In this paper, we present an efficient approach to solving quadratic Diophantine equations and analyze their time complexity. We propose a deterministic polynomial-time algorithm that provides an upper bound on the elementary operations required to solve such equations. We also present a non-deterministic polynomial-time algorithm for the construction of quadratic non-resiude modulo d, which is a more efficient alternative to the deterministic approach.
在本文中，我们提出了一种求解二次二叉方程的高效方法，并分析了其时间复杂性。我们提出了一种确定性多项式时间算法，为解此类方程所需的基本操作提供了上限。我们还提出了一种非确定性多项式时间算法，用于构造模数为 d 的二次非resiude，它是确定性方法的一种更高效的替代方法。
{"title":"Efficient Approaches to Solving Quadratic Diophantine Equations and their Time Complexity","authors":"Bal Bahadur Tamang, Ajaya Singh","doi":"10.3126/jnms.v6i2.63005","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63005","url":null,"abstract":"In this paper, we present an efficient approach to solving quadratic Diophantine equations and analyze their time complexity. We propose a deterministic polynomial-time algorithm that provides an upper bound on the elementary operations required to solve such equations. We also present a non-deterministic polynomial-time algorithm for the construction of quadratic non-resiude modulo d, which is a more efficient alternative to the deterministic approach.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"185 S498","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140428600","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}
In this paper, a one-step fourth-order block scheme for solving fourth order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODE) is developed using interpolation and collocation techniques. The derived schemes contain two hybrid points which are chosen such that 0 < w1 < w2 < 1 where w1 and w2 are defined as hybrid points. The characteristics of the developed schemes are analyzed. The obtained schemes are applied in block form to solve some fourth-order IVPs and the numerical results show the accuracy and effectiveness of the block scheme compared with some existing methods.
{"title":"Numerical Solution of Fourth-order Initial Value Problems Using Novel Fourth-order Block Algorithm","authors":"B. Akinnukawe, J. Kuboye, S. A. Okunuga","doi":"10.3126/jnms.v6i2.63016","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63016","url":null,"abstract":"In this paper, a one-step fourth-order block scheme for solving fourth order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODE) is developed using interpolation and collocation techniques. The derived schemes contain two hybrid points which are chosen such that 0 < w1 < w2 < 1 where w1 and w2 are defined as hybrid points. The characteristics of the developed schemes are analyzed. The obtained schemes are applied in block form to solve some fourth-order IVPs and the numerical results show the accuracy and effectiveness of the block scheme compared with some existing methods.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"66 S20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140429667","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}
Fractional calculus from the nineteenth century to date has gained considerable attention due to its versatile applications in various scientific and engineering domains. This work examines the complex relationship between fractional-order derivative and basic functions, unraveling the profound interplay between mathematics and simulation. In this study, we illustrate the Mittag-Leffler function, Grunwald-Letnikov’s, Riemann-Liouville’s, and Caputo’s fractional derivative and integral are presented with examples of basic functions and their graphical presentations. The purpose of this study is to examine the features of fractional derivatives from the perspective of researchers’ motivations and interests.
{"title":"A Comprehensive Study of Fractional-Order Derivative and Their Interplay with Basic Functions","authors":"H. Pandey, G. R. Phaijoo, Dil Bahadur Gurung","doi":"10.3126/jnms.v6i2.63023","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63023","url":null,"abstract":"Fractional calculus from the nineteenth century to date has gained considerable attention due to its versatile applications in various scientific and engineering domains. This work examines the complex relationship between fractional-order derivative and basic functions, unraveling the profound interplay between mathematics and simulation. In this study, we illustrate the Mittag-Leffler function, Grunwald-Letnikov’s, Riemann-Liouville’s, and Caputo’s fractional derivative and integral are presented with examples of basic functions and their graphical presentations. The purpose of this study is to examine the features of fractional derivatives from the perspective of researchers’ motivations and interests.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"23 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140429865","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 difference sequence spaces of type I-convergent, I-null, bounded I-convergent, and bounded I-null in 2−normed space are introduced and studied using the Orlicz function. Investigations into the pertinent characteristics of these spaces led us to the establishment of some inclusion relations.
{"title":"On I-Convergence Difference Sequence Spaces Defined by Orlicz Function in 2−Normed Space","authors":"J. L. Ghimire, Gobinda Adhikari, N. Pahari","doi":"10.3126/jnms.v6i2.63029","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63029","url":null,"abstract":"The difference sequence spaces of type I-convergent, I-null, bounded I-convergent, and bounded I-null in 2−normed space are introduced and studied using the Orlicz function. Investigations into the pertinent characteristics of these spaces led us to the establishment of some inclusion relations.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"12 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140430386","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 aim of this paper is to introduce and study a new class ℓ2 ((X, ||.||), γ̅, ω̅ ) of double sequences with their terms in a normed space X as a generalization of the familiar sequence space ℓ. Besides the investigation of the condition pertaining to the containment relations of the class ℓ2 ((X, ||.||), γ̅, ω̅ ) of same kind in terms of γ̅ and ω̅, our primary interest is to explore some of the preliminary results that characterize the linear topological structures of ℓ2 ((X, ||.||), γ̅, ω̅ ) when topologized it with suitable natural paranorm.
{"title":"On Topological Structure of Total Paranormed Double Sequence Space (ℓ 2 ((X, ||.||), γ, ¯ w¯), G)","authors":"Jagat Krishna Pokharel, N. Pahari, G. Paudel","doi":"10.3126/jnms.v6i2.63026","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63026","url":null,"abstract":"The aim of this paper is to introduce and study a new class ℓ2 ((X, ||.||), γ̅, ω̅ ) of double sequences with their terms in a normed space X as a generalization of the familiar sequence space ℓ. Besides the investigation of the condition pertaining to the containment relations of the class ℓ2 ((X, ||.||), γ̅, ω̅ ) of same kind in terms of γ̅ and ω̅, our primary interest is to explore some of the preliminary results that characterize the linear topological structures of ℓ2 ((X, ||.||), γ̅, ω̅ ) when topologized it with suitable natural paranorm.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"151 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140428568","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}
In this article, we investigate the viscoelastic plate equation with both delay and source terms. Initially, we give the local-global existence results. Later, we establish the blow-up results at infinite time by utilizing the energy method when E (0) < 0 under suitable conditions. Delays effect generally seems in many practical problems for instance medicine, biological, chemical, physical, thermal, economic phenomena, electrical engineering systems and mechanical applications.
本文研究了具有延迟项和源项的粘弹性板方程。首先，我们给出了局部-全局存在结果。随后，当 E (0) < 0 时，我们在合适的条件下利用能量法建立了无限时间的炸毁结果。延迟效应通常出现在许多实际问题中，如医学、生物、化学、物理、热学、经济现象、电气工程系统和机械应用等。
{"title":"Blow up at Infinite Time of Solutions for a Plate Equation with Delay Term","authors":"E. Pişkin, Hazal Yüksekkaya","doi":"10.3126/jnms.v6i2.63018","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63018","url":null,"abstract":"In this article, we investigate the viscoelastic plate equation with both delay and source terms. Initially, we give the local-global existence results. Later, we establish the blow-up results at infinite time by utilizing the energy method when E (0) < 0 under suitable conditions. Delays effect generally seems in many practical problems for instance medicine, biological, chemical, physical, thermal, economic phenomena, electrical engineering systems and mechanical applications.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140431088","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}
Dengue fever is found in tropical and subtropical regions around the world. It is a vector-borne disease that is transmitted by female aedes mosquitoes infected with one of four dengue viruses (DENV1- DENV4). SEIR compartmental model is used to examine the transmission of the disease in the present work. The model has four compartments for the human population, susceptible, exposed, infected, and recovered and also four compartments for the mosquito population immature, susceptible, exposed, and infected. The impact of temperature on the dynamics of dengue disease transmission is described by this model. The basic reproduction number of the model is computed by implementing the Next Generation Matrix Method. Sensitivity analysis is performed to establish the relative importance of the model parameters and mathematical results are shown graphically.
{"title":"Mathematical Study of Effect of Temperature on Transmission Dynamics of Dengue Disease","authors":"J. Kafle, Prakash Bayalkoti, G. R. Phaijoo","doi":"10.3126/jnms.v6i1.57476","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57476","url":null,"abstract":"Dengue fever is found in tropical and subtropical regions around the world. It is a vector-borne disease that is transmitted by female aedes mosquitoes infected with one of four dengue viruses (DENV1- DENV4). SEIR compartmental model is used to examine the transmission of the disease in the present work. The model has four compartments for the human population, susceptible, exposed, infected, and recovered and also four compartments for the mosquito population immature, susceptible, exposed, and infected. The impact of temperature on the dynamics of dengue disease transmission is described by this model. The basic reproduction number of the model is computed by implementing the Next Generation Matrix Method. Sensitivity analysis is performed to establish the relative importance of the model parameters and mathematical results are shown graphically.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121473015","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}
In this article, we show that the escaping, Julia, and Fatou sets of an almost abelian transcendental semigroup of finite type coincide with escaping, Julia and Fatou sets of their respective cyclic subsemigroups
{"title":"Dynamics of Almost Abelian Transcendental Semigroups","authors":"Bishnu H Subedi","doi":"10.3126/jnms.v6i1.57415","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57415","url":null,"abstract":"In this article, we show that the escaping, Julia, and Fatou sets of an almost abelian transcendental semigroup of finite type coincide with escaping, Julia and Fatou sets of their respective cyclic subsemigroups","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129288952","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}
Mathematics and architecture have strong logical interconnections. Ratios are good examples of their interconnectivity. Without mathematics, it is hard to believe the existence of science and arts. It is not an exaggeration to say that mathematics is everywhere. Nature is beautiful due to the proper ratios of various components in them and in relation to others. The Fibonacci sequence is one of nature’s numbering systems. It is abundant in nature. It has a close relationship with the golden ratio. Golden ratios and such Fibonacci numbers are found to be used in designing logos, magazine covers, plastic surgery, to name a few. These two are two fascinating topics for mathematicians, artists, natural scientists, and philosophers. This work presents a panoramic view of the Fibonacci numbers, and the Fibonacci sequences; their mathematical presentations, patterns, properties, and beauty.
{"title":"An Insight in the Beauty of the Fibonacci","authors":"I. Adhikari, Parameshwari Kattel","doi":"10.3126/jnms.v6i1.57655","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57655","url":null,"abstract":"Mathematics and architecture have strong logical interconnections. Ratios are good examples of their interconnectivity. Without mathematics, it is hard to believe the existence of science and arts. It is not an exaggeration to say that mathematics is everywhere. Nature is beautiful due to the proper ratios of various components in them and in relation to others. The Fibonacci sequence is one of nature’s numbering systems. It is abundant in nature. It has a close relationship with the golden ratio. Golden ratios and such Fibonacci numbers are found to be used in designing logos, magazine covers, plastic surgery, to name a few. These two are two fascinating topics for mathematicians, artists, natural scientists, and philosophers. This work presents a panoramic view of the Fibonacci numbers, and the Fibonacci sequences; their mathematical presentations, patterns, properties, and beauty.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129479868","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}
Research in mathematical sciences either builds up the insight or breaks the boundary of the literature of the pertaining mathematical research area. A mathematical research technique is an attentive, persistent and systematic approach based on the logical rules of inference and mathematical rules of inference to find something new. Mathematical modeling, construction of theorems with the proofs, design of algorithms, data with simulation could be considered as the fundamental tools in mathematical research. In this paper, we discuss some fundamental research tools which are useful to do research in mathematical sciences.
{"title":"Some Fundamental Research Tools in Mathematical Sciences","authors":"S. Khadka, Santosh Ghimire, Durga Jang K.c.","doi":"10.3126/jnms.v6i1.57434","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57434","url":null,"abstract":"Research in mathematical sciences either builds up the insight or breaks the boundary of the literature of the pertaining mathematical research area. A mathematical research technique is an attentive, persistent and systematic approach based on the logical rules of inference and mathematical rules of inference to find something new. Mathematical modeling, construction of theorems with the proofs, design of algorithms, data with simulation could be considered as the fundamental tools in mathematical research. In this paper, we discuss some fundamental research tools which are useful to do research in mathematical sciences.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114808197","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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