Pub Date : 2022-12-31DOI: 10.3126/nmsr.v39i2.51700
P. Reddy, K. N. Prakasha, I. N. Cangul
Randić index is one of the most famous topological graph indices. The energy of a graph was defined more than four decades ago for its molecular applications. The classical energy of a graph modeling a molecule is defined as the sum of absolute values of all the eigenvalues of the adjacency matrix corresponding to the modeling graph. There are several other versions of the energy notion obtained using other types of graph matrices. In this paper, we are introducing and investigating the Randić type Hadi energy RHE(G) of a graph G, determine several properties of it, and calculate RHE(G) for several interesting graphs.
{"title":"Randic Type Hadi Energy of a Graph","authors":"P. Reddy, K. N. Prakasha, I. N. Cangul","doi":"10.3126/nmsr.v39i2.51700","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51700","url":null,"abstract":"Randić index is one of the most famous topological graph indices. The energy of a graph was defined more than four decades ago for its molecular applications. The classical energy of a graph modeling a molecule is defined as the sum of absolute values of all the eigenvalues of the adjacency matrix corresponding to the modeling graph. There are several other versions of the energy notion obtained using other types of graph matrices. In this paper, we are introducing and investigating the Randić type Hadi energy RHE(G) of a graph G, determine several properties of it, and calculate RHE(G) for several interesting graphs.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116123576","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 : 2022-12-31DOI: 10.3126/nmsr.v39i2.51698
G. Paudel, N. Pahari, Sanjeev Kumar
The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of research in social science, management science, and mathematics. In this paper, we use the concept of Fuzzy real numbers to introduce and study the new double sequence spaces l∞ (M, λ, ρ), C F (M, λ, ρ) and CoF (M, λ, ρ) of fuzzy real numbers defined by the Orlicz function and study some of their properties like linear space structure, completeness, and solidness.
模糊逻辑和模糊集理论已经成功地应用于社会科学、管理科学和数学的各个研究领域。本文利用模糊实数的概念，引入并研究了由Orlicz函数定义的模糊实数的新的二重序列空间l∞(M， λ， ρ)、C F (M， λ， ρ)和CoF (M， λ， ρ)，并研究了它们的线性空间结构、完备性和可靠性等性质。
{"title":"Double Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function","authors":"G. Paudel, N. Pahari, Sanjeev Kumar","doi":"10.3126/nmsr.v39i2.51698","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51698","url":null,"abstract":"The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of research in social science, management science, and mathematics. In this paper, we use the concept of Fuzzy real numbers to introduce and study the new double sequence spaces l∞ (M, λ, ρ), C F (M, λ, ρ) and CoF (M, λ, ρ) of fuzzy real numbers defined by the Orlicz function and study some of their properties like linear space structure, completeness, and solidness.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"207 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124640199","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 : 2022-12-31DOI: 10.3126/nmsr.v39i2.51695
D. Khanal, Urmila Pyakurel, T. N. Dhamala, Stephen Dempe
Network associated with the set of elements and linearly ordered subset of elements, known as paths, satisfying the switching property is an abstract network. Due to the switching property, flows crossing at intersections are diverted to the non-crossing sides. Each element of an abstract network is equipped with two types of integral capacities: one is movement capacity which transships the flow from an element to its adjacent element and another is the storage capacity which holds the flow at the element. Due to insufficient movement capacity of intermediate elements, flow out from the source may not reach at the destination. If the flow out from the source is more than the minimum cut capacity, then the problem associated with the settlement of excess flow at appropriate intermediate elements is termed as network flow with intermediate storage. In this paper, we discuss the static and dynamic flow models with intermediate storage in an abstract network using temporal repetition of flow. We solve abstractmaximum dynamic flow and contraflow problems with intermediate storage.
{"title":"Abstract Temporally Repeated Flow with Intermediate Storage","authors":"D. Khanal, Urmila Pyakurel, T. N. Dhamala, Stephen Dempe","doi":"10.3126/nmsr.v39i2.51695","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51695","url":null,"abstract":"Network associated with the set of elements and linearly ordered subset of elements, known as paths, satisfying the switching property is an abstract network. Due to the switching property, flows crossing at intersections are diverted to the non-crossing sides. Each element of an abstract network is equipped with two types of integral capacities: one is movement capacity which transships the flow from an element to its adjacent element and another is the storage capacity which holds the flow at the element. Due to insufficient movement capacity of intermediate elements, flow out from the source may not reach at the destination. If the flow out from the source is more than the minimum cut capacity, then the problem associated with the settlement of excess flow at appropriate intermediate elements is termed as network flow with intermediate storage. In this paper, we discuss the static and dynamic flow models with intermediate storage in an abstract network using temporal repetition of flow. We solve abstractmaximum dynamic flow and contraflow problems with intermediate storage.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127211218","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 : 2022-07-27DOI: 10.3126/nmsr.v39i1.46915
R. Timsina, K. N. Uprety
Water movement in an unsaturated porous medium (soil) can be expressed by Richards equation with the mass conservation law and Darcy-Buckingham's law. This equation can be expressed in three different forms as pressure head-based, moisture content based and mixed from. In this study, we solve one dimensional Richards Equation in mixed form numerically using finite difference method with various time-stepping schemes: Forward Euler, Backward Euler, Crank-Nicolson and a Stabilized Runge-Kutta-Legendre Super Time-Stepping and we compare their performances using Dirichlet boundary condition on an isotropic homogeneous vertical soil column.
{"title":"Comparison of Finite Difference Schemes for Fluid Flow in Unsaturated Porous Medium (Soil)","authors":"R. Timsina, K. N. Uprety","doi":"10.3126/nmsr.v39i1.46915","DOIUrl":"https://doi.org/10.3126/nmsr.v39i1.46915","url":null,"abstract":"Water movement in an unsaturated porous medium (soil) can be expressed by Richards equation with the mass conservation law and Darcy-Buckingham's law. This equation can be expressed in three different forms as pressure head-based, moisture content based and mixed from. In this study, we solve one dimensional Richards Equation in mixed form numerically using finite difference method with various time-stepping schemes: Forward Euler, Backward Euler, Crank-Nicolson and a Stabilized Runge-Kutta-Legendre Super Time-Stepping and we compare their performances using Dirichlet boundary condition on an isotropic homogeneous vertical soil column.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131336528","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 : 2022-07-27DOI: 10.3126/nmsr.v39i1.46913
H. Nath
The Maximum static flow problem, in a single-source-single-sink network, deals with finding the maximum amount of flow from a source to a sink. Given a set of possible sinks, identification of the sink that maximizes the amount of the maximum flow is an important optimization problem. In this work, we consider the problem of identification of a sink when the possible sinks have given capacities. We devise a simple network transformation so that algorithms in the uncapacitated case can be used in the capacitated one proving that the problem can be solved with strongly polynomial time complexity. Further, we propose an algorithm whose average-case complexity is better than that of an iterative procedure that iterates over all the possible sinks.
{"title":"Maxstatic Sink Location Problem with Capacitated Sinks","authors":"H. Nath","doi":"10.3126/nmsr.v39i1.46913","DOIUrl":"https://doi.org/10.3126/nmsr.v39i1.46913","url":null,"abstract":"The Maximum static flow problem, in a single-source-single-sink network, deals with finding the maximum amount of flow from a source to a sink. Given a set of possible sinks, identification of the sink that maximizes the amount of the maximum flow is an important optimization problem. In this work, we consider the problem of identification of a sink when the possible sinks have given capacities. We devise a simple network transformation so that algorithms in the uncapacitated case can be used in the capacitated one proving that the problem can be solved with strongly polynomial time complexity. Further, we propose an algorithm whose average-case complexity is better than that of an iterative procedure that iterates over all the possible sinks.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123354454","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 : 2022-07-27DOI: 10.3126/nmsr.v39i1.46912
M. Adhikari, Urmila Pyakurel
In a capacitated network, an optimum solution of the maximum flow problem is to send as much flow as possible from the source node to the sink node as efficiently as possible by satisfying the capacity and conservation constraints. But, because of the limited capacity on the arcs, total amount of flow out going from the source may not reach to the sink. If the excess amount of flow can be stored at the intermediate nodes, total amount of flow outgoing from the source can be increased significantly. Similarly, different destinations have their own importance with respect to some circumstances. Motivated with these scenarios, we introduce the lexicographic maximum flow problems with intermediate storage in static and dynamic networks by assigning the priority order to the nodes. We extend this notion to arc reversals approach, a flow maximization technique, which is widely accepted in evacuation planning as it increases the outbound arc capacities by using the arc capacities on the opposite direction as well. Travel times along the anti-parallel arcs is considered to be unequal and we take into account the travel time of the reversed arcs to be equal to the travel time of the non-reversed arc towards which the arc is reversed. We present polynomial time algorithms for the solution of these problems.
{"title":"Lexicographic Maximum Flow Allowing Intermediate Storage","authors":"M. Adhikari, Urmila Pyakurel","doi":"10.3126/nmsr.v39i1.46912","DOIUrl":"https://doi.org/10.3126/nmsr.v39i1.46912","url":null,"abstract":"In a capacitated network, an optimum solution of the maximum flow problem is to send as much flow as possible from the source node to the sink node as efficiently as possible by satisfying the capacity and conservation constraints. But, because of the limited capacity on the arcs, total amount of flow out going from the source may not reach to the sink. If the excess amount of flow can be stored at the intermediate nodes, total amount of flow outgoing from the source can be increased significantly. Similarly, different destinations have their own importance with respect to some circumstances. Motivated with these scenarios, we introduce the lexicographic maximum flow problems with intermediate storage in static and dynamic networks by assigning the priority order to the nodes. We extend this notion to arc reversals approach, a flow maximization technique, which is widely accepted in evacuation planning as it increases the outbound arc capacities by using the arc capacities on the opposite direction as well. Travel times along the anti-parallel arcs is considered to be unequal and we take into account the travel time of the reversed arcs to be equal to the travel time of the non-reversed arc towards which the arc is reversed. We present polynomial time algorithms for the solution of these problems.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"142 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125840328","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 : 2021-12-31DOI: 10.3126/nmsr.v38i2.42708
R. Timsina, H. Khanal, A. Ludu, K. N. Uprety
Flow movement in unsaturated soil can be expressed by Richards equation. This equation can be obtained by applying the mass conversation law and the Darcy law. In this work, we solve one-dimensional Kirchhoff transformed Richards equation with loss of water due to the evaporation of unsaturated porous media (soils) and transpiration of plants numerically using Crank-Nicolson method. The result has compared with evapotranspiration function and without it in the governing equation. It has found that an additional work in time and flow movement is needs to reach the given boundary condition for the model without evapotranspiration.
{"title":"Numerical Solution of Water Flow in Unsaturated Soil with Evapotraspiration","authors":"R. Timsina, H. Khanal, A. Ludu, K. N. Uprety","doi":"10.3126/nmsr.v38i2.42708","DOIUrl":"https://doi.org/10.3126/nmsr.v38i2.42708","url":null,"abstract":"Flow movement in unsaturated soil can be expressed by Richards equation. This equation can be obtained by applying the mass conversation law and the Darcy law. In this work, we solve one-dimensional Kirchhoff transformed Richards equation with loss of water due to the evaporation of unsaturated porous media (soils) and transpiration of plants numerically using Crank-Nicolson method. The result has compared with evapotranspiration function and without it in the governing equation. It has found that an additional work in time and flow movement is needs to reach the given boundary condition for the model without evapotranspiration.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126159395","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 : 2021-12-31DOI: 10.3126/nmsr.v38i2.42704
S. Sonker, Rozy Jindal, L. Mishra
In this paper, a result on absolute Riesz summability for an infinite series by Bor has been extended using more variables. Further, we develop some well known results from our main result.
{"title":"Almost Inceasing Sequence for Absolute Riesz Summable Factor","authors":"S. Sonker, Rozy Jindal, L. Mishra","doi":"10.3126/nmsr.v38i2.42704","DOIUrl":"https://doi.org/10.3126/nmsr.v38i2.42704","url":null,"abstract":"In this paper, a result on absolute Riesz summability for an infinite series by Bor has been extended using more variables. Further, we develop some well known results from our main result.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126819261","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 : 2021-12-31DOI: 10.3126/nmsr.v38i2.42845
S. K. Sahani, L. Mishra
In this research work, we have introduced generalized Nörlund summability of derived Fourier series and its conjugate series and utilized it to several summability method. Further, a set of new and well known arbitrary result have been obtained by using main theorem. Considering suitable conditions a previous result has been obtained, which validates the current findings.
{"title":"Degree of Approximation of Signals by Norlund Summability of Derived Fourier series","authors":"S. K. Sahani, L. Mishra","doi":"10.3126/nmsr.v38i2.42845","DOIUrl":"https://doi.org/10.3126/nmsr.v38i2.42845","url":null,"abstract":"In this research work, we have introduced generalized Nörlund summability of derived Fourier series and its conjugate series and utilized it to several summability method. Further, a set of new and well known arbitrary result have been obtained by using main theorem. Considering suitable conditions a previous result has been obtained, which validates the current findings.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"T170 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125707291","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 : 2021-12-31DOI: 10.3126/nmsr.v38i2.42707
Bishnu H Subedi
In this paper, we compare existing results of the classical holomorphic dynamics with some of the existing results of holomorphic semigroup dynamics. We also prove some results of holomorphic semigroup dynamics, and we see whether there is a connection or contrast with classical one. Also, we see how far the results generalize, and what new phenomena appear.
{"title":"Comparision of Classical Holomorphic Dynamics and Holomorphic Semigroup Dynamics-I","authors":"Bishnu H Subedi","doi":"10.3126/nmsr.v38i2.42707","DOIUrl":"https://doi.org/10.3126/nmsr.v38i2.42707","url":null,"abstract":"In this paper, we compare existing results of the classical holomorphic dynamics with some of the existing results of holomorphic semigroup dynamics. We also prove some results of holomorphic semigroup dynamics, and we see whether there is a connection or contrast with classical one. Also, we see how far the results generalize, and what new phenomena appear.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124259903","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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