Pub Date : 2024-07-02DOI: 10.3126/nmsr.v41i1.67446
Shankar Pariyar, Jeevan Kafle
This work aims to investigate fractional differential equations using the Magnus Gösta Mittag-Leffler (GML) function and compare the finding with convention calculus approaches. It examines the solutions with one, two, and three parameters using the GML function for different values of α, β, and γ. We also test the convergence of the GML function of two parameters and check the validity and the computational time complexity. Moreover, we extend the GML function into three dimensions within the domain of complex variables utilizing numerical computing software. Graphs of the single-parameter GML E α (x), illustrates diverse disintegration rates across various α values, emphasizing dominant asymptotic trends over time periods.
{"title":"Generalizing the Mittag-Leffler Function for Fractional Differentiation and Numerical Computation","authors":"Shankar Pariyar, Jeevan Kafle","doi":"10.3126/nmsr.v41i1.67446","DOIUrl":"https://doi.org/10.3126/nmsr.v41i1.67446","url":null,"abstract":"This work aims to investigate fractional differential equations using the Magnus Gösta Mittag-Leffler (GML) function and compare the finding with convention calculus approaches. It examines the solutions with one, two, and three parameters using the GML function for different values of α, β, and γ. We also test the convergence of the GML function of two parameters and check the validity and the computational time complexity. Moreover, we extend the GML function into three dimensions within the domain of complex variables utilizing numerical computing software. Graphs of the single-parameter GML E α (x), illustrates diverse disintegration rates across various α values, emphasizing dominant asymptotic trends over time periods.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"49 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141687801","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 : 2024-07-02DOI: 10.3126/nmsr.v41i1.67457
Jagat Krishna Pokharel, N. Pahari, Ganesh Bahadur Basnet
This work aims to introduce and study new classes of generalized Cesàro summable vector-valued sequence spaces of bounded type. Besides exploring the completeness of the classes Ces(X, p) and Ces(X, p) ∞ when topologized with suitable natural p-normed, our primary interest is to study the β-dual of Ces(X, p).
{"title":"Generalized Cesàro Summable Vector Valued Sequence Space of Bounded Type","authors":"Jagat Krishna Pokharel, N. Pahari, Ganesh Bahadur Basnet","doi":"10.3126/nmsr.v41i1.67457","DOIUrl":"https://doi.org/10.3126/nmsr.v41i1.67457","url":null,"abstract":"This work aims to introduce and study new classes of generalized Cesàro summable vector-valued sequence spaces of bounded type. Besides exploring the completeness of the classes Ces(X, p) and Ces(X, p) ∞ when topologized with suitable natural p-normed, our primary interest is to study the β-dual of Ces(X, p).","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"14 1‐2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141686899","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 : 2024-07-02DOI: 10.3126/nmsr.v41i1.67453
A. Pokharel, Khagendra Adhikari, Ramesh Gautam
Measles is a highly contagious disease in human caused by virus. Despite the accessibility of successful vaccines, measles outbreaks still occur, presumably because of the lack of compliance with vaccination. We developed a mathematical model to evaluate the effects of vaccines in different age structures particularly focusing on two groups, to control and eradicate the disease, that may help the planner. Using our model, we formulate the basic reproduction number R 0 that determines, whether the disease persists or dies out. In addition, we carry out sensitivity analysis to identify important parameters that can play a significant role in the control and prevention of measles in different groups of individuals. Furthermore, we investigate the behavior of the disease and effect of vaccination on disease dynamics over a long period.
麻疹是一种由病毒引起的人类高度传染病。尽管已经有了成功的疫苗，但麻疹疫情仍时有发生，这可能是由于人们对疫苗接种缺乏依从性。我们开发了一个数学模型，用于评估疫苗在不同年龄结构中的效果，特别是针对控制和根除该疾病的两个群体，这可能会对规划者有所帮助。利用我们的模型，我们提出了基本繁殖数 R 0，它决定了疾病是持续还是消亡。此外，我们还进行了敏感性分析，以确定在不同人群中控制和预防麻疹中起重要作用的重要参数。此外，我们还研究了疾病的行为以及疫苗接种对疾病长期动态的影响。
{"title":"Modelling the Impact of Vaccination on the Control of Measles in Nepal","authors":"A. Pokharel, Khagendra Adhikari, Ramesh Gautam","doi":"10.3126/nmsr.v41i1.67453","DOIUrl":"https://doi.org/10.3126/nmsr.v41i1.67453","url":null,"abstract":"Measles is a highly contagious disease in human caused by virus. Despite the accessibility of successful vaccines, measles outbreaks still occur, presumably because of the lack of compliance with vaccination. We developed a mathematical model to evaluate the effects of vaccines in different age structures particularly focusing on two groups, to control and eradicate the disease, that may help the planner. Using our model, we formulate the basic reproduction number R 0 that determines, whether the disease persists or dies out. In addition, we carry out sensitivity analysis to identify important parameters that can play a significant role in the control and prevention of measles in different groups of individuals. Furthermore, we investigate the behavior of the disease and effect of vaccination on disease dynamics over a long period.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"41 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688144","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 : 2024-07-02DOI: 10.3126/nmsr.v41i1.67463
Pitambar Tiwari, C. R. Bhatta
Convexity in connection with integral inequalities is an interesting research domain in recent years. The convexity theory plays a fundamental role in the development of various branches of applied sciences since it includes the theory of convex functions that possesses two important attributes viz. a boundary point is where the maximum value is reached and any local minimum value is a global one. Convexities and inequalities are connected which has a basic character in many branches of pure and applied disciplines. The most important inequality related to convex function is the Hermite-Hadamard integral inequality. The extensions, enhancements and generalizations of this inequality has motivated the researchers in recent years. This paper is an extension of some inequalities connected with difference of the left-hand part as well as the right-hand part from the integral mean in Hermite- Hadamard’s inequality for the case of m- convex functions.
近年来，与积分不等式相关的凸性是一个有趣的研究领域。凸性理论在应用科学各分支的发展中起着基础性作用，因为它包括凸函数理论，而凸函数理论具有两个重要属性，即边界点是达到最大值的地方，任何局部最小值都是全局最小值。凸函数和不等式是相互关联的，在纯粹学科和应用学科的许多分支中都具有基本特征。与凸函数有关的最重要的不等式是 Hermite-Hadamard 积分不等式。近年来，对这一不等式的扩展、增强和概括激发了研究人员的热情。本文是对 Hermite- Hadamard 不等式中左手部分和右手部分与积分平均值之差的一些不等式的扩展，适用于 m 个凸函数的情况。
{"title":"Hermite-Hadamart Integral Inequality for Differentiable m- Convex Functions","authors":"Pitambar Tiwari, C. R. Bhatta","doi":"10.3126/nmsr.v41i1.67463","DOIUrl":"https://doi.org/10.3126/nmsr.v41i1.67463","url":null,"abstract":"Convexity in connection with integral inequalities is an interesting research domain in recent years. The convexity theory plays a fundamental role in the development of various branches of applied sciences since it includes the theory of convex functions that possesses two important attributes viz. a boundary point is where the maximum value is reached and any local minimum value is a global one. Convexities and inequalities are connected which has a basic character in many branches of pure and applied disciplines. The most important inequality related to convex function is the Hermite-Hadamard integral inequality. The extensions, enhancements and generalizations of this inequality has motivated the researchers in recent years. This paper is an extension of some inequalities connected with difference of the left-hand part as well as the right-hand part from the integral mean in Hermite- Hadamard’s inequality for the case of m- convex functions.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"311 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141686805","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 : 2024-07-02DOI: 10.3126/nmsr.v41i1.67458
S. K. Sahani, S.K. Tiwari, B. Sonat, Madhav Poudel
Five theorems on the identification of a convex sequence of signals via the absolute sum of elements of trigonometric series are established in this study. Several well-known results are specific cases of these theorems. When the function has bounded variation, it also addresses several special circumstances of fuzzy numbers.
{"title":"On The Determination of a Convex Sequence of Signals by Absolute Sum of Factors of Trigonometric Series","authors":"S. K. Sahani, S.K. Tiwari, B. Sonat, Madhav Poudel","doi":"10.3126/nmsr.v41i1.67458","DOIUrl":"https://doi.org/10.3126/nmsr.v41i1.67458","url":null,"abstract":"Five theorems on the identification of a convex sequence of signals via the absolute sum of elements of trigonometric series are established in this study. Several well-known results are specific cases of these theorems. When the function has bounded variation, it also addresses several special circumstances of fuzzy numbers. ","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"137 4‐5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141686927","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 : 2024-07-02DOI: 10.3126/nmsr.v41i1.67461
Ramesh Chandra Timsina
In this work, we compare finite difference schemes to finite volume scheme for axially symmetric 2D heat equation with Dirichlet and Neumann boundary conditions. Using cylindrical coordinate geometry, we describe a mathematical model of axially symmetric heat conduction for a stationary, homogeneous isotrophic solid with uniform thermal conductivity in a hollow cylinder with an exact solution in a particular case. We obtain the numerical solution of the PDE adapting finite difference and finite volume discretization techniques. Compared to the exact solution, we explore that the numerical schemes are the sufficient tools for the solution of linear or nonlinear PDE with prescribed boundary conditions. Furthermore, the numerical solution discrepancies in the results obtained from Explicit, Implicit and Crank-Nicolson schemes in Finite Difference Method (FDM) are extremely close to the exact solution in the case of Dirichlet boundary condition. The solution from the Explicit scheme is slightly far from the exactsolution and the solutions from Implicit and Crank-Nicolson schemes are extremely close to the exact solution in the case of Neumann boundary condition. Likewise, the numerical solutions obtained in the Finite volume method (FVM) are extremely close to the exact solution in the case of the Dirichlet boundary condition and slightly away from the exact solution in the case of the Neumann boundary condition.
{"title":"A comparison of Finite difference schemes to Finite volume scheme for axially symmetric 2D heat equation","authors":"Ramesh Chandra Timsina","doi":"10.3126/nmsr.v41i1.67461","DOIUrl":"https://doi.org/10.3126/nmsr.v41i1.67461","url":null,"abstract":"In this work, we compare finite difference schemes to finite volume scheme for axially symmetric 2D heat equation with Dirichlet and Neumann boundary conditions. Using cylindrical coordinate geometry, we describe a mathematical model of axially symmetric heat conduction for a stationary, homogeneous isotrophic solid with uniform thermal conductivity in a hollow cylinder with an exact solution in a particular case. We obtain the numerical solution of the PDE adapting finite difference and finite volume discretization techniques. Compared to the exact solution, we explore that the numerical schemes are the sufficient tools for the solution of linear or nonlinear PDE with prescribed boundary conditions. Furthermore, the numerical solution discrepancies in the results obtained from Explicit, Implicit and Crank-Nicolson schemes in Finite Difference Method (FDM) are extremely close to the exact solution in the case of Dirichlet boundary condition. The solution from the Explicit scheme is slightly far from the exactsolution and the solutions from Implicit and Crank-Nicolson schemes are extremely close to the exact solution in the case of Neumann boundary condition. Likewise, the numerical solutions obtained in the Finite volume method (FVM) are extremely close to the exact solution in the case of the Dirichlet boundary condition and slightly away from the exact solution in the case of the Neumann boundary condition.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"67 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141687340","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.v39i2.51694
J. Kafle, Ramuna Pandey, Bekha Ratna Dangol, C. N. Tiwari, Parameswari Kattel
The earth pressure coefficient (K) determines the nature of (tendency of) deformation of the granular mass during flow or deposition. When flow velocity is increasing, K takes its active state Kact and the flow is divergent. When the flow velocity is decreasing, K takes its passive state Kpas and the flow is convergent. The mathematical relations presented here and their 2-D and 3-D plots highlight that the passive and active earth coefficients strongly depend on the internal angle (δ) and basal angle (ϕ) of frictions. The mathematical relation for dry granular mass flow is extended to find these coefficients in soil mechanics. Results further show that active earth pressure drops as the internal angle of friction increases, but passive earth pressure rises. The earth's pressure is at rest if the wall is in its natural position
{"title":"Influence of Friction Angles on Earth Pressures in Dry Granular Flow Dynamics and Soil Mechanics","authors":"J. Kafle, Ramuna Pandey, Bekha Ratna Dangol, C. N. Tiwari, Parameswari Kattel","doi":"10.3126/nmsr.v39i2.51694","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51694","url":null,"abstract":"The earth pressure coefficient (K) determines the nature of (tendency of) deformation of the granular mass during flow or deposition. When flow velocity is increasing, K takes its active state Kact and the flow is divergent. When the flow velocity is decreasing, K takes its passive state Kpas and the flow is convergent. The mathematical relations presented here and their 2-D and 3-D plots highlight that the passive and active earth coefficients strongly depend on the internal angle (δ) and basal angle (ϕ) of frictions. The mathematical relation for dry granular mass flow is extended to find these coefficients in soil mechanics. Results further show that active earth pressure drops as the internal angle of friction increases, but passive earth pressure rises. The earth's pressure is at rest if the wall is in its natural position","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"26 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":"114221099","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.v39i2.51693
Santosh Ghimire
N. Kolmogorov introduced a law of the iterated logarithm, abbreviated LIL, in the case of independent random variables. Over the years, an analog of his result has been introduced in various contexts of analysis. Here, we introduce a similar LIL in the context of sums of Rademacher functions.
N. Kolmogorov在独立随机变量的情况下引入了迭代对数定律，缩写为LIL。多年来，在各种分析环境中引入了与他的结果类似的方法。这里，我们在Rademacher函数和的背景下引入一个类似的LIL。
{"title":"An Upper Bound in a Law of the Iterated Logarithm for Rademacher Function","authors":"Santosh Ghimire","doi":"10.3126/nmsr.v39i2.51693","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51693","url":null,"abstract":"N. Kolmogorov introduced a law of the iterated logarithm, abbreviated LIL, in the case of independent random variables. Over the years, an analog of his result has been introduced in various contexts of analysis. Here, we introduce a similar LIL in the context of sums of Rademacher functions.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"127 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":"126873801","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.v39i2.51692
Jhabi Lal Ghimire, N. Pahari
In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ||.||) valued difference sequences with the help of Orlicz function M . This is a generalization of the classical sequence space c0. Our primary interest is to explore some linear structures and investigate the conditions relating to the containment relation of the class c0 (M, (X, ||.||), ā, ᾱ) in terms of different ā and ᾱ.
{"title":"On Certain Linear Structure of Orlicz Space c0 (M, (X, ||.||), ā, ᾱ) of Vector Valued Difference Sequence","authors":"Jhabi Lal Ghimire, N. Pahari","doi":"10.3126/nmsr.v39i2.51692","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51692","url":null,"abstract":"In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ||.||) valued difference sequences with the help of Orlicz function M . This is a generalization of the classical sequence space c0. Our primary interest is to explore some linear structures and investigate the conditions relating to the containment relation of the class c0 (M, (X, ||.||), ā, ᾱ) in terms of different ā and ᾱ.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"25 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":"127208508","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.v39i2.51697
Bhuwan Prasad Ojha
In most cases, the space of all sequences converging to zero or the space of bounded sequences is always embedded in complete normed linear spaces. This concept, however, was modified by B.S. Tsirelson by constructing reflexive complete normed linear spaces with monotone unconditional Schauder basis without embedded copies of sequences converging to zero or the space of bounded sequence. In this article, a relation with any four non-negative integers has been proved, and this concept is used to prove the triangle inequality of a slightly different Tsirelson’s type of norm in the space of all real sequences with finite support. Furthermore, all properties of the norm have been studied for a different type of norm function in the space of real sequences with finite support.
{"title":"A Review of the Tsirleson's Space Norm","authors":"Bhuwan Prasad Ojha","doi":"10.3126/nmsr.v39i2.51697","DOIUrl":"https://doi.org/10.3126/nmsr.v39i2.51697","url":null,"abstract":"In most cases, the space of all sequences converging to zero or the space of bounded sequences is always embedded in complete normed linear spaces. This concept, however, was modified by B.S. Tsirelson by constructing reflexive complete normed linear spaces with monotone unconditional Schauder basis without embedded copies of sequences converging to zero or the space of bounded sequence. In this article, a relation with any four non-negative integers has been proved, and this concept is used to prove the triangle inequality of a slightly different Tsirelson’s type of norm in the space of all real sequences with finite support. Furthermore, all properties of the norm have been studied for a different type of norm function in the space of real sequences with finite support.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"1 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":"130447998","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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