"A. Hatemi-J, Youssef El-Khatib","doi":"10.3844/jmssp.2021.83.87","DOIUrl":"https://doi.org/10.3844/jmssp.2021.83.87","url":null,"abstract":"Corresponding Author: Abdulnasser Hatemi-J College of Business and Economics, Department of Accounting and Finance, UAE University, United Arab Emirates Email: AHatemi@uaeu.ac.ae Abstract: The current article handles the valuation of currency options in the market that is suffering from a financial crisis. The standard formulas for this purpose do not perform accurately. European foreign currency exchange options for both the call and the put versions are dealt with. It is assumed that the value of the underlying asset is a stochastic process that follows a modified Black Scholes model with an augmented stochastic volatility to account for the impact of the crisis. Under these settings, a closed form solution is offered for the option-pricing problem on foreign currency. The underlying solution is mathematically proved. In addition, some simulation results and an application are provided. The results based on the new formula accord better with reality compared to the standard formula.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"16 1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80205103","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 : 2020-10-14DOI: 10.3844/jmssp.2020.212.223
F. Kachapova
Based on the definition of Beth-Kripke model by Dragalin, we describe Beth model from the topological point of view. We show the relation of the topological definition with more traditional relational definition of Beth model that is based on forcing. We apply the topological definition to construct a Beth model for a theory of intuitionistic functionals of high types and to prove its consistency
{"title":"Topological Beth Model and its Application to Functionals of High Types","authors":"F. Kachapova","doi":"10.3844/jmssp.2020.212.223","DOIUrl":"https://doi.org/10.3844/jmssp.2020.212.223","url":null,"abstract":"Based on the definition of Beth-Kripke model by Dragalin, we describe Beth model from the topological point of view. We show the relation of the topological definition with more traditional relational definition of Beth model that is based on forcing. We apply the topological definition to construct a Beth model for a theory of intuitionistic functionals of high types and to prove its consistency","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"56 1","pages":"212-223"},"PeriodicalIF":0.3,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89229400","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 : 2020-09-14DOI: 10.3844/JMSSP.2020.182.197
A. Taranto, Shahjahan Khan
The Grid Trading Problem (GTP) of mathematical finance, used in portfolio loss minimization, generalized dynamic hedging and algorithmic trading, is researched by examining the impact of the drawdown and drawup of discrete random walks and of Ito diffusions on the Bi-Directional Grid Constrained (BGC) stochastic process for profit Pt and equity E_t over time. A comprehensive Discrete Difference Equation (DDE) and a continuous Stochastic Differential Equation (SDE) are derived and proved for the GTP. This allows fund managers and traders the ability to better stress test the impact of volatility to reduce risk and generate positive returns. These theorems are then simulated to complement the theoretical models with charts. Not only does this research extend a rich mathematical problem that can be further researched in its own right, but it also extends the applications into the above areas of finance.
{"title":"Drawdown and Drawup of Bi-Directional Grid Constrained Stochastic Processes","authors":"A. Taranto, Shahjahan Khan","doi":"10.3844/JMSSP.2020.182.197","DOIUrl":"https://doi.org/10.3844/JMSSP.2020.182.197","url":null,"abstract":"The Grid Trading Problem (GTP) of mathematical finance, used in portfolio loss minimization, generalized dynamic hedging and algorithmic trading, is researched by examining the impact of the drawdown and drawup of discrete random walks and of Ito diffusions on the Bi-Directional Grid Constrained (BGC) stochastic process for profit Pt and equity E_t over time. A comprehensive Discrete Difference Equation (DDE) and a continuous Stochastic Differential Equation (SDE) are derived and proved for the GTP. This allows fund managers and traders the ability to better stress test the impact of volatility to reduce risk and generate positive returns. These theorems are then simulated to complement the theoretical models with charts. Not only does this research extend a rich mathematical problem that can be further researched in its own right, but it also extends the applications into the above areas of finance.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"3 1","pages":"182-197"},"PeriodicalIF":0.3,"publicationDate":"2020-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87189277","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 : 2020-08-21DOI: 10.3844/jmssp.2020.176.181
A. Indumathi, A. Esi, N. Subramanian
Corresponding Author: Ayhan Esi Department of Basic Engineering Sciences, Malatya Turgut Ozal University, 44040, Malatya, Turkey Email: aesi23@hotmail.com Abstract: In this article, we give an overview of other commonly used basis for the triple sequence space of Bernstein polynomials, the Bernstein basis and put forward a matrix representation of Bernstein polynomials for the triple sequence space and its many useful properties.
{"title":"On Matrix Representation of Bernstein Polynomials for Triple Sequences","authors":"A. Indumathi, A. Esi, N. Subramanian","doi":"10.3844/jmssp.2020.176.181","DOIUrl":"https://doi.org/10.3844/jmssp.2020.176.181","url":null,"abstract":"Corresponding Author: Ayhan Esi Department of Basic Engineering Sciences, Malatya Turgut Ozal University, 44040, Malatya, Turkey Email: aesi23@hotmail.com Abstract: In this article, we give an overview of other commonly used basis for the triple sequence space of Bernstein polynomials, the Bernstein basis and put forward a matrix representation of Bernstein polynomials for the triple sequence space and its many useful properties.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"21 1","pages":"176-181"},"PeriodicalIF":0.3,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80015581","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 : 2020-06-26DOI: 10.3844/jmssp.2020.104.112
Aisha Aliyu Yakubu, F. Abdullah, Ahmad Izani Md. Ismail, Y. Yatim
A susceptible-infected-recovered compartmental model incorporating maternally derived immunity compartment is analyzed in this study. The stability of the pertussis-disease-free and endemic equilibrium is studied. The basic reproduction number is obtained and its behavior analyzed by varying parameters. Numerical simulations indicated that when the waning parameter is increased, the frequency at which the population attains stability varies. However, the infected population does not go extinct even at equilibrium.
{"title":"Dynamical Analysis on the Transmission of Pertussis with Maternally Derived Immunity","authors":"Aisha Aliyu Yakubu, F. Abdullah, Ahmad Izani Md. Ismail, Y. Yatim","doi":"10.3844/jmssp.2020.104.112","DOIUrl":"https://doi.org/10.3844/jmssp.2020.104.112","url":null,"abstract":"A susceptible-infected-recovered compartmental model incorporating maternally derived immunity compartment is analyzed in this study. The stability of the pertussis-disease-free and endemic equilibrium is studied. The basic reproduction number is obtained and its behavior analyzed by varying parameters. Numerical simulations indicated that when the waning parameter is increased, the frequency at which the population attains stability varies. However, the infected population does not go extinct even at equilibrium.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"65 1","pages":"104-112"},"PeriodicalIF":0.3,"publicationDate":"2020-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72824399","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 : 2020-06-09DOI: 10.3844/jmssp.2020.90.103
A. Azeez, Mutambayi Ruffin, N. James, Qin Yongsong
In many clinical and reliability research reports, the outcomes of basic interest is the time to a particular event happens in order to indicate the person’s “true†state of health or survival status. Different models have been used to analyze such data separately, but may be unsuitable if the longitudinal and health status measures are correlated. In this study, mixed effect and Cox model of latent class are jointly modelled for the correlation between the covariates, observed and unobserved health status variable with binary latent class indicators. A Bayesian approach for Maximum likelihood estimates is implemented using Markov Chain Monte Carlo (MCMC) techniques. The repeated and survival measures are independently assumed to be a Gaussian process for latent bivariate. The joint model is applied to TB cohort study for the HIV comorbidity effect on event time for Tuberculosis patients. R package is used for curvilinear repeated measures of latent class model and joint latent class models for both repeated measures and survival time event.
{"title":"Joint Modelling of Longitudinal-Time-To-Event with Categorical Variable Indicators of Latent Classes: Application to Tuberculosis Data","authors":"A. Azeez, Mutambayi Ruffin, N. James, Qin Yongsong","doi":"10.3844/jmssp.2020.90.103","DOIUrl":"https://doi.org/10.3844/jmssp.2020.90.103","url":null,"abstract":"In many clinical and reliability research reports, the outcomes of basic interest is the time to a particular event happens in order to indicate the person’s “true†state of health or survival status. Different models have been used to analyze such data separately, but may be unsuitable if the longitudinal and health status measures are correlated. In this study, mixed effect and Cox model of latent class are jointly modelled for the correlation between the covariates, observed and unobserved health status variable with binary latent class indicators. A Bayesian approach for Maximum likelihood estimates is implemented using Markov Chain Monte Carlo (MCMC) techniques. The repeated and survival measures are independently assumed to be a Gaussian process for latent bivariate. The joint model is applied to TB cohort study for the HIV comorbidity effect on event time for Tuberculosis patients. R package is used for curvilinear repeated measures of latent class model and joint latent class models for both repeated measures and survival time event.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"43 1","pages":"90-103"},"PeriodicalIF":0.3,"publicationDate":"2020-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84629989","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 : 2020-06-02DOI: 10.3844/jmssp.2020.76.89
M. Yaremenko
This article is dedicated to expanding our comprehension of the regularity of the solutions to the Cauchy problem for the quasilinear second-order parabolic partial differential equations under fair general conditions on the nonlinear perturbations. In this paper have been obtained that the sequence of the weak solutions uz ∈ V1,02, z = 1,2,..... to the Cauchy problems for the Equations (15) under the initial conditions uz (0,x) = φ0z converges to the weak solution to the Cauchy problem for the Equation (1) under the initial condition u(0, x) = u0 in V1,02.
本文扩展了我们对拟线性二阶抛物型偏微分方程在一般非线性扰动条件下Cauchy问题解的正则性的理解。本文得到了弱解uz∈V1,02, z = 1,2，.....的序列方程(15)在初始条件uz (0,x) = φ0z下的柯西问题收敛于方程(1)在初始条件u(0, x) = u0下的柯西问题的弱解。
{"title":"The Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential Equations","authors":"M. Yaremenko","doi":"10.3844/jmssp.2020.76.89","DOIUrl":"https://doi.org/10.3844/jmssp.2020.76.89","url":null,"abstract":"This article is dedicated to expanding our comprehension of the regularity of the solutions to the Cauchy problem for the quasilinear second-order parabolic partial differential equations under fair general conditions on the nonlinear perturbations. In this paper have been obtained that the sequence of the weak solutions uz ∈ V1,02, z = 1,2,..... to the Cauchy problems for the Equations (15) under the initial conditions uz (0,x) = φ0z converges to the weak solution to the Cauchy problem for the Equation (1) under the initial condition u(0, x) = u0 in V1,02.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"27 1","pages":"76-89"},"PeriodicalIF":0.3,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77959425","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 : 2020-05-24DOI: 10.3844/jmssp.2020.62.75
Okeh Uchechukwu Marius, Onyeagu I. Sidney
The area under the Receiver Operating Characteristic (ROC) curve (AUC) is a summary measure when comparing two ROC curves. However, this summary measure is less informative when two ROC curves cross and have the same AUCs. In order to detect differences between ROC curves and to be able to tackle the problem of exchangeability of the labels between two diagnostic tests within subject, an alternative permutation test based on between-subject permutations of the labels of the subjects within each diagnostic test is proposed for assessing a change in the AUCs in a continuous matched pair of data from two diagnostic test procedures having both non-diseased and diseased subject in each of the test. The Wilcoxon signed rank test statistic was modified as a permutation test under the null hypothesis of equality of AUCs. An algorithm for carrying out complete enumeration of all the distinct permutations of the paired test results was developed which provides exact p-values. Using simulated data, the proposed test compares in statistical power to the modified sign test proposed by Braun and Alonzo but the proposed test has better operating characteristics, that is greater statistical power to detect a crossing alternative and is less conservative in test size and in the range of parameters of at least 0.8 of AUCs on the average with a correlation of at least 0.4 and small to moderately large sample sizes. Similarly in applying real life data, the proposed test has the more likelihood of rejecting null hypothesis of equality of AUC1 and AUC2 at nominal level of 0.05 with the proposed test having a p-value of 0.0312 against the Braun and Alonzo’s test with a p-value of 0.0387. This is because the proposed test is modified to adjust for the presence of zero differences in values and considers the signs of values as well as the absolute ranks of values. Also the estimates of AUC1 and AUC2 for the two diagnostic tests are 0.668 and 0.887 respectively showing that AUC2, that is 2hour 100g Oral Glucose Tolerance Test (OGTT) is superior to AUC1 (2hour 70g OGTT) at a time that the specificity is greater than 0.7.
{"title":"A Permutation Test for Comparing Two Correlated Receiver Operating Characteristic Curves","authors":"Okeh Uchechukwu Marius, Onyeagu I. Sidney","doi":"10.3844/jmssp.2020.62.75","DOIUrl":"https://doi.org/10.3844/jmssp.2020.62.75","url":null,"abstract":"The area under the Receiver Operating Characteristic (ROC) curve (AUC) is a summary measure when comparing two ROC curves. However, this summary measure is less informative when two ROC curves cross and have the same AUCs. In order to detect differences between ROC curves and to be able to tackle the problem of exchangeability of the labels between two diagnostic tests within subject, an alternative permutation test based on between-subject permutations of the labels of the subjects within each diagnostic test is proposed for assessing a change in the AUCs in a continuous matched pair of data from two diagnostic test procedures having both non-diseased and diseased subject in each of the test. The Wilcoxon signed rank test statistic was modified as a permutation test under the null hypothesis of equality of AUCs. An algorithm for carrying out complete enumeration of all the distinct permutations of the paired test results was developed which provides exact p-values. Using simulated data, the proposed test compares in statistical power to the modified sign test proposed by Braun and Alonzo but the proposed test has better operating characteristics, that is greater statistical power to detect a crossing alternative and is less conservative in test size and in the range of parameters of at least 0.8 of AUCs on the average with a correlation of at least 0.4 and small to moderately large sample sizes. Similarly in applying real life data, the proposed test has the more likelihood of rejecting null hypothesis of equality of AUC1 and AUC2 at nominal level of 0.05 with the proposed test having a p-value of 0.0312 against the Braun and Alonzo’s test with a p-value of 0.0387. This is because the proposed test is modified to adjust for the presence of zero differences in values and considers the signs of values as well as the absolute ranks of values. Also the estimates of AUC1 and AUC2 for the two diagnostic tests are 0.668 and 0.887 respectively showing that AUC2, that is 2hour 100g Oral Glucose Tolerance Test (OGTT) is superior to AUC1 (2hour 70g OGTT) at a time that the specificity is greater than 0.7.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"33 1","pages":"62-75"},"PeriodicalIF":0.3,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76670418","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 : 2020-05-14DOI: 10.3844/JMSSP.2020.54.61
Awad Abdelrahman, Osman O. O. Yousif, KH. I. Osman
Nonlinear Conjugate Gradient (CG) methods are extensively used for solving large-scale unconstrained optimization problems. Numerous of studies constructed scales and modifications have been conducted recently to improve (CG) methods. In this paper, a simple modified by its conjugate gradient method was proposed. In addition to, established global convergence property and sufficient descent condition, under Strong Wolfe line search. Numerical result shows that the proposed formula is competitive when compared to other well-known (CG) parameters.
{"title":"A Robust Modification of Hestenes–Stiefel Conjugate Gradient Method with Strong Wolfe Line Search","authors":"Awad Abdelrahman, Osman O. O. Yousif, KH. I. Osman","doi":"10.3844/JMSSP.2020.54.61","DOIUrl":"https://doi.org/10.3844/JMSSP.2020.54.61","url":null,"abstract":"Nonlinear Conjugate Gradient (CG) methods are extensively used for solving large-scale unconstrained optimization problems. Numerous of studies constructed scales and modifications have been conducted recently to improve (CG) methods. In this paper, a simple modified by its conjugate gradient method was proposed. In addition to, established global convergence property and sufficient descent condition, under Strong Wolfe line search. Numerical result shows that the proposed formula is competitive when compared to other well-known (CG) parameters.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"29 1","pages":"54-61"},"PeriodicalIF":0.3,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85547250","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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