Pub Date : 2022-04-25DOI: 10.52280/pujm.2022.540401
Gu¨l UG˘ UR Kaymanli, Cumali Ekici
In this paper, we work on the ruled surfaces obtained by a quasi normal and quasi binormal vectors along a spacelike space curve in three dimensional Minkowski space. Time evolution equations depending on quasi curvatures are obtained. Studying directional evolutions of both quasi normal and quasi binormal ruled surfaces by using their directrices, we investigate some geometric properties such as inextensibilty, developability, flatness and minimality of these ruled surfaces.
{"title":"Evolutions of the Ruled Surfaces along a Spacelike Space Curve","authors":"Gu¨l UG˘ UR Kaymanli, Cumali Ekici","doi":"10.52280/pujm.2022.540401","DOIUrl":"https://doi.org/10.52280/pujm.2022.540401","url":null,"abstract":"In this paper, we work on the ruled surfaces obtained by a\u0000quasi normal and quasi binormal vectors along a spacelike space curve in\u0000three dimensional Minkowski space. Time evolution equations depending\u0000on quasi curvatures are obtained. Studying directional evolutions of both\u0000quasi normal and quasi binormal ruled surfaces by using their directrices,\u0000we investigate some geometric properties such as inextensibilty, developability,\u0000flatness and minimality of these ruled surfaces.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129232112","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 : 2022-04-25DOI: 10.52280/pujm.2022.540402
S. Handibag, R. M. Wayal
In this article, the Laplace decomposition method is implemented to solve nonlinear partial differential equations. Third-order KdV and mKdV equations with initial conditions have been considered to check the validity of the proposed method. Results obtained by this method are compared with the exact solutions in literature numerically as well as graphically and are found to be in good agreement with each other. The proposed method finds the solutions without any discretization, perturbation, linearization, or restrictive assumptions. Obtained results show that the LDM is highly accurate and easy to apply for NLPDEs in various fields.
{"title":"A Study of Third-order KdV and mKdV Equations by Laplace Decomposition Method","authors":"S. Handibag, R. M. Wayal","doi":"10.52280/pujm.2022.540402","DOIUrl":"https://doi.org/10.52280/pujm.2022.540402","url":null,"abstract":"In this article, the Laplace decomposition method is implemented to solve nonlinear partial differential equations. Third-order KdV and mKdV equations with initial conditions have been considered to check the validity of the proposed method. Results obtained by this method are compared with the exact solutions in literature numerically as well as\u0000graphically and are found to be in good agreement with each other. The proposed method finds the solutions without any discretization, perturbation, linearization, or restrictive assumptions. Obtained results show that the LDM is highly accurate and easy to apply for NLPDEs in various fields.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123558843","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 : 2022-04-25DOI: 10.52280/pujm.2022.540405
Sadaqat Hussain, Raziuddin Siddiqui
Previously we have extended the notion of tangent complex of first order to second order and proposed various morphisms in order to connect the tangent complex to well known Grassmannian complex. Now we are motivated to find similar constructions and maps for order greater than 2. Therefore in this paper we present the maps and other ingredients for the tangent complex of order three in dialogarithmic settings. This work will play a key role in the generalization of these constructions.
{"title":"Maps in Tangent Complex of Order Three","authors":"Sadaqat Hussain, Raziuddin Siddiqui","doi":"10.52280/pujm.2022.540405","DOIUrl":"https://doi.org/10.52280/pujm.2022.540405","url":null,"abstract":"Previously we have extended the notion of tangent complex of first order to second order and proposed various morphisms in order to connect the tangent complex to well known Grassmannian complex. Now we are motivated to find similar constructions and maps for order greater than 2. Therefore in this paper we present the maps and other ingredients\u0000for the tangent complex of order three in dialogarithmic settings. This work will play a key role in the generalization of these constructions.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126756926","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 : 2022-04-25DOI: 10.52280/pujm.2022.540403
M. Khalid, Javed Khan, A. Iqbal
In this article, the functional equations of classical polylogarithmic groups for higher weights have been introduced and their relations with configuration of complexes have been defined via morphisms. Furthermore, these functional equations and homomorphisms have been generalized and their proofs have also been given. Through the use of these functional equations, the bi-complex form of the associated diagrams has been shown.
{"title":"Generalized Functional Equations of Polylogarithmic Groups","authors":"M. Khalid, Javed Khan, A. Iqbal","doi":"10.52280/pujm.2022.540403","DOIUrl":"https://doi.org/10.52280/pujm.2022.540403","url":null,"abstract":"In this article, the functional equations of classical polylogarithmic groups for higher weights have been introduced and their relations with configuration of complexes have been defined via morphisms. Furthermore, these functional equations and homomorphisms have been generalized and their proofs have also been given. Through the use of these functional equations, the bi-complex form of the associated diagrams has\u0000been shown.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125397982","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 : 2022-02-25DOI: 10.52280/pujm.2022.540203
S. Mustafa, Shumaila Naheed, Hina Basharat
There are number of inference techniques that can be used for the estimation of the unknown parameters which are based on precise crisp data, but there are many situations where we deal with imprecise and vague data. In this situation the classical mathematical tools cannot help us to estimate the parameters. This impreciseness can be covered by introducing fuzzy concepts. This study deals with the maximum likelihood estimation for the parameters of Rayleigh distribution using Newton Raphson algorithm. A real-life data set analysis is presented by considering set of luminous intensity of light emitting diodes and finding of this study illustrates that proposed inferential technique is useful to deal with fuzziness of data when statistical inference of Rayleigh distribution is carried out for imprecise or fuzzy data.
{"title":"Statistical Inference for the Parameter of Rayleigh Distribution Through Fuzzy\u0000Membership Function","authors":"S. Mustafa, Shumaila Naheed, Hina Basharat","doi":"10.52280/pujm.2022.540203","DOIUrl":"https://doi.org/10.52280/pujm.2022.540203","url":null,"abstract":"There are number of inference techniques that can be used for the estimation of the unknown parameters which are based on precise crisp data, but there are many situations where we deal with imprecise and vague data. In this situation the classical mathematical tools cannot help us to estimate the parameters. This impreciseness can be covered by\u0000introducing fuzzy concepts. This study deals with the maximum likelihood estimation for the parameters of Rayleigh distribution using Newton Raphson algorithm. A real-life data set analysis is presented by considering set of luminous intensity of light emitting diodes and finding of this study illustrates that proposed inferential technique is useful to deal with fuzziness of data when statistical inference of Rayleigh distribution is carried out for imprecise or fuzzy data.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128115857","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 problem of solving nonlinear equations (real or complex) is a nontrivial task in many areas of science and engineering. Usually, the analytic methods for such equations are not directly affordable and require an iterative approach for getting an approximate solution. Keeping in view the above facts, we suggest and analyze some new iterative methods for solving nonlinear equation of the form f(u) = 0 by using the decomposition technique coupled with a system of equations and threepoints Gaussian quadrature formula. We also determine the convergence order of our proposed iterative methods. Some test examples are given to endorse and validate the performance of new methods as compared to previously well-known methods.
{"title":"Solution of nonlinear equations using three point Gaussian quadrature formula and\u0000decomposition technique","authors":"Gul Sana, M. Noor, K. Noor","doi":"10.52280/2021.531205","DOIUrl":"https://doi.org/10.52280/2021.531205","url":null,"abstract":"The problem of solving nonlinear equations (real or complex)\u0000is a nontrivial task in many areas of science and engineering. Usually,\u0000the analytic methods for such equations are not directly affordable and\u0000require an iterative approach for getting an approximate solution. Keeping in view the above facts, we suggest and analyze some new iterative\u0000methods for solving nonlinear equation of the form f(u) = 0 by using the\u0000decomposition technique coupled with a system of equations and threepoints Gaussian quadrature formula. We also determine the convergence\u0000order of our proposed iterative methods. Some test examples are given\u0000to endorse and validate the performance of new methods as compared to\u0000previously well-known methods.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126826120","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 : 2021-12-24DOI: 10.52280//pujm.2021.531201
Hakeem A. Othman
As applications on infra − β − open set for new classes of mappings and new concepts topological spaces are introduced, namely, infra- β−continuous, infra−β−irresolute, infra−β−open(closed) mapping, infra − β − τi (i = 0, 1, 2, 3, 4), infra − β − compact and infra − β − connected space. Some of special results and properties which belong to these various applications are established and studied. Moreover, the relations and opposite relations between these new concepts and others are discussed and counter examples are given in order to investigate opposite relations.
{"title":"Infra − β − Closed(Open) Sets : New","authors":"Hakeem A. Othman","doi":"10.52280//pujm.2021.531201","DOIUrl":"https://doi.org/10.52280//pujm.2021.531201","url":null,"abstract":"As applications on infra − β − open set for new classes of mappings and new concepts topological spaces are introduced, namely, infra- β−continuous, infra−β−irresolute, infra−β−open(closed) mapping, infra − β − τi (i = 0, 1, 2, 3, 4), infra − β − compact and\u0000infra − β − connected space. Some of special results and properties which belong to these various applications are established and studied. Moreover, the relations and opposite relations between these new concepts and others are discussed and counter examples are given in order to investigate opposite relations.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114708784","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 : 2021-12-24DOI: 10.52280/pujm.2021.531203
F. Safdar, M. Attique
The generalized fractional integral has been one of the most useful operators for modelling non-local behaviors by fractional differential equations. It is considered, for several integral inequalities by introducing the concept of exponentially (s, m)-preinvexity. These variants derived via an extended Mittag-Leffler function based on boundedness, continuity and Hermite-Hadamard type inequalities. The consequences associated with fractional integral operators are more general and also present the results for convexity theory. Moreover, we point out that the variants are useful in solving the problems of science, engineering and technology where the Mittag-Leffler function occurs naturally.
{"title":"Some new generalizations for exponentially (s, m)-preinvex functions considering\u0000generalized fractional integral operators","authors":"F. Safdar, M. Attique","doi":"10.52280/pujm.2021.531203","DOIUrl":"https://doi.org/10.52280/pujm.2021.531203","url":null,"abstract":"The generalized fractional integral has been one of the most useful operators for modelling non-local behaviors by fractional differential equations. It is considered, for several integral inequalities by introducing the concept of exponentially (s, m)-preinvexity. These variants\u0000derived via an extended Mittag-Leffler function based on boundedness, continuity and Hermite-Hadamard type inequalities. The consequences associated with fractional integral operators are more general and also present the results for convexity theory. Moreover, we point out that the variants are useful in solving the problems of science, engineering and\u0000technology where the Mittag-Leffler function occurs naturally.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121238668","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 : 2021-12-24DOI: 10.52280/pujm.2021.531204
Salma Khan, M. Gulistan, H. Wahab
This article introduces a new concept, called q-rung orthopair fuzzy hypersoft set (q-ROF Hypersoft sets). We introduce a theme of some fundamental operations such as q-ROF Hypersoft-subset, q-ROF Hypersoft null-set, q-ROF Hypersoft absolute-set, union, intersection, and complement. We also present ”AND” and ”OR” operators. To check out the validity of q-ROF Hypersoft sets, we use some numerical examples
{"title":"Development of the structure of q-Rung Orthopair Fuzzy Hypersoft Set with basic Operations","authors":"Salma Khan, M. Gulistan, H. Wahab","doi":"10.52280/pujm.2021.531204","DOIUrl":"https://doi.org/10.52280/pujm.2021.531204","url":null,"abstract":"This article introduces a new concept, called q-rung orthopair fuzzy hypersoft set (q-ROF Hypersoft sets). We introduce a theme of some fundamental operations such as q-ROF Hypersoft-subset, q-ROF Hypersoft null-set, q-ROF Hypersoft absolute-set, union, intersection, and complement. We also present ”AND” and ”OR” operators. To check out the validity of q-ROF Hypersoft sets, we use some numerical examples","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127951250","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 : 2021-12-24DOI: 10.52280/pujm.2021.531202
Muhammad Tahir, Naila Sadaf
In this paper, we prove an important property of metric space which is the existence and uniqueness of completion. Firstly we gave completion of a complex-valued dislocated metric space and then prove its uniqueness.
{"title":"Completion of Complex Valued Dislocated Metric Space","authors":"Muhammad Tahir, Naila Sadaf","doi":"10.52280/pujm.2021.531202","DOIUrl":"https://doi.org/10.52280/pujm.2021.531202","url":null,"abstract":"In this paper, we prove an important property of metric space\u0000which is the existence and uniqueness of completion. Firstly we gave\u0000completion of a complex-valued dislocated metric space and then prove\u0000its uniqueness.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125665897","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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