Pub Date : 2021-12-31DOI: 10.3126/nmsr.v38i2.42700
D. Khanal, Urmila Pyakurel, S. Dempe
Contraflow is one of the best and widely accepted techniques in evacuation planning problems, where the reversal of arcs is made to increase the amount and decrease the time of ow transmission. At the time of evacuation, if the flow value leaving the source node exceeds the bottleneck capacity of the network, then the storage of excess flow at comparatively safer intermediate nodes can be a milestone to save the life of evacuees. In this paper, we introduce the maximum dynamic contraflow problem in a general network and earliest arrival contraflow problem in two-terminal series-parallel network with asymmetric transit times on anti-parallel arcs. We present polynomial time solution strategies with orientation dependent transit times by allowing the storage of flow at intermediate nodes.
{"title":"Dynamic Contraflow with Orientation Dependent Transit Times Allowing Intermediate Storage","authors":"D. Khanal, Urmila Pyakurel, S. Dempe","doi":"10.3126/nmsr.v38i2.42700","DOIUrl":"https://doi.org/10.3126/nmsr.v38i2.42700","url":null,"abstract":"Contraflow is one of the best and widely accepted techniques in evacuation planning problems, where the reversal of arcs is made to increase the amount and decrease the time of ow transmission. At the time of evacuation, if the flow value leaving the source node exceeds the bottleneck capacity of the network, then the storage of excess flow at comparatively safer intermediate nodes can be a milestone to save the life of evacuees. In this paper, we introduce the maximum dynamic contraflow problem in a general network and earliest arrival contraflow problem in two-terminal series-parallel network with asymmetric transit times on anti-parallel arcs. We present polynomial time solution strategies with orientation dependent transit times by allowing the storage of flow at intermediate nodes.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"48 58","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114058288","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 : 2021-06-30DOI: 10.3126/nmsr.v38i1.38894
S. Shrestha, Gokul Kc, D. B. Gurung
The human body is made by 100 trillion cells. The uncontrolled and abnormal growth of cells causes tumors. Due to the presence of tumor, the skin surface temperature of body provides abnormal behavior than normal. Most of the breast tumor develops in lobules and milk ducts of glandular layer. In this study, tumor is assumed in glandular layer. The study of this work is focused to find the temperature distribution in tumor embedded female breast tissue with different tumor location and different tumor size. For this, the finite element method is used to solve two-dimensional Pennes bio heat equation. The results show that the skin surface temperature of breast is higher with nearest tumor from areola. The temperature variation in breast tissue with tumors located at symmetrical position about the central line of the breast are identical.
{"title":"Mathematical Study of Two-Dimensional Temperature Variation in Tumor Embedded Breast Tissue","authors":"S. Shrestha, Gokul Kc, D. B. Gurung","doi":"10.3126/nmsr.v38i1.38894","DOIUrl":"https://doi.org/10.3126/nmsr.v38i1.38894","url":null,"abstract":"The human body is made by 100 trillion cells. The uncontrolled and abnormal growth of cells causes tumors. Due to the presence of tumor, the skin surface temperature of body provides abnormal behavior than normal. Most of the breast tumor develops in lobules and milk ducts of glandular layer. In this study, tumor is assumed in glandular layer. The study of this work is focused to find the temperature distribution in tumor embedded female breast tissue with different tumor location and different tumor size. For this, the finite element method is used to solve two-dimensional Pennes bio heat equation. The results show that the skin surface temperature of breast is higher with nearest tumor from areola. The temperature variation in breast tissue with tumors located at symmetrical position about the central line of the breast are identical.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"134 2-3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133529030","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 : 2021-06-30DOI: 10.3126/nmsr.v38i1.38872
Pushpalatha Mahalank, B. K. Majhi, I. N. Cangul
In many areas of science, lattice structures are very useful phenomenons. In network sciences, in chemistry and in social sciences, we face them in the solution of many daily life problems. Several large lattice structures can also be thought as graphs and in that way, are useful in the study of large networks. A very recently defined and studied class of such networks are snake graphs which has close relations with number theory due to the use of continued fractions. Following the works on square snake graphs, in this work, we study some non-Zagreb type topological graph indices of some interesting lattice structures called as double square snake graphs. We first obtain the vertex and edge partitions of these graphs and calculate their indices by means of these partitions.
{"title":"Some Topological Indices of Double Square Snake Graphs","authors":"Pushpalatha Mahalank, B. K. Majhi, I. N. Cangul","doi":"10.3126/nmsr.v38i1.38872","DOIUrl":"https://doi.org/10.3126/nmsr.v38i1.38872","url":null,"abstract":" In many areas of science, lattice structures are very useful phenomenons. In network sciences, in chemistry and in social sciences, we face them in the solution of many daily life problems. Several large lattice structures can also be thought as graphs and in that way, are useful in the study of large networks. A very recently defined and studied class of such networks are snake graphs which has close relations with number theory due to the use of continued fractions. Following the works on square snake graphs, in this work, we study some non-Zagreb type topological graph indices of some interesting lattice structures called as double square snake graphs. We first obtain the vertex and edge partitions of these graphs and calculate their indices by means of these partitions.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116680669","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 : 2021-06-30DOI: 10.3126/nmsr.v38i1.38901
S. Sonker, A. Munjal, L. Mishra
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{"title":"Indexed Absolute Cesaro Summability for Infinite Series","authors":"S. Sonker, A. Munjal, L. Mishra","doi":"10.3126/nmsr.v38i1.38901","DOIUrl":"https://doi.org/10.3126/nmsr.v38i1.38901","url":null,"abstract":"Available with fulltext.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125813679","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 : 2021-06-30DOI: 10.3126/nmsr.v38i1.38910
Tadaaki Igawa, T. Minamide, Miyu Nakano
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{"title":"The Pillai-Chowla Method for an Error Term in The Mean Square of δK(n)","authors":"Tadaaki Igawa, T. Minamide, Miyu Nakano","doi":"10.3126/nmsr.v38i1.38910","DOIUrl":"https://doi.org/10.3126/nmsr.v38i1.38910","url":null,"abstract":"Available with fulltext.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"243 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127691622","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 : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34092
D. Paudyal
This paper describes a method of obtaining approximate sum of infinite series of positive terms by using integrals under its historical background. It has shown the application of improper integrals to determine whether the given innate series is convergent or divergent. Here, the limits of the integrals and the series usually extend to infinity though they may be slowly convergent. We have also established a relation to approximate the sum of infinite series of positive terms with a suitable example.
{"title":"Approximating the Sum of Infinite Series of Non Negative Terms with reference to Integral Test","authors":"D. Paudyal","doi":"10.3126/NMSR.V37I1-2.34092","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34092","url":null,"abstract":"This paper describes a method of obtaining approximate sum of infinite series of positive terms by using integrals under its historical background. It has shown the application of improper integrals to determine whether the given innate series is convergent or divergent. Here, the limits of the integrals and the series usually extend to infinity though they may be slowly convergent. We have also established a relation to approximate the sum of infinite series of positive terms with a suitable example.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"221 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130642023","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 : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34065
P. Chand
In this paper, using the variant of Frontini-Sormani method, some higher order methods for finding the roots (simple and multiple) of nonlinear equations are proposed. In particular, we have constructed an optimal fourth order method and a family of sixth order method for finding a simple root. Further, an optimal fourth order method for finding a multiple root of a nonlinear equation is also proposed. We have used different weight functions to a cubically convergent For ntini-Sormani method for the construction of these methods. The proposed methods are tested on numerical examples and compare the results with some existing methods. Further, we have presented the basins of attraction of these methods to understand their dynamics visually.
{"title":"Optimal Methods for Finding Simple and Multiple Roots of Nonlinear Equations and their Basins of Attraction","authors":"P. Chand","doi":"10.3126/NMSR.V37I1-2.34065","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34065","url":null,"abstract":"In this paper, using the variant of Frontini-Sormani method, some higher order methods for finding the roots (simple and multiple) of nonlinear equations are proposed. In particular, we have constructed an optimal fourth order method and a family of sixth order method for finding a simple root. Further, an optimal fourth order method for finding a multiple root of a nonlinear equation is also proposed. We have used different weight functions to a cubically convergent For ntini-Sormani method for the construction of these methods. The proposed methods are tested on numerical examples and compare the results with some existing methods. Further, we have presented the basins of attraction of these methods to understand their dynamics visually.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126110817","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 : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34070
A. Munjal
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{"title":"Absolute Summability for N-Tupled Triangle Matrices on Sequence Space","authors":"A. Munjal","doi":"10.3126/NMSR.V37I1-2.34070","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34070","url":null,"abstract":"Available with fulltext. \u0000 ","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122696446","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 : 2020-12-31DOI: 10.3126/NMSR.V37I1-2.34098
Bishnu H Subedi, A. Singh
In this paper, we prove that the escaping set of a transcendental semi group is S-forward invari-ant. We also prove that if a holomorphic semi group is a belian, then the Fatou, Julia, and escaping sets are S-completely invariant. We also investigate certain cases and conditions that the holomorphic semi group dynamics exhibits the similar dynamical behavior just like a classical holomorphic dynamics. Frequently, we also examine certain amount of connections and contrasts between classical holomorphic dynamics and holomorphic semi group dynamics.
{"title":"A Comparison of Classical Holomorphic Dynamics and Holomorphic Semigroup Dynamics-II","authors":"Bishnu H Subedi, A. Singh","doi":"10.3126/NMSR.V37I1-2.34098","DOIUrl":"https://doi.org/10.3126/NMSR.V37I1-2.34098","url":null,"abstract":"In this paper, we prove that the escaping set of a transcendental semi group is S-forward invari-ant. We also prove that if a holomorphic semi group is a belian, then the Fatou, Julia, and escaping sets are S-completely invariant. We also investigate certain cases and conditions that the holomorphic semi group dynamics exhibits the similar dynamical behavior just like a classical holomorphic dynamics. Frequently, we also examine certain amount of connections and contrasts between classical holomorphic dynamics and holomorphic semi group dynamics.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123419015","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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