In this paper we consider the application of a a new class of cumulative distribution function proposed by Ramos, Dey, Louzada and Lachos in [9] to the debugging theory. We study the Hausdorff approximation of the shifted Heaviside step function by this family. Numerical examples, illustrating our results are presented using programming environment Mathematica. We give also real examples with data provided in [30] using the new software reliability model. Dataset included [31] Year 2000 compatibility modifications, operating system upgrade, and signaling message processing. AMS Subject Classification: 68N30, 41A46
{"title":"APPLICATION OF A NEW CLASS CUMULATIVE LIFETIME DISTRIBUTION TO SOFTWARE RELIABILITY ANALYSIS","authors":"N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev","doi":"10.12732/CAA.V22I4.4","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.4","url":null,"abstract":"In this paper we consider the application of a a new class of cumulative distribution function proposed by Ramos, Dey, Louzada and Lachos in [9] to the debugging theory. We study the Hausdorff approximation of the shifted Heaviside step function by this family. Numerical examples, illustrating our results are presented using programming environment Mathematica. We give also real examples with data provided in [30] using the new software reliability model. Dataset included [31] Year 2000 compatibility modifications, operating system upgrade, and signaling message processing. AMS Subject Classification: 68N30, 41A46","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45736022","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}
{"title":"ELASTICITY WITH MIXED FINITE ELEMENT","authors":"O. Koubaiti, J. EL-Mekkaoui, A. Elkhalfi","doi":"10.12732/CAA.V22I4.1","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.1","url":null,"abstract":"","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42951784","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}
A high level of service for medical supplies and effective inventory policies are essential objectives for all health care industries. Medicine shortages and improper use of pharmaceuticals can not only lead to financial losses but also have a significant impact on patients. Many health systems and hospitals experience difficulties in achieving these goals as they have not addressed how medicines are managed, supplied, and used to save lives and improve health. Studies are essential to understand operations in health care industries and to offer decision support tools that improve health policy, public health, patient safety, and strategic decision-making in the pharmaceutical inventory model. We present a deterministic inventory model for pharmaceutical items having time dependent quadratic demand under the effect of deterioration. We develop a procedure for determining optimal solutions for inventory and the number of deliveries to achieve hospital (Customer Service Level) CSL targets with a minimum total cost of the system. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution which could minimize the average total cost per unit time has been discussed. A numerical example illustrates the model application and behavior using MATLAB. 512 R. UTHAYAKUMAR AND S. THARANI AMS Subject Classification: 97M60
{"title":"AN INVENTORY MODEL FOR DETERIORATING PHARMACEUTICAL ITEMS WITH TIME DEPENDENT DEMAND UNDER COMPLETE BACKLOGGING","authors":"R. Uthayakumar, S. Tharani","doi":"10.12732/CAA.V22I4.2","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.2","url":null,"abstract":"A high level of service for medical supplies and effective inventory policies are essential objectives for all health care industries. Medicine shortages and improper use of pharmaceuticals can not only lead to financial losses but also have a significant impact on patients. Many health systems and hospitals experience difficulties in achieving these goals as they have not addressed how medicines are managed, supplied, and used to save lives and improve health. Studies are essential to understand operations in health care industries and to offer decision support tools that improve health policy, public health, patient safety, and strategic decision-making in the pharmaceutical inventory model. We present a deterministic inventory model for pharmaceutical items having time dependent quadratic demand under the effect of deterioration. We develop a procedure for determining optimal solutions for inventory and the number of deliveries to achieve hospital (Customer Service Level) CSL targets with a minimum total cost of the system. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution which could minimize the average total cost per unit time has been discussed. A numerical example illustrates the model application and behavior using MATLAB. 512 R. UTHAYAKUMAR AND S. THARANI AMS Subject Classification: 97M60","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42787360","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}
In this work, we establish several results about the existence and uniqueness of solutions for some neutral differential equations with state-dependent delays. We assume that the linear part generates a strongly continuous semigroup on a general Banach space. AMS Subject Classification: 34G20, 34K20, 34K30
{"title":"EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR SOME NEUTRAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAYS","authors":"K. Daoudi, J. Henderson, Abdelghnai Ouahab","doi":"10.12732/CAA.V22I3.1","DOIUrl":"https://doi.org/10.12732/CAA.V22I3.1","url":null,"abstract":"In this work, we establish several results about the existence and uniqueness of solutions for some neutral differential equations with state-dependent delays. We assume that the linear part generates a strongly continuous semigroup on a general Banach space. AMS Subject Classification: 34G20, 34K20, 34K30","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46362298","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}
H T Banks, K B Flores, I G Rosen, E M Rutter, Melike Sirlanci, W Clayton Thompson
We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.
{"title":"THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs.","authors":"H T Banks, K B Flores, I G Rosen, E M Rutter, Melike Sirlanci, W Clayton Thompson","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.</p>","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"22 3","pages":"415-446"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9365078/pdf/nihms-1826881.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40690116","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}
Conjugate gradient methods are probably the most famous iterative methods for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a new search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical result shows that the proposed formula is superior and more efficient when compared to other CG coefficients. AMS Subject Classification: 90C26, 65H10
{"title":"GLOBAL CONVERGENCE OF THE TMR METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS","authors":"T. Bouali, M. Belloufi, R. Guefaifia","doi":"10.12732/CAA.V21I1.2","DOIUrl":"https://doi.org/10.12732/CAA.V21I1.2","url":null,"abstract":"Conjugate gradient methods are probably the most famous iterative methods for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a new search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical result shows that the proposed formula is superior and more efficient when compared to other CG coefficients. AMS Subject Classification: 90C26, 65H10","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46452553","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}
Various properties of composition operators on weighted Hardy spaces have been studied by different authors [3] Cowen and Kriete obtained a nice correlation between hyponormality of composition operator on H2. [9] E.A. Nordgeen, studied some results on the hyponormality of composition operators and their adjoints. [13] S. Panayappan D.Senthil kumar and Mohenraj have investigated on M-Quasihyponormality of composition operators and their adjoints. [15] T. Veluchamy have investigated parahyponormal * paranormal and posinormal operators.
{"title":"(M,K)-QUASI CLASS Q AND (M,K)-QUASI *CLASS Q COMPOSITION OPERATORS ON WEIGHTED HARDY SPACE","authors":"A. Devika, G. Suresh","doi":"10.12732/CAA.V21I1.1","DOIUrl":"https://doi.org/10.12732/CAA.V21I1.1","url":null,"abstract":"Various properties of composition operators on weighted Hardy spaces have been studied by different authors [3] Cowen and Kriete obtained a nice correlation between hyponormality of composition operator on H2. [9] E.A. Nordgeen, studied some results on the hyponormality of composition operators and their adjoints. [13] S. Panayappan D.Senthil kumar and Mohenraj have investigated on M-Quasihyponormality of composition operators and their adjoints. [15] T. Veluchamy have investigated parahyponormal * paranormal and posinormal operators.","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48404248","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}
The uniqueness of positive solution to the elliptic model ∆u+ u[a+ g(u, v)] = 0 in Ω, ∆v + v[a+ h(u, v)] = 0 in Ω, u = v = 0 on ∂Ω, were investigated. AMS Subject Classification: 35Jxx
{"title":"Growth Conditions for Uniqueness of Smooth Positive Solutions to an Elliptic Model","authors":"J. H. Kang","doi":"10.12732/caa.v20i4.7","DOIUrl":"https://doi.org/10.12732/caa.v20i4.7","url":null,"abstract":"The uniqueness of positive solution to the elliptic model ∆u+ u[a+ g(u, v)] = 0 in Ω, ∆v + v[a+ h(u, v)] = 0 in Ω, u = v = 0 on ∂Ω, were investigated. AMS Subject Classification: 35Jxx","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"20 1","pages":"575-584"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66376295","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 : 2010-01-01DOI: 10.1007/978-3-642-11220-1_11
G. Anastassiou
{"title":"HIGHER ORDER FUZZY KOROVKIN THEORY USING INEQUALITIES","authors":"G. Anastassiou","doi":"10.1007/978-3-642-11220-1_11","DOIUrl":"https://doi.org/10.1007/978-3-642-11220-1_11","url":null,"abstract":"","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"10 1","pages":"159-190"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51070815","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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