Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1538596
Abdul Majid, M. Aslam, Saima Altaf
Abstract In the presence of heteroscedasticity, the ordinary least-squares (OLS) estimator remains no more efficient while the popular Almon technique is being considered for a finite distributed lag model (DLM). The available literature proposes few adaptive estimators which are more efficient than the OLS estimator when there is heteroscedasticity of unknown form. This study suggests the similar adaptation combined with the Almon technique in order to get more efficient estimator of vector of lag coefficients in the DLM. Performance of the proposed estimator has been evaluated through the Monte Carlo simulations. The simulation results show an attractive performance of the proposed estimator in terms of efficiency.
{"title":"Efficient estimation of distributed lag model in presence of heteroscedasticity of unknown form: A Monte Carlo evidence","authors":"Abdul Majid, M. Aslam, Saima Altaf","doi":"10.1080/25742558.2018.1538596","DOIUrl":"https://doi.org/10.1080/25742558.2018.1538596","url":null,"abstract":"Abstract In the presence of heteroscedasticity, the ordinary least-squares (OLS) estimator remains no more efficient while the popular Almon technique is being considered for a finite distributed lag model (DLM). The available literature proposes few adaptive estimators which are more efficient than the OLS estimator when there is heteroscedasticity of unknown form. This study suggests the similar adaptation combined with the Almon technique in order to get more efficient estimator of vector of lag coefficients in the DLM. Performance of the proposed estimator has been evaluated through the Monte Carlo simulations. The simulation results show an attractive performance of the proposed estimator in terms of efficiency.","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/10.1080/25742558.2018.1538596","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45950393","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: 10.1080/25742558.2018.1517428
C. Boonpok
Abstract This paper deals with the concepts of -sets and -closed sets in a strong generalized topological space and investigate properties of several low separation axioms of strong generalized topologies constructed by the families of these sets. Some properties of - and - strong generalized topological spaces will be given. Finally, several characterizations of weakly -continuous functions are discussed.
{"title":"(ζ, δ(µ))-closed sets in strong generalized topological spaces","authors":"C. Boonpok","doi":"10.1080/25742558.2018.1517428","DOIUrl":"https://doi.org/10.1080/25742558.2018.1517428","url":null,"abstract":"Abstract This paper deals with the concepts of -sets and -closed sets in a strong generalized topological space and investigate properties of several low separation axioms of strong generalized topologies constructed by the families of these sets. Some properties of - and - strong generalized topological spaces will be given. Finally, several characterizations of weakly -continuous functions are discussed.","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/10.1080/25742558.2018.1517428","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47713953","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: 10.1080/23311835.2018.1434924
J. Manafian
In this paper, the extended trial equation method, the -expansion method and the -expansion method are used in examining the analytical solution of the non-linear Schrödinger equation (NLSE) with fourth-order dispersion. The proposed methods are based on the integration method and a wave transformation. The NLSE with fourth-order dispersion is an equation that arises in soliton radiation, soliton communications with dispersion caused by the hindrance in presence of higher order dispersion terms. We successfully get some solutions with the kink structure.
{"title":"Optical solitons in a power-law media with fourth-order dispersion by three integration methods","authors":"J. Manafian","doi":"10.1080/23311835.2018.1434924","DOIUrl":"https://doi.org/10.1080/23311835.2018.1434924","url":null,"abstract":"In this paper, the extended trial equation method, the -expansion method and the -expansion method are used in examining the analytical solution of the non-linear Schrödinger equation (NLSE) with fourth-order dispersion. The proposed methods are based on the integration method and a wave transformation. The NLSE with fourth-order dispersion is an equation that arises in soliton radiation, soliton communications with dispersion caused by the hindrance in presence of higher order dispersion terms. We successfully get some solutions with the kink structure.","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/10.1080/23311835.2018.1434924","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44534295","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: 10.1080/25742558.2018.1462658
E. Vatandoost, Y. Golkhandy Pour
Abstract Recently, the nullity, the algebraic multiplicity of the number zero in the spectrum of the adjacency matrix, of a molecular graph has received a lot of attention as it has a number of direct applications in organic chemistry. In this regard, many researchers have been trying to find an upper or lower bound for the maximum nullity (minimum rank), (), for a graph . In this paper, using a well-known result, which presents the spectrum of a Cayley graph in terms of irreducible characters of the underlying group, and using representation and character of groups, we give a lower bound for the maximum nullity of Cayley graph, , where is a cyclic group, or such that is a cyclic group and is an arbitrary finite group, for , with determine the spectrum of Cayley graphs.
{"title":"Maximum nullity of some Cayley graphs","authors":"E. Vatandoost, Y. Golkhandy Pour","doi":"10.1080/25742558.2018.1462658","DOIUrl":"https://doi.org/10.1080/25742558.2018.1462658","url":null,"abstract":"Abstract Recently, the nullity, the algebraic multiplicity of the number zero in the spectrum of the adjacency matrix, of a molecular graph has received a lot of attention as it has a number of direct applications in organic chemistry. In this regard, many researchers have been trying to find an upper or lower bound for the maximum nullity (minimum rank), (), for a graph . In this paper, using a well-known result, which presents the spectrum of a Cayley graph in terms of irreducible characters of the underlying group, and using representation and character of groups, we give a lower bound for the maximum nullity of Cayley graph, , where is a cyclic group, or such that is a cyclic group and is an arbitrary finite group, for , with determine the spectrum of Cayley graphs.","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/10.1080/25742558.2018.1462658","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43738692","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: 10.1080/23311835.2018.1426205
M. Samraiz, S. Iqbal, J. Pečarić
In this paper, we present a variety of integral inequalities in and spaces for the integral operator involving generalized Mittag-Leffler function in its kernel, Hilfer fractional derivative, generalized Riemann-Liouville and Riemann-Liouville k-fractional integral operators.
{"title":"Generalized integral inequalities for fractional calculus","authors":"M. Samraiz, S. Iqbal, J. Pečarić","doi":"10.1080/23311835.2018.1426205","DOIUrl":"https://doi.org/10.1080/23311835.2018.1426205","url":null,"abstract":"In this paper, we present a variety of integral inequalities in and spaces for the integral operator involving generalized Mittag-Leffler function in its kernel, Hilfer fractional derivative, generalized Riemann-Liouville and Riemann-Liouville k-fractional integral operators.","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/10.1080/23311835.2018.1426205","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45302627","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: 10.1080/23311835.2018.1433577
Snigdhayan Mahanta, G. Choudhury
Abstract This paper deals with the steady-state behavior of an M/G/1 queue with two types of general heterogeneous service to the arriving customers and Bernoulli feedback. We first derive the steady-state probability generating functions for the queue size distributions at a random epoch as well as at a departure epoch. Next, we derive the mean queue size at random epoch and the mean waiting time. Also, we obtain the mean busy period of this model and discuss some important particular cases.
{"title":"On queue with two types of general heterogeneous service with Bernoulli feedback","authors":"Snigdhayan Mahanta, G. Choudhury","doi":"10.1080/23311835.2018.1433577","DOIUrl":"https://doi.org/10.1080/23311835.2018.1433577","url":null,"abstract":"Abstract This paper deals with the steady-state behavior of an M/G/1 queue with two types of general heterogeneous service to the arriving customers and Bernoulli feedback. We first derive the steady-state probability generating functions for the queue size distributions at a random epoch as well as at a departure epoch. Next, we derive the mean queue size at random epoch and the mean waiting time. Also, we obtain the mean busy period of this model and discuss some important particular cases.","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/10.1080/23311835.2018.1433577","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44345867","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 : 2018-01-01Epub Date: 2018-11-23DOI: 10.1080/25742558.2018.1551504
Qiyuan Pan, Rong Wei
Multiple imputation (MI) has become the most popular approach in handling missing data. Closely associated with MI, the fraction of missing information (FMI) is an important parameter for diagnosing the impact of missing data. Currently γ m , the sample value of FMI estimated from MI of a limited m, is used as the estimate of γ0, the population value of FMI, where m is the number of imputations of the MI. This FMI estimation method, however, has never been adequately justified and evaluated. In this paper, we quantitatively demonstrated that E(γ m ) decreases with the increase of m so that E(γ m ) > γ0 for any finite m. As a result γm would inevitably overestimate γ0. Three improved FMI estimation methods were proposed. The major conclusions were substantiated by the results of the MI trials using the data of the 2012 Physician Workflow Mail Survey of the National Ambulatory Medical Care Survey, USA.
{"title":"Improved methods for estimating fraction of missing information in multiple imputation.","authors":"Qiyuan Pan, Rong Wei","doi":"10.1080/25742558.2018.1551504","DOIUrl":"10.1080/25742558.2018.1551504","url":null,"abstract":"<p><p>Multiple imputation (MI) has become the most popular approach in handling missing data. Closely associated with MI, the fraction of missing information (FMI) is an important parameter for diagnosing the impact of missing data. Currently γ <sub><i>m</i></sub> , the sample value of FMI estimated from MI of a limited <i>m</i>, is used as the estimate of γ<sub>0</sub>, the population value of FMI, where <i>m</i> is the number of imputations of the MI. This FMI estimation method, however, has never been adequately justified and evaluated. In this paper, we quantitatively demonstrated that <i>E</i>(γ <sub><i>m</i></sub> ) decreases with the increase of <i>m</i> so that <i>E</i>(γ <sub><i>m</i></sub> ) > γ<sub>0</sub> for any finite <i>m</i>. As a result <i>γ</i> <sub><i>m</i></sub> would inevitably overestimate γ<sub>0</sub>. Three improved FMI estimation methods were proposed. The major conclusions were substantiated by the results of the MI trials using the data of the 2012 Physician Workflow Mail Survey of the National Ambulatory Medical Care Survey, USA.</p>","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":"5 ","pages":"1551504"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1551504","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37080820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-01DOI: 10.1080/23311835.2017.1421003
Mahboobeh Zangeneh Sirdari, M. Islam
Abstract When the interest is in making statements about change based on repeated measurements of discrete data, one way to do so is using Markov chain models. Goodness of fit test to find a good model is very important in analyzing the underlying patterns and relationships in the repeated measures data. To test for the various associations in the models, the likelihood ratio and Wald tests are used. However, it has been observed that the efficient score tests can provide equally good tests and can provide an easier alternative. In this paper, we provide an extension of Tsiatis method for goodness of fit test on higher order Markov chains. In our method, we follow the approach of Tsiatis goodness of fit test in logistic regression models. New method provided in this paper is applied to real-life data to examine the suitability of the techniques.
{"title":"Goodness of fit test for higher order binary Markov chain models","authors":"Mahboobeh Zangeneh Sirdari, M. Islam","doi":"10.1080/23311835.2017.1421003","DOIUrl":"https://doi.org/10.1080/23311835.2017.1421003","url":null,"abstract":"Abstract When the interest is in making statements about change based on repeated measurements of discrete data, one way to do so is using Markov chain models. Goodness of fit test to find a good model is very important in analyzing the underlying patterns and relationships in the repeated measures data. To test for the various associations in the models, the likelihood ratio and Wald tests are used. However, it has been observed that the efficient score tests can provide equally good tests and can provide an easier alternative. In this paper, we provide an extension of Tsiatis method for goodness of fit test on higher order Markov chains. In our method, we follow the approach of Tsiatis goodness of fit test in logistic regression models. New method provided in this paper is applied to real-life data to examine the suitability of the techniques.","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/10.1080/23311835.2017.1421003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49045887","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: 10.1080/25742558.2018.1521084
M. Safavi, A. Khajehnasiri
Abstract This paper proposed an effective numerical method to obtain the solution of nonlinear two-dimensional mixed Volterra-Fredholm integro-differential equations. For this purpose, the two-dimensional block-pulse functions (2D-BPFs) operational matrix of integration and differentiation has been presented. The 2D-BPFs method converts nonlinear two-dimensional mixed Volterra-Fredholm integro-differential equations to an algebraic system of equations which is computable as well. Error analysis and some numerical examples are presented to illustrate the effectiveness and accuracy of the method.
{"title":"Numerical solution of nonlinear mixed Volterra-Fredholm integro-differential equations by two-dimensional block-pulse functions","authors":"M. Safavi, A. Khajehnasiri","doi":"10.1080/25742558.2018.1521084","DOIUrl":"https://doi.org/10.1080/25742558.2018.1521084","url":null,"abstract":"Abstract This paper proposed an effective numerical method to obtain the solution of nonlinear two-dimensional mixed Volterra-Fredholm integro-differential equations. For this purpose, the two-dimensional block-pulse functions (2D-BPFs) operational matrix of integration and differentiation has been presented. The 2D-BPFs method converts nonlinear two-dimensional mixed Volterra-Fredholm integro-differential equations to an algebraic system of equations which is computable as well. Error analysis and some numerical examples are presented to illustrate the effectiveness and accuracy of the method.","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/10.1080/25742558.2018.1521084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48228273","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: 10.1080/25742558.2018.1458553
Rafaqat Noreen, M. Khan
Abstract Continuing the study of irresolute paratopological groups, our focus in this paper is to define and study the boundedness for irresolute paratopological groups. Premeager property for irresolute paratopological groups is discussed. It is proved that every open subgroup of a quasi-bounded, premeager irresolute paratopological group is premeager. For bounded homomorphisms on an irresolute paratopological group, new notions -quasi bounded and -quasi bounded homomorphisms are introduced and discussed.
{"title":"Quasi-boundedness of irresolute paratopological groups","authors":"Rafaqat Noreen, M. Khan","doi":"10.1080/25742558.2018.1458553","DOIUrl":"https://doi.org/10.1080/25742558.2018.1458553","url":null,"abstract":"Abstract Continuing the study of irresolute paratopological groups, our focus in this paper is to define and study the boundedness for irresolute paratopological groups. Premeager property for irresolute paratopological groups is discussed. It is proved that every open subgroup of a quasi-bounded, premeager irresolute paratopological group is premeager. For bounded homomorphisms on an irresolute paratopological group, new notions -quasi bounded and -quasi bounded homomorphisms are introduced and discussed.","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/10.1080/25742558.2018.1458553","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49605691","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}