Pub Date : 2023-02-27DOI: 10.52280/pujm.2023.550201
Mubashir Qayyum, Imbsat Oscar
In this manuscript, modification of homotopy perturbation method (HPM) is proposed for integro-differential equations by coupling the least square method (LSM) with HPM. Improved accuracy in a very few iterations is the general advantage of this technique. The proposed method is applied to different higher order integro-differential equations of linear and nonlinear nature, and results are compared with exact as well as available solutions from the literature. Numerical and graphical analysis reveal that the proposed algorithm is reliable for integro-differential equations and hence can be utilized for more complex problems.
{"title":"Modification of Homotopy Perturbation Algorithm Through Least Square\u0000Optimizer for Higher Order Integro-Differential Equations","authors":"Mubashir Qayyum, Imbsat Oscar","doi":"10.52280/pujm.2023.550201","DOIUrl":"https://doi.org/10.52280/pujm.2023.550201","url":null,"abstract":"In this manuscript, modification of homotopy perturbation method (HPM) is proposed for integro-differential equations by coupling the least square method (LSM) with HPM. Improved accuracy in a very few iterations is the general advantage of this technique. The proposed method is applied to different higher order integro-differential equations\u0000of linear and nonlinear nature, and results are compared with exact as well as available solutions from the literature. Numerical and graphical analysis reveal that the proposed algorithm is reliable for integro-differential equations and hence can be utilized for more complex problems.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128515481","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 : 2023-01-31DOI: 10.52280/pujm.2023.550103
S. Parveen, Nadeem ul Hassan Awan, F. Farooq, Sajjad Hussain
In this article, we used M-polynomials to investigate the rela-tionships between topological indices and physicochemical properties of some blood cancer treatment drugs; we used the curvilinear regression method on drugs like azacitidine, buslfan, and mercaptopurine, among others. This article also includes M-polynomial proofs of the closed form of some topological indices of said drugs. The study could be a new at-tempt to improve QSPR model prediction analysis by utilizing the afore-mentioned molecular descriptors, which are used to investigate chemical, medical, and pharmacological properties. Finally, this work demonstrates that topological descriptors can be a cornerstone to designing and synthe-size new blood cancer treatments and other disease drugs.
{"title":"Topological Descriptors and QSPR Models of Drugs used in Blood Cancer","authors":"S. Parveen, Nadeem ul Hassan Awan, F. Farooq, Sajjad Hussain","doi":"10.52280/pujm.2023.550103","DOIUrl":"https://doi.org/10.52280/pujm.2023.550103","url":null,"abstract":"In this article, we used M-polynomials to investigate the rela-tionships between topological\u0000indices and physicochemical properties of some blood cancer treatment drugs; we used the curvilinear regression method on drugs like azacitidine, buslfan, and mercaptopurine, among others. This article also includes M-polynomial proofs of the closed form of some topological indices of said drugs. The study could be a new at-tempt to improve QSPR model prediction analysis by utilizing the afore-mentioned molecular descriptors, which are used to investigate chemical, medical, and pharmacological properties. Finally, this work demonstrates that topological descriptors can be a cornerstone to designing and synthe-size new blood cancer treatments and other disease drugs.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121498263","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 : 2023-01-30DOI: 10.52280/pujm.2023.550102
Muhammad Amir, M. Awais, Asifa Ashraf, R. Ali
In this paper, we use the natural decomposition method (NDM) for solving inviscid Burger equation (BE). The NDM is associated with the Adomain decomposition method (ADM) and the natural transform method. Applying the analytic method, we solved successfully both lin-ear and non-linear partial differential equations. By applying the NDM, we compute the best approximation solution of linear and non-linear par-tial differential equations. In our experiments, we report comparisons with the exact solution.
{"title":"Analytical Method for Solving Inviscid Burger Equation","authors":"Muhammad Amir, M. Awais, Asifa Ashraf, R. Ali","doi":"10.52280/pujm.2023.550102","DOIUrl":"https://doi.org/10.52280/pujm.2023.550102","url":null,"abstract":"In this paper, we use the natural decomposition method (NDM) for solving\u0000inviscid Burger equation (BE). The NDM is associated with the Adomain decomposition\u0000method (ADM) and the natural transform method. Applying the analytic method, we\u0000solved successfully both lin-ear and non-linear partial differential equations. By applying\u0000the NDM, we compute the best approximation solution of linear and non-linear par-tial\u0000differential equations. In our experiments, we report comparisons with the exact solution.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127079346","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 : 2023-01-28DOI: 10.52280/pujm.2023.550101
Hassan Zafar, M. Javaid
: Metric dimension is one of the distance based graph - theoretic parameters which is widely used in the various disciplines of sciences such as computer science, chemistry, and engineering. The local fractional metric dimension is latest derived form of metric dimension and it is used to find the solutions of integer programming problems. In this paper, we have computed local fractional metric dimension of different families of Toeplitz networks. It is also proved that the local fractional metric dimension of these Toeplitz networks remain bounded when the order of the networks approaches to infinity
{"title":"Metric Based Fractional Dimension of Toeplitz Networks","authors":"Hassan Zafar, M. Javaid","doi":"10.52280/pujm.2023.550101","DOIUrl":"https://doi.org/10.52280/pujm.2023.550101","url":null,"abstract":": Metric dimension is one of the distance based graph - theoretic parameters which is widely used in the various disciplines of sciences such as computer science, chemistry, and engineering. The local fractional metric dimension is latest derived form of metric dimension and it is used to find the solutions of integer programming problems. In this paper, we have computed local fractional metric dimension of different families of\u0000Toeplitz networks. It is also proved that the local fractional metric dimension of these Toeplitz networks remain bounded when the order of the\u0000networks approaches to infinity","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115493623","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 : 2022-12-28DOI: 10.52280//pujm.2022.541201
Ipek Akkilin, Salim Yuce
In this article, the translation hypersurfaces in Euclidean 4- space are defined as the sum of three curves with distinct parameters with unit speed, and non-planar. These curves are called the generator curves of the hypersurface. Utilizing the hypersurface theory in Euclidean 4-space, unit normal vector field, shape (Weingarten) operator matrix, fundamental forms, Gaussian curvature and mean curvature have been expressed for the translation hypersurfaces. Finally, the computational example is stated to efficiency of the theoretical results.
{"title":"Translation Hypersurfaces in Euclidean 4-Spaces","authors":"Ipek Akkilin, Salim Yuce","doi":"10.52280//pujm.2022.541201","DOIUrl":"https://doi.org/10.52280//pujm.2022.541201","url":null,"abstract":"In this article, the translation hypersurfaces in Euclidean 4- space are defined as the sum of three curves with distinct parameters with unit speed, and non-planar. These curves are called the generator curves of the hypersurface. Utilizing the hypersurface theory in Euclidean 4-space, unit normal vector field, shape (Weingarten) operator matrix, fundamental forms, Gaussian curvature and mean curvature have been expressed for the\u0000translation hypersurfaces. Finally, the computational example is stated to\u0000efficiency of the theoretical results.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116676148","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 : 2022-12-28DOI: 10.52280/pujm.2022.541202
Abdul Wahab, M. Z. Iqbal, Muhammad Zeshan Ali, Attia Hameed
The purpose of the work is to generate the ordinary differential equations and their solutions for the probability density function, quantile rate function, survival rate function, inverse survival rate function, haz-ard rate function and reversed hazard rate function of the Length Biased Exponential Distribution. The ordinary differential equations and their so-lutions are obtained using the Math of differentiation and integration as a tool together with their boundary conditions. The boundaries and para-meters that portrayed the distribution unavoidably decide the nature, presence, uniqueness, arrangement and the various possible solutions of these ordinary differential equations are better approaches to understand these characteristics. The work will be helpful to analyze the lifetime growth or risk and is of great significance in the field of ecological studies. The method can be very useful for the other probability distributions and can serve as a substitute for the approximation study.
{"title":"Classes of Ordinary Differential Equations of Length Biased Exponential Distribution and their Solutions","authors":"Abdul Wahab, M. Z. Iqbal, Muhammad Zeshan Ali, Attia Hameed","doi":"10.52280/pujm.2022.541202","DOIUrl":"https://doi.org/10.52280/pujm.2022.541202","url":null,"abstract":"The purpose of the work is to generate the ordinary differential equations and their\u0000solutions for the probability density function, quantile rate function, survival rate function, inverse survival rate function, haz-ard rate function and reversed hazard rate function of the Length Biased Exponential Distribution. The ordinary differential equations and their so-lutions are obtained using the Math of differentiation and integration as a tool together with their boundary conditions. The boundaries and para-meters that portrayed the distribution unavoidably decide the nature, presence, uniqueness, arrangement and the various possible solutions of these ordinary differential equations are better approaches to understand these characteristics. The work will be helpful to analyze the lifetime growth or risk and is of great significance in the field of ecological studies. The method can be very useful for the other probability distributions and can serve as a substitute for the\u0000approximation study.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129864534","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 : 2022-12-28DOI: 10.52280/pujm.2022.5412035
Iqra Zaman, FM Bhatti
In this paper, we study Young Fibonacci graphs Gn, a special family of graphs that are constructed with the help of integer partitions. Young diagrams are also used in the construction of graphs. The family of graphs is rich in structure. Thus, we investigate various properties of the family of graphs which include degree based structure and topological in-dices. Topological indices like Zagreb Index, Wiener Index, Randic Index and Connective Eccentricity Index of these graphs are computed. We also study the eigenvalues and energy of the graph.
{"title":"On the Structural Properties and Some Topological Indices of Young-Fibonacci Graphs","authors":"Iqra Zaman, FM Bhatti","doi":"10.52280/pujm.2022.5412035","DOIUrl":"https://doi.org/10.52280/pujm.2022.5412035","url":null,"abstract":"In this paper, we study Young Fibonacci graphs Gn, a special family of graphs\u0000that are constructed with the help of integer partitions. Young diagrams are also used in\u0000the construction of graphs. The family of graphs is rich in structure. Thus, we investigate\u0000various properties of the family of graphs which include degree based structure and\u0000topological in-dices. Topological indices like Zagreb Index, Wiener Index, Randic Index\u0000and Connective Eccentricity Index of these graphs are computed. We also study the\u0000eigenvalues and energy of the graph.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127595696","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 : 2022-11-30DOI: 10.52280/pujm.2022.541103
M. Z. Ullah
An optimal eighth-order multipoint numerical iterative method is constructed to find the simple root of scalar nonlinear equations. It is a three-point numerical iterative method that uses three evaluations of func-tion f(¢) associated with a scalar nonlinear equation and one of its deriv-atives f0 (¢). The four functional evaluations are required to achieve the eighth-order convergence. According to Kung-Traub conjecture (KTC), an iterative numerical multipoint method without memory can achieve maximum order of convergence 2n¡1 where n is the total number of func-tion evaluations in a single instance of the method. Therefore, following the KTC, the proposed method in this article is optimal.
{"title":"An optimal eighth-order multipoint numerical iterative method to find simple root of\u0000scalar nonlinear equations","authors":"M. Z. Ullah","doi":"10.52280/pujm.2022.541103","DOIUrl":"https://doi.org/10.52280/pujm.2022.541103","url":null,"abstract":"An optimal eighth-order multipoint numerical iterative method is constructed to find the\u0000simple root of scalar nonlinear equations. It is a three-point numerical iterative method that uses three evaluations of func-tion f(¢) associated with a scalar nonlinear equation and one of its deriv-atives f0 (¢). The four functional evaluations are required to achieve the eighth-order convergence. According to Kung-Traub conjecture (KTC), an iterative numerical multipoint method without memory can achieve maximum order of convergence 2n¡1 where n is the total number of func-tion evaluations in a single instance of the method. Therefore, following the KTC, the proposed method in this article is\u0000optimal.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130499365","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 : 2022-11-30DOI: 10.52280/pujm.2022.541101
Muhammad Amer Latif
In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constructed for harmonically convex mappings. We investigate some properties of these mappings and provide some refinement inequalities for the Hermite-Hadamard type inequalities that have already been established for harmonic convex functions.
{"title":"Mappings related to Hermite-Hadamard type inequalities for harmonically convex\u0000functions","authors":"Muhammad Amer Latif","doi":"10.52280/pujm.2022.541101","DOIUrl":"https://doi.org/10.52280/pujm.2022.541101","url":null,"abstract":"In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constructed for harmonically convex mappings. We investigate some properties of these mappings and provide some refinement inequalities for the Hermite-Hadamard type inequalities that have already been established for harmonic convex functions.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121938358","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 : 2022-11-30DOI: 10.52280/pujm.2022.541102
Gautam Patel, Kaushal Patel
We investigate a kernel space which is a particular class of Hilbert space. We discuss various properties of the reproducing kernel. In particular, our aim to construct kernel in reproducing space of the specific function space (Sobolev space) with the inner product and norm. Also, we derive the reproducing kernel for Neumann boundary conditions.
{"title":"Reproducing Kernel for Neumann Boundary Conditions","authors":"Gautam Patel, Kaushal Patel","doi":"10.52280/pujm.2022.541102","DOIUrl":"https://doi.org/10.52280/pujm.2022.541102","url":null,"abstract":"We investigate a kernel space which is a particular class of Hilbert space. We discuss various properties of the reproducing kernel. In particular, our aim to construct kernel in reproducing space of the specific function space (Sobolev space) with the inner product and norm. Also, we derive the reproducing kernel for Neumann boundary conditions.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116508430","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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