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Certain fractional integral operators pertaining to S-function 关于S-函数的某些分数积分算子
Cogent mathematics & statistics Pub Date : 2020-01-01 DOI: 10.1080/25742558.2020.1781506
D.L. Suthar
{"title":"Certain fractional integral operators pertaining to S-function","authors":"D.L. Suthar","doi":"10.1080/25742558.2020.1781506","DOIUrl":"https://doi.org/10.1080/25742558.2020.1781506","url":null,"abstract":"Abstract Fractional integral operators introduced by Saxena and Kumbhat involving Fox’s H-function as kernel are applied, and find new image formulas of S-function and properties are established. Also, by implementing Euler, Whittaker and K-transforms on the resulting formulas. On account of S-function, a number of results involving special functions can be obtained merely by giving particular values for the parameters.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1781506","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43712969","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}
引用次数: 2
Lipschitz isomorphism and fixed point theorem for normed groups 赋范群的Lipschitz同构与不动点定理
Cogent mathematics & statistics Pub Date : 2020-01-01 DOI: 10.1080/25742558.2020.1859673
M. Sarfraz, F. Ali, Yongjin Li
{"title":"Lipschitz isomorphism and fixed point theorem for normed groups","authors":"M. Sarfraz, F. Ali, Yongjin Li","doi":"10.1080/25742558.2020.1859673","DOIUrl":"https://doi.org/10.1080/25742558.2020.1859673","url":null,"abstract":"Abstract This paper aims to propose normed structures for groups and to establish the Lipschitz mapping of a normed group to itself. We also investigate some conjugate and isomorphic Lipschitz mappings to determine the equivalent norm and inverse Lipschitz mappings. Specifically, in the main result, we present a fixed point theorem for self-mappings satisfying certain contraction principles on a complete normed group.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1859673","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49214194","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}
引用次数: 1
Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion 分数布朗运动驱动的脉冲中立型随机泛函积分微分方程的稳定性
Cogent mathematics & statistics Pub Date : 2020-01-01 DOI: 10.1080/25742558.2020.1782120
M. Diop, K. Ezzinbi, L. Issaka, K. Ramkumar
{"title":"Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion","authors":"M. Diop, K. Ezzinbi, L. Issaka, K. Ramkumar","doi":"10.1080/25742558.2020.1782120","DOIUrl":"https://doi.org/10.1080/25742558.2020.1782120","url":null,"abstract":"Abstract The aim of this work is to study the stability for some integro-differential equations with impulses driven by fractional Brownian motion with noncompact semigroup in Hilbert spaces. We assume that the linear part has a resolvent operator not necessary compact but is operator norm continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Mönch fixed point theorem. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1782120","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44260050","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}
引用次数: 9
Existence of solutions for the infinite systems of integral equations in the space L ∞(∂ n ) 空间L∞（⏴n）中无穷大积分方程组解的存在性
Cogent mathematics & statistics Pub Date : 2020-01-01 DOI: 10.1080/25742558.2020.1712759
A. Samadi, Shahram Banaei
{"title":"Existence of solutions for the infinite systems of integral equations in the space L ∞(∂ n )","authors":"A. Samadi, Shahram Banaei","doi":"10.1080/25742558.2020.1712759","DOIUrl":"https://doi.org/10.1080/25742558.2020.1712759","url":null,"abstract":"Abstract In this paper, by applying the behavior of measure of noncompactness in L ∞( n ), we study the existence of solutions of an infinite system of integral equations in the space L ∞( n ). Finally, an example is included to show the usefulness of the outcome.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1712759","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45024688","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}
引用次数: 0
Approximation by finite mixtures of continuous density functions that vanish at infinity 在无穷远处消失的连续密度函数的有限混合近似
Cogent mathematics & statistics Pub Date : 2019-03-01 DOI: 10.1080/25742558.2020.1750861
TrungTin Nguyen, H. Nguyen, Faicel Chamroukhi, G. McLachlan
{"title":"Approximation by finite mixtures of continuous density functions that vanish at infinity","authors":"TrungTin Nguyen, H. Nguyen, Faicel Chamroukhi, G. McLachlan","doi":"10.1080/25742558.2020.1750861","DOIUrl":"https://doi.org/10.1080/25742558.2020.1750861","url":null,"abstract":"Abstract Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is often left unclear. We prove that finite mixture models constructed from pdfs in can be used to conduct approximation of various classes of approximands in a number of different modes. That is, we prove approximands in can be uniformly approximated, approximands in can be uniformly approximated on compact sets, and approximands in can be approximated with respect to the , for . Furthermore, we also prove that measurable functions can be approximated, almost everywhere.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1750861","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44982358","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}
引用次数: 46
An extension of Darbo’s theorem and its application to existence of solution for a system of integral equations Darbo定理的推广及其在一类积分方程组解的存在性中的应用
Cogent mathematics & statistics Pub Date : 2019-01-01 DOI: 10.1080/25742558.2019.1614319
Shahram Banaei
{"title":"An extension of Darbo’s theorem and its application to existence of solution for a system of integral equations","authors":"Shahram Banaei","doi":"10.1080/25742558.2019.1614319","DOIUrl":"https://doi.org/10.1080/25742558.2019.1614319","url":null,"abstract":"Abstract In this paper, we extend Darbo’s fixed point theorem in Banach space via the concept of the class of operators O(f;.) and obtain a tripled fixed point theorem. The main tool applied in our investigation is the technique of measures of noncompactness. Finally, as an application of our obtained results, we analyze the existence of solutions for a system of integral equations.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1614319","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45954309","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}
引用次数: 9
On bounding the Thompson metric by Schatten norms 关于用Schatten范数限定汤普森度规的问题
Cogent mathematics & statistics Pub Date : 2019-01-01 DOI: 10.1080/25742558.2019.1614318
David A. Snyder
{"title":"On bounding the Thompson metric by Schatten norms","authors":"David A. Snyder","doi":"10.1080/25742558.2019.1614318","DOIUrl":"https://doi.org/10.1080/25742558.2019.1614318","url":null,"abstract":"Abstract The Thompson metric provides key geometric insights in the study of non-linear matrix equations and in many optimization problems. However, knowing that an approximate solution is within units, in the Thompson metric, of the actual solution provides little insight into how good the approximation is as a matrix or vector approximation. That is, bounding the Thompson metric between an approximate and accurate solution to a problem does not provide obvious bounds either for the spectral or the Frobenius norm, both Schatten norms, of the difference between the approximation and accurate solution. This paper reports such an upper bound, namely that where denotes the Schatten p-norm and denotes the Thompson metric between and . Furthermore, a more geometric proof leads to a slightly better bound in the case of the Frobenius norm, .","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1614318","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47805778","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}
引用次数: 1
Computer Algebra and Algorithms for Unbiased Moment Estimation of Arbitrary Order. 任意阶无偏矩估计的计算机代数与算法。
Cogent mathematics & statistics Pub Date : 2019-01-01 Epub Date: 2019-12-21 DOI: 10.1080/25742558.2019.1701917
Inna Gerlovina, Alan E Hubbard
{"title":"Computer Algebra and Algorithms for Unbiased Moment Estimation of Arbitrary Order.","authors":"Inna Gerlovina,&nbsp;Alan E Hubbard","doi":"10.1080/25742558.2019.1701917","DOIUrl":"https://doi.org/10.1080/25742558.2019.1701917","url":null,"abstract":"<p><p>While unbiased central moment estimators of lower orders (such as a sample variance) are easily obtainable and often used in practice, derivation of unbiased estimators of higher orders might be more challenging due to long math and tricky combinatorics. Moreover, higher orders necessitate calculation of estimators of powers and products that also amount to these orders. We develop a software algorithm that allows the user to obtain unbiased estimators of an arbitrary order and provide results up to the 6th order, including powers and products of lower orders. The method also extends to finding pooled estimates of higher central moments of several different populations (<i>e.g.</i> for two-sample tests). We introduce an R package <i>Umoments</i> that calculates one- and two-sample estimates and generates intermediate results used to obtain these estimators.</p>","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1701917","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38573734","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}
引用次数: 4
Mathematical modelling and analysis of alcohol-methamphetamine co-abuse in the Western Cape Province of South Africa 南非西开普省酒精-甲基苯丙胺共同滥用的数学模型和分析
Cogent mathematics & statistics Pub Date : 2019-01-01 DOI: 10.1080/25742558.2019.1641175
T. O. Orwa, F. Nyabadza
{"title":"Mathematical modelling and analysis of alcohol-methamphetamine co-abuse in the Western Cape Province of South Africa","authors":"T. O. Orwa, F. Nyabadza","doi":"10.1080/25742558.2019.1641175","DOIUrl":"https://doi.org/10.1080/25742558.2019.1641175","url":null,"abstract":"Abstract Substance/drug abuse poses a significant threat to the health and socio-economic fabric of individuals and nations. The combined abuse of alcohol and the highly addictive methamphetamine has worsened the drug epidemic in South Africa, especially in the Western Cape province. In this paper, a mathematical model is formulated to model the dynamics of alcohol and methamphetamine co-abuse. We prove that the equilibria of the submodels are locally and globally asymptotically stable when the sub-model threshold parameters are less than unity. The basic reproduction number due to co-abuse is shown to be the maximum of the two sub-model reproduction numbers. Sensitivity analysis reveals that the most sensitive parameters in the co-abuse epidemic are the alcohol and methamphetamine recruitment rates β1 and β2 respectively. The prevalence curve is indicative of a persistent drug problem in the region. Hence, the need to promote social programs that raise awareness of the dangers posed by multiple substance abuse, through educational campaigns in learning institutions, social media and health institutions. Transmission control must focus on enhancing the quitting process while promoting support services to drug users during and after treatment to minimize cases of relapse.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1641175","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49563582","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}
引用次数: 5
Model selection among growth curve models that have the same number of parameters 具有相同数量参数的生长曲线模型之间的模型选择
Cogent mathematics & statistics Pub Date : 2019-01-01 DOI: 10.1080/25742558.2019.1660503
D. Satoh
{"title":"Model selection among growth curve models that have the same number of parameters","authors":"D. Satoh","doi":"10.1080/25742558.2019.1660503","DOIUrl":"https://doi.org/10.1080/25742558.2019.1660503","url":null,"abstract":"Abstract A model selection method was proposed to determine the most appropriate model among growth curve models that have the same number of parameters. It uses a measure of mean relative squared error and regression equations from difference equations for growth curve models. The difference equations have exact solutions that are on exact solutions of differential equations as growth curve models. The regression equations from the difference equations perfectly reproduce their parameter estimates. The proposed method selects an appropriate model when data are on an exact solution of a differential equation. It was verified to be practical with six actual datasets when the Gompertz curve and logistic curve models, which are often used for forecasting, were alternative growth curve models.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1660503","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42228491","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}
引用次数: 8
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