Pub Date : 2018-01-01DOI: 10.1080/23311835.2018.1432521
Samia Bushnaq, S. Khan, K. Shah, G. Zaman
Abstract This manuscript is concerned to the existence and stability of HIV/AIDS infection model with fractional order derivative. The corresponding derivative is taken in Caputo-Fabrizio sense, which is a new approach for such type of biological models. With the help of Sumudu transform, some new results are handled. Further for the corresponding results, existence theory and uniqueness for the equilibrium solution are provided via using nonlinear functional analysis and fixed point theory due to Banach.
{"title":"Mathematical analysis of HIV/AIDS infection model with Caputo-Fabrizio fractional derivative","authors":"Samia Bushnaq, S. Khan, K. Shah, G. Zaman","doi":"10.1080/23311835.2018.1432521","DOIUrl":"https://doi.org/10.1080/23311835.2018.1432521","url":null,"abstract":"Abstract This manuscript is concerned to the existence and stability of HIV/AIDS infection model with fractional order derivative. The corresponding derivative is taken in Caputo-Fabrizio sense, which is a new approach for such type of biological models. With the help of Sumudu transform, some new results are handled. Further for the corresponding results, existence theory and uniqueness for the equilibrium solution are provided via using nonlinear functional analysis and fixed point theory due to Banach.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1432521","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48227091","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 : 2018-01-01DOI: 10.1080/23311835.2018.1426184
V. Aghapouramin, M. Nikmehr
The concept of nil-M-McCoy (nil-McCoy ring relative to monoid M), which are generalizations of McCoy ring and nil-M-Armendariz rings have been introduced, and we investigate their properties. It is shown that every NI ring is nil-M-McCoy for any unique product monoid M, it has also been shown that every semicommutative rings is nil-M-McCoy for any unique product monoid and any strictly totally ordered monoid M. Moreover, it is proved that for an ideal I of R, if I is semicommutative and R / I is nil-M-McCoy then R is nil-M-McCoy for any strictly totally ordered monoid. We extend and unify many known results related to McCoy rings and nil-Armendariz ring.
{"title":"On nil-McCoy rings relative to a monoid","authors":"V. Aghapouramin, M. Nikmehr","doi":"10.1080/23311835.2018.1426184","DOIUrl":"https://doi.org/10.1080/23311835.2018.1426184","url":null,"abstract":"The concept of nil-M-McCoy (nil-McCoy ring relative to monoid M), which are generalizations of McCoy ring and nil-M-Armendariz rings have been introduced, and we investigate their properties. It is shown that every NI ring is nil-M-McCoy for any unique product monoid M, it has also been shown that every semicommutative rings is nil-M-McCoy for any unique product monoid and any strictly totally ordered monoid M. Moreover, it is proved that for an ideal I of R, if I is semicommutative and R / I is nil-M-McCoy then R is nil-M-McCoy for any strictly totally ordered monoid. We extend and unify many known results related to McCoy rings and nil-Armendariz ring.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1426184","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48528022","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 : 2018-01-01DOI: 10.1080/25742558.2018.1509426
K. Eke, J. G. Oghonyon
Abstract We defined the class of generalized weakly C-contractive mappings in partial metric spaces and proved some fixed-point results for such maps in ordered partial metric spaces without exploiting the continuity of any of the functions. We also establish fixed-point theorem for the integral type of these maps. Example is given to support the validity of our result. Our result generalizes the results of Chen and Zhu [3] and others in the literature
{"title":"Some fixed point theorems in ordered partial metric spaces with applications","authors":"K. Eke, J. G. Oghonyon","doi":"10.1080/25742558.2018.1509426","DOIUrl":"https://doi.org/10.1080/25742558.2018.1509426","url":null,"abstract":"Abstract We defined the class of generalized weakly C-contractive mappings in partial metric spaces and proved some fixed-point results for such maps in ordered partial metric spaces without exploiting the continuity of any of the functions. We also establish fixed-point theorem for the integral type of these maps. Example is given to support the validity of our result. Our result generalizes the results of Chen and Zhu [3] and others in the literature","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1509426","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49351018","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 : 2018-01-01DOI: 10.1080/25742558.2018.1507131
Shahnaz Fakouri, S. Rahmany, Abdolali Basiri
Abstract The regular representation of the radical of a differential ideal has various applications such as solving the membership problem, computing Taylor expansion of solutions, finding the Lie symmetries, and solving dynamical systems. Presently, there is no algorithm giving all regular representations for all possible values of the parameters for a polynomial differential ideal with parametric coefficients. In this article, we propose a new algorithm that computes all different regular representations with respect to all possible states of the parameters. Also, we present an efficient criterion to reduce some ineffectual computations. Implementing the algorithm in Maple and several examples reported in this article demonstrate the high efficiency of the algorithm.
{"title":"A new algorithm for computing regular representations for radicals of parametric differential ideals","authors":"Shahnaz Fakouri, S. Rahmany, Abdolali Basiri","doi":"10.1080/25742558.2018.1507131","DOIUrl":"https://doi.org/10.1080/25742558.2018.1507131","url":null,"abstract":"Abstract The regular representation of the radical of a differential ideal has various applications such as solving the membership problem, computing Taylor expansion of solutions, finding the Lie symmetries, and solving dynamical systems. Presently, there is no algorithm giving all regular representations for all possible values of the parameters for a polynomial differential ideal with parametric coefficients. In this article, we propose a new algorithm that computes all different regular representations with respect to all possible states of the parameters. Also, we present an efficient criterion to reduce some ineffectual computations. Implementing the algorithm in Maple and several examples reported in this article demonstrate the high efficiency of the algorithm.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1507131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49037019","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 : 2018-01-01DOI: 10.1080/23311835.2018.1447222
N. Rafatimaleki, M. Rostamy-Malkhalifeh, F. Hosseinzadeh lotfi
Abstract Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In Data Envelopment Analysis (DEA), it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS. Although DEA models can determine the efficiency of a Decision Making Unit (DMU), but they cannot present efficient frontiers of PPS. In this paper, we propose a new method to determine all strong efficient (Pareto-efficient) DMUs and strong defining hyperplanes of the PPS with constant returns to scale including the Pareto-efficient DMUs. Furthermore, we apply the newly proposed method to find the normal vectors or gradient of the strong defining hyperplanes of the PPS including strong efficient DMUs which are under evaluation. Consequently, the equations of these hyperplanes are determined. To illustrate the applicability of the proposed method, some numerical examples are finally provided. Our method can be easily implemented using existing packages for operation research, such as GAMS.
{"title":"Finding the strong defining hyperplanes of production possibility set with constant returns to scale using the linear independent vectors","authors":"N. Rafatimaleki, M. Rostamy-Malkhalifeh, F. Hosseinzadeh lotfi","doi":"10.1080/23311835.2018.1447222","DOIUrl":"https://doi.org/10.1080/23311835.2018.1447222","url":null,"abstract":"Abstract Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In Data Envelopment Analysis (DEA), it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS. Although DEA models can determine the efficiency of a Decision Making Unit (DMU), but they cannot present efficient frontiers of PPS. In this paper, we propose a new method to determine all strong efficient (Pareto-efficient) DMUs and strong defining hyperplanes of the PPS with constant returns to scale including the Pareto-efficient DMUs. Furthermore, we apply the newly proposed method to find the normal vectors or gradient of the strong defining hyperplanes of the PPS including strong efficient DMUs which are under evaluation. Consequently, the equations of these hyperplanes are determined. To illustrate the applicability of the proposed method, some numerical examples are finally provided. Our method can be easily implemented using existing packages for operation research, such as GAMS.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1447222","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47784196","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 : 2018-01-01DOI: 10.1080/23311835.2018.1559457
Adel Almarashi, M. Alghamdi, I. Mechai
Abstract In this paper, we introduce a new diagnosing technique for chronic kidney disease by using Artificial Neural Network (ANN). Where, the required data for the computational health-care system is collected from various hospitals at Jazan region, Saudi Arabia. Furthermore, in order to prove the convergence of this method, a ridge function is used in the hidden layer as a basis for the neurons. The technique applied for different number of neurons, and in each case a least square error is provided for choosing the best possible approximation.
{"title":"A new mathematical model for diagnosing chronic diseases (kidney failure) using ANN","authors":"Adel Almarashi, M. Alghamdi, I. Mechai","doi":"10.1080/23311835.2018.1559457","DOIUrl":"https://doi.org/10.1080/23311835.2018.1559457","url":null,"abstract":"Abstract In this paper, we introduce a new diagnosing technique for chronic kidney disease by using Artificial Neural Network (ANN). Where, the required data for the computational health-care system is collected from various hospitals at Jazan region, Saudi Arabia. Furthermore, in order to prove the convergence of this method, a ridge function is used in the hidden layer as a basis for the neurons. The technique applied for different number of neurons, and in each case a least square error is provided for choosing the best possible approximation.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1559457","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45427385","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 : 2018-01-01DOI: 10.1080/25742558.2018.1511238
Vahid Parvaneh, Z. Kadelburg, R. J. Shahkoohi, H. Hosseinzadeh
Abstract In this article, we obtain fixed point results under some rational contractive conditions for mappings in the setup of ordered ρ-metric spaces. Also, three examples and an application to existence of local solutions for first-order periodic problems are provided to illustrate the results presented herein.
{"title":"Fixed point results for generalized rational Geraghty contractive mappings in extended b-metric spaces","authors":"Vahid Parvaneh, Z. Kadelburg, R. J. Shahkoohi, H. Hosseinzadeh","doi":"10.1080/25742558.2018.1511238","DOIUrl":"https://doi.org/10.1080/25742558.2018.1511238","url":null,"abstract":"Abstract In this article, we obtain fixed point results under some rational contractive conditions for mappings in the setup of ordered ρ-metric spaces. Also, three examples and an application to existence of local solutions for first-order periodic problems are provided to illustrate the results presented herein.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1511238","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46237163","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 : 2018-01-01DOI: 10.1080/25742558.2018.1478698
O. Almalik, E. Heuvel
Abstract Meta-analysis is a statistical methodology that combines the outcomes of several independent studies. Either a fixed-effects or a random-effects model is used to combine the results of the independent studies. The choice depends on whether the outcomes can be considered homogeneous or not. Several methods have been developed to test the homogeneity of effect sizes. Although many of them have been compared already, they have not been studied in more realistic practical settings where individuals all have their own risk of an event and a complete overview is lacking. In this article, we investigate the performance of 10 statistical methods to test homogeneity of a binary exposure on a binary clinical outcome, using an extensive simulation study and a real life meta-analysis. We evaluated the Type I error and the statistical power. The fixed-effects regression model for treatment and study interaction was found to be a slightly liberal test, while the Q-statistic and the Bliss statistic can be considered conservative tests. The random-effects regression model, the Peto statistic and the I2 perform rather poorly compared to the other methods. All chi-square tests that are based on the calculation of a specific odds ratio and the fixed-effects logistic regression analysis perform best. Among these chi-square tests, we recommend the Breslow–Day test, but only for convenience purposes, since it is available in most statistical software packages and the other tests are not.
{"title":"Testing homogeneity of effect sizes in pooling 2x2 contingency tables from multiple studies: a comparison of methods","authors":"O. Almalik, E. Heuvel","doi":"10.1080/25742558.2018.1478698","DOIUrl":"https://doi.org/10.1080/25742558.2018.1478698","url":null,"abstract":"Abstract Meta-analysis is a statistical methodology that combines the outcomes of several independent studies. Either a fixed-effects or a random-effects model is used to combine the results of the independent studies. The choice depends on whether the outcomes can be considered homogeneous or not. Several methods have been developed to test the homogeneity of effect sizes. Although many of them have been compared already, they have not been studied in more realistic practical settings where individuals all have their own risk of an event and a complete overview is lacking. In this article, we investigate the performance of 10 statistical methods to test homogeneity of a binary exposure on a binary clinical outcome, using an extensive simulation study and a real life meta-analysis. We evaluated the Type I error and the statistical power. The fixed-effects regression model for treatment and study interaction was found to be a slightly liberal test, while the Q-statistic and the Bliss statistic can be considered conservative tests. The random-effects regression model, the Peto statistic and the I2 perform rather poorly compared to the other methods. All chi-square tests that are based on the calculation of a specific odds ratio and the fixed-effects logistic regression analysis perform best. Among these chi-square tests, we recommend the Breslow–Day test, but only for convenience purposes, since it is available in most statistical software packages and the other tests are not.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1478698","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42059323","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 : 2018-01-01DOI: 10.1080/25742558.2018.1487500
M. İlkhan, E. Kara
Abstract Bourbaki complete metric spaces are important since they are a class between compact metric spaces and complete metric spaces. The aim of the present paper is to introduce the statistical Bourbaki–Cauchy sequence as a new concept and to give an equivalent condition for a metric space to be Bourbaki complete. Also, Bourbaki complete and Bourbaki-bounded metric spaces are characterized in terms of functions which preserve statistical Bourbaki–Cauchy sequences.
{"title":"A new type of statistical Cauchy sequence and its relation to Bourbaki completeness","authors":"M. İlkhan, E. Kara","doi":"10.1080/25742558.2018.1487500","DOIUrl":"https://doi.org/10.1080/25742558.2018.1487500","url":null,"abstract":"Abstract Bourbaki complete metric spaces are important since they are a class between compact metric spaces and complete metric spaces. The aim of the present paper is to introduce the statistical Bourbaki–Cauchy sequence as a new concept and to give an equivalent condition for a metric space to be Bourbaki complete. Also, Bourbaki complete and Bourbaki-bounded metric spaces are characterized in terms of functions which preserve statistical Bourbaki–Cauchy sequences.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1487500","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49073307","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 : 2018-01-01DOI: 10.1080/25742558.2018.1470145
F. Shokrollahi
Abstract A new framework for pricing European currency option is developed in the case where the spot exchange rate follows a subdiffusive fractional Black–Scholes. An analytic formula for pricing European currency call option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a currency option under transaction costs is obtained as time-step , which can be used as the actual price of an option. In addition, we also show that time-step and long-range dependence have a significant impact on option pricing.
{"title":"Subdiffusive fractional Black–Scholes model for pricing currency options under transaction costs","authors":"F. Shokrollahi","doi":"10.1080/25742558.2018.1470145","DOIUrl":"https://doi.org/10.1080/25742558.2018.1470145","url":null,"abstract":"Abstract A new framework for pricing European currency option is developed in the case where the spot exchange rate follows a subdiffusive fractional Black–Scholes. An analytic formula for pricing European currency call option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a currency option under transaction costs is obtained as time-step , which can be used as the actual price of an option. In addition, we also show that time-step and long-range dependence have a significant impact on option pricing.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1470145","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49199828","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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