In 1934, Hopf established an elegant inequality bounding the exponential integral function. In 1959, Gautschi established an improvement of Hopf’s results. In 1969, Luke also established two inequalities with each improving Hopf’s results. In 1997, Alzer also established another improvement of Hopf’s results. In this paper, we provide two new proofs of Luke’s first inequality and as an application of this inequality, we provide a new proof and a generalization of Gautschi’s results. Furthermore, we establish some inequalities which are analogous to Luke’s second inequality and Alzer’s inequality. The techniques adopted in proving our results are simple and straightforward.
{"title":"On Some Bounds for the Exponential Integral Function","authors":"K. Nantomah","doi":"10.3126/jnms.v4i2.41463","DOIUrl":"https://doi.org/10.3126/jnms.v4i2.41463","url":null,"abstract":"In 1934, Hopf established an elegant inequality bounding the exponential integral function. In 1959, Gautschi established an improvement of Hopf’s results. In 1969, Luke also established two inequalities with each improving Hopf’s results. In 1997, Alzer also established another improvement of Hopf’s results. In this paper, we provide two new proofs of Luke’s first inequality and as an application of this inequality, we provide a new proof and a generalization of Gautschi’s results. Furthermore, we establish some inequalities which are analogous to Luke’s second inequality and Alzer’s inequality. The techniques adopted in proving our results are simple and straightforward.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126435124","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}
There are different types of contraction in the existing literature for the generalization of Banach’s contraction principle. Our aim in this paper is to generalize cyclic contraction so that it can explain all types of cyclic contraction as a particular case. Besides all contractions in the existing literature we introduce some new types of cyclic contraction before defining the generalized cyclic contraction.
{"title":"Fixed Point Theorems on Some New Types of Cyclic Contractions and Their Generalization","authors":"D. R. Joshi, P. Tripathi, C. R. Bhatta","doi":"10.3126/jnms.v4i2.41461","DOIUrl":"https://doi.org/10.3126/jnms.v4i2.41461","url":null,"abstract":"There are different types of contraction in the existing literature for the generalization of Banach’s contraction principle. Our aim in this paper is to generalize cyclic contraction so that it can explain all types of cyclic contraction as a particular case. Besides all contractions in the existing literature we introduce some new types of cyclic contraction before defining the generalized cyclic contraction.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"599 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121980750","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}
Lohans de Oliveira Miranda, Lossian Barbosa Bacelar Miranda
We disclose a simple and straightforward method of solving single-order linear partial differential equations. The advantage of the method is that it is applicable to any orders and the big disadvantage is that it is restricted to a single order at a time. As it is very easy compared to classical methods, it has didactic value.
{"title":"One Solution for Many Linear Partial Differential Equations With Terms of Equal Orders","authors":"Lohans de Oliveira Miranda, Lossian Barbosa Bacelar Miranda","doi":"10.3126/jnms.v4i2.41462","DOIUrl":"https://doi.org/10.3126/jnms.v4i2.41462","url":null,"abstract":"We disclose a simple and straightforward method of solving single-order linear partial differential equations. The advantage of the method is that it is applicable to any orders and the big disadvantage is that it is restricted to a single order at a time. As it is very easy compared to classical methods, it has didactic value.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125829591","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}
Network interdiction problem arises when an unwanted agent attacks the network system to deteriorate its transshipment efficiency. Literature is flourished with models and solution approaches for the problem. This paper considers a single commodity lexicographic maximum flow problem on a directed network with capacitated vertices to study two network flow problems under an arc interdiction. In the first, the objective is to find an arc on input network to be destroyed so that the residual lexicographically maximum flow is lexicographically minimum. The second problem aims to find a flow pattern resulting lexicographically maximum flow on the input network so that the total residual flow, if an arc is destroyed, is maximum. The paper proposes strongly polynomial time solution procedures for these problems.
{"title":"Lexicographically Maximum Flows under an Arc Interdiction","authors":"Phanindra Prasad Bhandari, S. Khadka","doi":"10.3126/jnms.v4i2.41459","DOIUrl":"https://doi.org/10.3126/jnms.v4i2.41459","url":null,"abstract":"Network interdiction problem arises when an unwanted agent attacks the network system to deteriorate its transshipment efficiency. Literature is flourished with models and solution approaches for the problem. This paper considers a single commodity lexicographic maximum flow problem on a directed network with capacitated vertices to study two network flow problems under an arc interdiction. In the first, the objective is to find an arc on input network to be destroyed so that the residual lexicographically maximum flow is lexicographically minimum. The second problem aims to find a flow pattern resulting lexicographically maximum flow on the input network so that the total residual flow, if an arc is destroyed, is maximum. The paper proposes strongly polynomial time solution procedures for these problems.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129060098","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 study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ank ; δ) & (Ank ; γ; δ): Generalized summability method │A; δ │k & │A; γ; δ│k have been applied for determining the sufficient conditions, where k ≥ 1; δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.
{"title":"Absolute │A; δ │k and │A; γ; δ│k Summability for n-tupled Triangle Matrices","authors":"S. Sonker, A. Munjal, L. Mishra","doi":"10.3126/jnms.v3i2.33957","DOIUrl":"https://doi.org/10.3126/jnms.v3i2.33957","url":null,"abstract":"In this study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ank ; δ) & (Ank ; γ; δ): Generalized summability method │A; δ │k & │A; γ; δ│k have been applied for determining the sufficient conditions, where k ≥ 1; δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129406984","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}
We prove that there exist three different transcendental entire functions that can have infinite number of domains which lie in the different periodic component of each of these functions and their compositions.
{"title":"Periodic Components of the Fatou Set of Three Transcendental Entire Functions and Their Compositions","authors":"Bishnu H Subedi, A. Singh","doi":"10.3126/jnms.v3i1.33002","DOIUrl":"https://doi.org/10.3126/jnms.v3i1.33002","url":null,"abstract":"We prove that there exist three different transcendental entire functions that can have infinite number of domains which lie in the different periodic component of each of these functions and their compositions.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125121061","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}
B. O. Fagbemigun, Adesanmi Alao Mogbademu, J. Olaleru
The concept of Φh-convexity is extended for functions defined on closed Φh-convex subsets of linear spaces. Consequently, some double integral inequalities of Hermite-Hadamard type defined on time-scaled linear spaces are established for Φh-convex functions.
{"title":"Double Integral Inequalities of Hermite-Hadamard-Type for ɸh-Convex Functions on Linear Spaces","authors":"B. O. Fagbemigun, Adesanmi Alao Mogbademu, J. Olaleru","doi":"10.3126/jnms.v2i2.33006","DOIUrl":"https://doi.org/10.3126/jnms.v2i2.33006","url":null,"abstract":"The concept of Φh-convexity is extended for functions defined on closed Φh-convex subsets of linear spaces. Consequently, some double integral inequalities of Hermite-Hadamard type defined on time-scaled linear spaces are established for Φh-convex functions.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"51 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122845623","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, we present simple and exact eigenvalues for both the solid- and fluid-phases of the real two-phase general model developed by Pudasaini (2012); we call these phase-eigenvalues, the solid- phase-eigenvalues and the fluid-phase-eigenvalues. Results are compared by applying the derived phase- eigenvalues that incorporate the phase-interactions in the two-phase debris movements against the simple and classical solid and fluid eigenvalues without any phase interaction. We have constructed several different set of eigenvalues including the coupled phase eigenvalues by using rational factorization method. At first, we consider for general debris height; factorizing the solid and fluid lateral pressure contributions by considering the negligible pressure gradient; negligible solid lateral pressure; negligible fluid lateral pressure; negligible solid and fluid lateral pressure. Secondly, for a thin debris ow height, we also construct the fourth set of eigenvalues in three different cases. These phase-eigenvalues incorporate strong interaction between the solid and fluid dynamics. The simulation results are produced by taking all these different sets of coupled phase-eigenvalues and are compared with the classical uncoupled set of solid and fluid eigenvalues. The results indicate the importance of phase-eigenvalues and supports for a complete description of the phase- eigenvalues for the enhanced description of real two-phase debris flows and landslide motions.
{"title":"Determination of Phase-Eigenvalues by Rational Factorization and Enhanced Simulation of Two-Phase Mass Flow","authors":"Puskar R. Pokhrel, B. M. Tuladhar","doi":"10.3126/jnms.v2i2.33011","DOIUrl":"https://doi.org/10.3126/jnms.v2i2.33011","url":null,"abstract":"In this paper, we present simple and exact eigenvalues for both the solid- and fluid-phases of the real two-phase general model developed by Pudasaini (2012); we call these phase-eigenvalues, the solid- phase-eigenvalues and the fluid-phase-eigenvalues. Results are compared by applying the derived phase- eigenvalues that incorporate the phase-interactions in the two-phase debris movements against the simple and classical solid and fluid eigenvalues without any phase interaction. We have constructed several different set of eigenvalues including the coupled phase eigenvalues by using rational factorization method. At first, we consider for general debris height; factorizing the solid and fluid lateral pressure contributions by considering the negligible pressure gradient; negligible solid lateral pressure; negligible fluid lateral pressure; negligible solid and fluid lateral pressure. Secondly, for a thin debris ow height, we also construct the fourth set of eigenvalues in three different cases. These phase-eigenvalues incorporate strong interaction between the solid and fluid dynamics. The simulation results are produced by taking all these different sets of coupled phase-eigenvalues and are compared with the classical uncoupled set of solid and fluid eigenvalues. The results indicate the importance of phase-eigenvalues and supports for a complete description of the phase- eigenvalues for the enhanced description of real two-phase debris flows and landslide motions.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"199 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126843137","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}
Sustainable forest management is one of the challenging issues in the present century. In this manuscript, we have employed the model of control theory to control the consequence of toxicity and illegal logging of mature trees in the ecosystem of Sundarban, the largest mangrove forest in the world. In this investigation, we have momentarily mentioned some of the fields in which these challenges are present. These fields especially consist of sustainable forest management of ecosystem. We have reflected on the modified Leslie-Gower response function to set up as the alternative resource for industries when forestry resources are devastated. The boundedness, persistence, equilibria and stability are examined along with bionomic equilibria and optimal harvesting strategy. Our main aim is to investigate the spans and applications of control theory in real life situation, especially in efficient and sustainable forest growth.
{"title":"An Ecological Model for Sustainable Forest Management of Eco-system Based on Optimal Control Theory","authors":"M. Hasan, M. H. A. Biswas, M. Uddin","doi":"10.3126/jnms.v2i1.33014","DOIUrl":"https://doi.org/10.3126/jnms.v2i1.33014","url":null,"abstract":"Sustainable forest management is one of the challenging issues in the present century. In this manuscript, we have employed the model of control theory to control the consequence of toxicity and illegal logging of mature trees in the ecosystem of Sundarban, the largest mangrove forest in the world. In this investigation, we have momentarily mentioned some of the fields in which these challenges are present. These fields especially consist of sustainable forest management of ecosystem. We have reflected on the modified Leslie-Gower response function to set up as the alternative resource for industries when forestry resources are devastated. The boundedness, persistence, equilibria and stability are examined along with bionomic equilibria and optimal harvesting strategy. Our main aim is to investigate the spans and applications of control theory in real life situation, especially in efficient and sustainable forest growth.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114275559","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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