The soft set is a mapping from a parameter to the crisp subset of universe. Molodtsov introduced the concept of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects. In this paper the concept of measurable soft sets are introduced and their properties are discussed. The open problem of this paper is to develop measurable functions and lebesgue integral in soft set theory context.
{"title":"Measurable Soft Sets","authors":"A. Mukherjee, A. Saha, A. Das","doi":"10.12816/0023170","DOIUrl":"https://doi.org/10.12816/0023170","url":null,"abstract":"The soft set is a mapping from a parameter to the crisp subset of universe. Molodtsov introduced the concept of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects. In this paper the concept of measurable soft sets are introduced and their properties are discussed. The open problem of this paper is to develop measurable functions and lebesgue integral in soft set theory context.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126631970","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 paper, we apply the variational homotopy perturbation method to resolve the generalized Fisher’s equation. The numerical solutions are obtained as series solutions and compared with the exact solution. The result showed that this algorithm based on the VHPM method is very effective and can be applied to other problems.
{"title":"An Efficient Algorithm for Generalized Fisher's Equation by the Variational Homotopy Perturbation Method","authors":"D. Ziane, K. Belghaba, M. Cherif","doi":"10.12816/0023169","DOIUrl":"https://doi.org/10.12816/0023169","url":null,"abstract":"In this paper, we apply the variational homotopy perturbation method to resolve the generalized Fisher’s equation. The numerical solutions are obtained as series solutions and compared with the exact solution. The result showed that this algorithm based on the VHPM method is very effective and can be applied to other problems.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124588152","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}
Using the technique of differential subordination, we obtain certain results for starlike and parabolic starlike functions involving the differential operator zf ′(z) f(z) ( 1 + α zf ′′(z) f ′(z) ) . We study the above operator for multivalent functions and also conclude some results for univalent functions.
{"title":"Certain Results on Starlike and Parabolic Starlike Functions","authors":"R. Brar, S. S. Billing","doi":"10.12816/0023171","DOIUrl":"https://doi.org/10.12816/0023171","url":null,"abstract":"Using the technique of differential subordination, we obtain certain results for starlike and parabolic starlike functions involving the differential operator zf ′(z) f(z) ( 1 + α zf ′′(z) f ′(z) ) . We study the above operator for multivalent functions and also conclude some results for univalent functions.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128709078","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 variety of algebras is called strongly solid if and only if every its identity is a strong hyperidentity. The clone of a strongly solid variety is free with respect to itself. M-solid varieties generalize the concept of solidity. In this paper, we describe the clone of an arbitrary M-strongly solid variety.
{"title":"M-Strongly Solid Varieties and Q-Free Clones","authors":"S. Phuapong","doi":"10.12816/0019894","DOIUrl":"https://doi.org/10.12816/0019894","url":null,"abstract":"A variety of algebras is called strongly solid if and only if every its identity is a strong hyperidentity. The clone of a strongly solid variety is free with respect to itself. M-solid varieties generalize the concept of solidity. In this paper, we describe the clone of an arbitrary M-strongly solid variety.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129610845","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}
Soft Set theory is one of the recent topics gaining signicance in nding rational and logical solutions to various real life problems which involve uncertainty, impreciseness and vagueness. In this article we have introduced the notions of reduct weighted intuitionistic fuzzy soft multi sets of weighted interval valued intuitionistic fuzzy soft multi set and propose an adjustable approach to weighted interval-valued intuitionistic fuzzy soft set based decision making by using reduct weighted intuitionistic fuzzy soft sets and level soft sets of reduct intuitionistic fuzzy soft sets. Some illustrative example is employed to show the feasibility of our approach in practical applications.
{"title":"A Novel Approach to Weighted Interval-Valued Intuitionistic Fuzzy Soft Multi Sets Based Decision Making","authors":"A. Mukherjee, A. Das","doi":"10.12816/0019895","DOIUrl":"https://doi.org/10.12816/0019895","url":null,"abstract":"Soft Set theory is one of the recent topics gaining signicance in nding rational and logical solutions to various real life problems which involve uncertainty, impreciseness and vagueness. In this article we have introduced the notions of reduct weighted intuitionistic fuzzy soft multi sets of weighted interval valued intuitionistic fuzzy soft multi set and propose an adjustable approach to weighted interval-valued intuitionistic fuzzy soft set based decision making by using reduct weighted intuitionistic fuzzy soft sets and level soft sets of reduct intuitionistic fuzzy soft sets. Some illustrative example is employed to show the feasibility of our approach in practical applications.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117246263","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}
Our matter is to investigate conditions of transitivity of Arens products in non regular Banach algebras. To this end we introduce the notion of links, i.e. some special elements of the second dual of a Banach algebra that allow a transitive passage between dierent Arens products. There will be two classes of links, both closed two sided ideals of the second dual space. We shall characterize these classes, determining some of their properties and giving a few examples.
{"title":"On Mixed Transitivity of Arens Products","authors":"C. Peña","doi":"10.12816/0019896","DOIUrl":"https://doi.org/10.12816/0019896","url":null,"abstract":"Our matter is to investigate conditions of transitivity of Arens products in non regular Banach algebras. To this end we introduce the notion of links, i.e. some special elements of the second dual of a Banach algebra that allow a transitive passage between dierent Arens products. There will be two classes of links, both closed two sided ideals of the second dual space. We shall characterize these classes, determining some of their properties and giving a few examples.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130669583","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 study, we will apply homotopy perturbation transform method (HPTM) to solve Lane-Emden and Emden-Fowler equations and we will also make a comparison between the result obtained by this method and the exact solutions of the same equations presented in other research. The results showed that HPTM has a high eciency and eectiveness in solving these equations and can be applied to other nonlinear partial dierential equations to obtain approximate or exat solutions
{"title":"Application of Homotopy Perturbation Transform Method to Resolve Lane , Emden and Emden , Fowler Equations","authors":"D. Ziane, M. Cherif, K. Belghaba","doi":"10.12816/0019897","DOIUrl":"https://doi.org/10.12816/0019897","url":null,"abstract":"In this study, we will apply homotopy perturbation transform method (HPTM) to solve Lane-Emden and Emden-Fowler equations and we will also make a comparison between the result obtained by this method and the exact solutions of the same equations presented in other research. The results showed that HPTM has a high eciency and eectiveness in solving these equations and can be applied to other nonlinear partial dierential equations to obtain approximate or exat solutions","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127131077","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 paper, we establish a common xed point theorem for two pairs of mappings satisfying an almost generalized contractive condition for comparable elements in a partially ordered metric space. Our results generalize and extend the main results in [2] to multivalued mappings. As corollaries we obtain the results in [8, 9], and many others.
{"title":"Common Fixed Points of Hybrid Pairs of Mappings in Ordered Metric Spaces","authors":"R. Rashwan, I. Shimaa","doi":"10.12816/0017357","DOIUrl":"https://doi.org/10.12816/0017357","url":null,"abstract":"In this paper, we establish a common xed point theorem for two pairs of mappings satisfying an almost generalized contractive condition for comparable elements in a partially ordered metric space. Our results generalize and extend the main results in [2] to multivalued mappings. As corollaries we obtain the results in [8, 9], and many others.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116752988","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. Al-Ali, K. Almutairi, E. K. Rawy, M. Abou-Dina, A. Ghaleb
A previously introduced boundary integral method is used to find an approximate solution to a problem of plane, uncoupled thermoelasticity inside an ellipse with hump. Part of the boundary is under a given variable pressure, while the other part is completely fixed. The singular behavior of the solution is put in evidence at those points where the boundary conditions change. The solution is then sought for in the form of series in Cartesian harmonics, enriched with a specially chosen harmonic function with singular boundary behavior to simulate the existing singularities. The results are analyzed in detail and the functions of practical interest are represented on the boundary and also inside the domain by three-dimensional plots. This model may be useful in analyzing the stresses that arise in long elastic pad supports under real conditions.
{"title":"Deformation and Stresses in Long Thermoelastic Pad Supports under Prescribed Temperature by a Boundary Integral Method","authors":"A. Al-Ali, K. Almutairi, E. K. Rawy, M. Abou-Dina, A. Ghaleb","doi":"10.12816/0017356","DOIUrl":"https://doi.org/10.12816/0017356","url":null,"abstract":"A previously introduced boundary integral method is used to find an approximate solution to a problem of plane, uncoupled thermoelasticity inside an ellipse with hump. Part of the boundary is under a given variable pressure, while the other part is completely fixed. The singular behavior of the solution is put in evidence at those points where the boundary conditions change. The solution is then sought for in the form of series in Cartesian harmonics, enriched with a specially chosen harmonic function with singular boundary behavior to simulate the existing singularities. The results are analyzed in detail and the functions of practical interest are represented on the boundary and also inside the domain by three-dimensional plots. This model may be useful in analyzing the stresses that arise in long elastic pad supports under real conditions.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127841975","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 paper, the fractional homotopy perturbation transform method (FHPTM) is employed to obtain approximate analytical solutions of the time-fractional KdV, K(2,2) and Burgers equations. The FHPTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHPTM is an appropriate method for solving nonlinear fractional derivative equation.
{"title":"Fractional Homotopy Perturbation Transform Method for Solving the Time-Fractional KDV , K ( 2 , 2 ) and Burgers Equations","authors":"D. Ziane, K. Belghaba, M. Cherif","doi":"10.12816/0017358","DOIUrl":"https://doi.org/10.12816/0017358","url":null,"abstract":"In this paper, the fractional homotopy perturbation transform method (FHPTM) is employed to obtain approximate analytical solutions of the time-fractional KdV, K(2,2) and Burgers equations. The FHPTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHPTM is an appropriate method for solving nonlinear fractional derivative equation.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115744335","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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