Pub Date : 2023-11-24DOI: 10.9734/arjom/2023/v19i11762
Rohit Kumar Verma, Som Kumari
Discrete memory-free channels with a very low capacity are known as noisy channels. Our recent study has yielded some new insights into the channel capacity of noisy channels, which could prove useful in the development of mathematical models for these channels and other contexts.
{"title":"Non-Shannon Perspective on Channel Capacity for Binary Source Codes Using Weighted Conditional Entropy","authors":"Rohit Kumar Verma, Som Kumari","doi":"10.9734/arjom/2023/v19i11762","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11762","url":null,"abstract":"Discrete memory-free channels with a very low capacity are known as noisy channels. Our recent study has yielded some new insights into the channel capacity of noisy channels, which could prove useful in the development of mathematical models for these channels and other contexts.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"2018 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139239437","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 : 2023-11-22DOI: 10.9734/arjom/2023/v19i11761
Gujun Wang, Min Xiao, Feng Zhu
Aims: In order to study the rule of entropy in different graph transformations, this paper introduces and further generalizes the ladder graph from different perspectives, including pinwheel ladders and 3-dimensional ladders. Then the problem of entropy comes down to the calculation of spanning trees in these graphs. Place and Duration of Study: School of Mathematical Sciences, Jiangsu University, between January 2023 and October 2023. Methodology: A method by seeking similar terms was generalized to help study the essential principle in these graphs. By similarity diagonalization and computer aided calculation, the exact expressions for the number of spanning trees in these graphs are obtained.
{"title":"Counting Spanning Trees in The Ladders","authors":"Gujun Wang, Min Xiao, Feng Zhu","doi":"10.9734/arjom/2023/v19i11761","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11761","url":null,"abstract":"Aims: In order to study the rule of entropy in different graph transformations, this paper introduces and further generalizes the ladder graph from different perspectives, including pinwheel ladders and 3-dimensional ladders. Then the problem of entropy comes down to the calculation of spanning trees in these graphs. Place and Duration of Study: School of Mathematical Sciences, Jiangsu University, between January 2023 and October 2023. Methodology: A method by seeking similar terms was generalized to help study the essential principle in these graphs. By similarity diagonalization and computer aided calculation, the exact expressions for the number of spanning trees in these graphs are obtained.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139248642","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 : 2023-11-17DOI: 10.9734/arjom/2023/v19i11760
Wanjala Patrick Makila, O. M. Onyango, S. A. Nyongesa
Let an operator T belong to an operator ideal J, then for any operators A and B which can be composed with T asBTA then BTA (in) J. Indeed, J contains the class of finite rank Banach Space operators. Now given L(X; Y ). Then J(X; Y ) (subseteq) L(X; Y ) such that J(X; Y ) = {T : X (gets) Y : T (subseteq) }. Thus an operator ideal is a subclass J of L containing every identity operator acting on a one-dimensional Banach space such that: S + T (in) J(X; Y ) where S; T (in) J(X; Y ). If W;Z;X; Y (in) K;A (in) L(W;X);B (in) L(Y;Z) then BTA (in) J(W;Z) whenever T (in) J(X; These properties compare very well with the algebraic notion of ideals in Banach Algebras within whose classes lie compact operators, weakly compact operators, finitely strictly regular operators, completely continuous operators, strictly singular operators among others. Thus, the aim of this paper is to characterize the various classes of ideals in Banach spaces. Special attention is given to the characteristics involving the ideal properties, the metric approximation properties, the hereditary properties in relation to the ideal extensions in the Hahn-Banach space, projection and embedments in the biduals of the Banach Space.
让一个算子 T 属于一个算子理想 J，那么对于任何可以与 T 组成 BTA 的算子 A 和 B，则 BTA （in）J。现在给定 L(X; Y ).那么 J(X; Y )(subseteq) L(X; Y ) 这样 J(X; Y ) = {T : X (gets) Y : T (subseteq) }。因此，一个算子理想是 L 的子类 J，它包含作用于一维巴拿赫空间的每一个同一算子，使得：S + T (in) J(X; Y ) 其中 S; T (in) J(X; Y ).如果 W；Z；X；Y (in) K；A (in) L(W；X)；B (in) L(Y；Z)，那么只要 T(in) J(X)，BTA (in) J(W；Z)；这些性质与巴拿赫代数中理想的代数概念非常相似，在巴拿赫代数的理想类中有紧凑算子、弱紧凑算子、有限严格正则算子、完全连续算子、严格奇异算子等等。因此，本文的目的是描述巴拿赫空间中各类理想的特征。本文特别关注涉及理想特性、度量逼近特性、与哈恩-巴拿赫空间中理想扩展相关的遗传特性、巴拿赫空间双元中的投影和嵌入等特性。
{"title":"Classification of Ideals in Banach Spaces","authors":"Wanjala Patrick Makila, O. M. Onyango, S. A. Nyongesa","doi":"10.9734/arjom/2023/v19i11760","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11760","url":null,"abstract":"Let an operator T belong to an operator ideal J, then for any operators A and B which can be composed with T asBTA then BTA (in) J. Indeed, J contains the class of finite rank Banach Space operators. Now given L(X; Y ). Then J(X; Y ) (subseteq) L(X; Y ) such that J(X; Y ) = {T : X (gets) Y : T (subseteq) }. Thus an operator ideal is a subclass J of L containing every identity operator acting on a one-dimensional Banach space such that: S + T (in) J(X; Y ) where S; T (in) J(X; Y ). If W;Z;X; Y (in) K;A (in) L(W;X);B (in) L(Y;Z) then BTA (in) J(W;Z) whenever T (in) J(X; These properties compare very well with the algebraic notion of ideals in Banach Algebras within whose classes lie compact operators, weakly compact operators, finitely strictly regular operators, completely continuous operators, strictly singular operators among others. Thus, the aim of this paper is to characterize the various classes of ideals in Banach spaces. Special attention is given to the characteristics involving the ideal properties, the metric approximation properties, the hereditary properties in relation to the ideal extensions in the Hahn-Banach space, projection and embedments in the biduals of the Banach Space.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"37 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139266127","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 : 2023-11-07DOI: 10.9734/arjom/2023/v19i11758
Qiang Wang, Qingwei Tu
In this paper, we mainly find all solutions of the diophantine equation (left (1-frac{1}{mathit{x}}right)) (left (1-frac{1}{mathit{y}}right)) (left (1-frac{1}{mathit{z}}right)) = (frac{1}{mathit{l}}) in integer variables ((mathit{x}), (mathit{y}), (mathit{z}), (mathit{l}) ).
{"title":"Integer Solutions of the Diophantine Equation (left (1-frac{1}{mathit{x}}right)) (left (1-frac{1}{mathit{y}}right)) (left (1-frac{1}{mathit{z}}right)) = (frac{1}{mathit{l}})","authors":"Qiang Wang, Qingwei Tu","doi":"10.9734/arjom/2023/v19i11758","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11758","url":null,"abstract":"In this paper, we mainly find all solutions of the diophantine equation (left (1-frac{1}{mathit{x}}right)) (left (1-frac{1}{mathit{y}}right)) (left (1-frac{1}{mathit{z}}right)) = (frac{1}{mathit{l}}) in integer variables ((mathit{x}), (mathit{y}), (mathit{z}), (mathit{l}) ).","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476113","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 : 2023-10-31DOI: 10.9734/arjom/2023/v19i11756
Ravi Parkash Bhokal, Manoj Kumar, Ashish Kumar
The purpose of this research article is to introduce a new iteration scheme and to prove J-iterationconvergence and stability results for it. We also claim the newly introduced iterative scheme has better efficiency than some of the existing iterations in the literature. Our claim is supported by numerical example.
{"title":"Fixed Point Results for Generalized Non-linear Operators with Convergence Analysis","authors":"Ravi Parkash Bhokal, Manoj Kumar, Ashish Kumar","doi":"10.9734/arjom/2023/v19i11756","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11756","url":null,"abstract":"The purpose of this research article is to introduce a new iteration scheme and to prove J-iterationconvergence and stability results for it. We also claim the newly introduced iterative scheme has better efficiency than some of the existing iterations in the literature. Our claim is supported by numerical example.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"59 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813437","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 : 2023-10-31DOI: 10.9734/arjom/2023/v19i11757
Vaishali Deshmukh, B. P. S. Jadon, Ruchi Singh, S. K. Malhotra
The purpose of the paper is to obtain common fixed point results on interval-valued fuzzy metric space for occasionally weakly compatible maps (OWC) using contractive conditions. With the concept of (tau)norm, interval numbers, and some important properties of interval-valued (tau)norm.
{"title":"Fixed Point Results on Interval-Valued Fuzzy Metric Space using notation of Pairwise Compatible Maps and Occasionally Weakly Compatible Maps with Application","authors":"Vaishali Deshmukh, B. P. S. Jadon, Ruchi Singh, S. K. Malhotra","doi":"10.9734/arjom/2023/v19i11757","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11757","url":null,"abstract":"The purpose of the paper is to obtain common fixed point results on interval-valued fuzzy metric space for occasionally weakly compatible maps (OWC) using contractive conditions. With the concept of (tau)norm, interval numbers, and some important properties of interval-valued (tau)norm.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"59 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135976691","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 : 2023-10-30DOI: 10.9734/arjom/2023/v19i11755
Gao Zhinan, Lu Xingyan, Wei Yuxuan, Zhu Feng
As we all know, the number of spanning trees can be calculated by virtue of the famous Kirchhoff’s matrix-tree theorem. However, it doesn’t work when coming across complex graphs with thousands of edges and vertices or more. Hence, how to obtain accurate solutions of the number of spanning trees of general fan graphs becomes a subject to several studies of many places like computer science, physics and mathematics. In this paper, we focus on calculating different types of graphs generated by adding vertices and edges to the fan graph. Particularly, we define a new graph called "C-graph", which brings a unique angle of view for us to recognize the construction of original graphs. Moreover, we introduce a new iterative relation about the general fan graph, simplifying the calculation. Therefore, we can obtain functions of the number of spanning trees obtained from given fan graphs, which are also suitable for larger and more complex conditions. Finally, we discuss the effect of vertices and edges on the number of spanning trees, finding out that edges have greater impact. Additionally, by using Kirchhoff’s matrix-tree theorem, we verified the rationality of our results.
{"title":"The Number of Spanning Trees of General Fan Graphs","authors":"Gao Zhinan, Lu Xingyan, Wei Yuxuan, Zhu Feng","doi":"10.9734/arjom/2023/v19i11755","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11755","url":null,"abstract":"As we all know, the number of spanning trees can be calculated by virtue of the famous Kirchhoff’s matrix-tree theorem. However, it doesn’t work when coming across complex graphs with thousands of edges and vertices or more. Hence, how to obtain accurate solutions of the number of spanning trees of general fan graphs becomes a subject to several studies of many places like computer science, physics and mathematics. In this paper, we focus on calculating different types of graphs generated by adding vertices and edges to the fan graph. Particularly, we define a new graph called \"C-graph\", which brings a unique angle of view for us to recognize the construction of original graphs. Moreover, we introduce a new iterative relation about the general fan graph, simplifying the calculation. Therefore, we can obtain functions of the number of spanning trees obtained from given fan graphs, which are also suitable for larger and more complex conditions. Finally, we discuss the effect of vertices and edges on the number of spanning trees, finding out that edges have greater impact. Additionally, by using Kirchhoff’s matrix-tree theorem, we verified the rationality of our results.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"150 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136104142","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 : 2023-10-26DOI: 10.9734/arjom/2023/v19i11754
Heeramani Tiwari, None Padmavati
Aims/ Objectives: The objective of this paper is to introduce the notion of generalized (alpha) - (beta) - (psi) contractive mappings involving rational expressions and establish existence and uniqueness of fixed points of Berinde type generalized (alpha) - (beta) - (psi) contractive mappings in the context of partial metric spaces. Additionally, we provide an example in support of our results.
{"title":"Berinde-Type Generalized (alpha) - (beta) - (psi) Contractive Mappings in Partial Metric Spaces and Some Related Fixed Points","authors":"Heeramani Tiwari, None Padmavati","doi":"10.9734/arjom/2023/v19i11754","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11754","url":null,"abstract":"Aims/ Objectives: The objective of this paper is to introduce the notion of generalized (alpha) - (beta) - (psi) contractive mappings involving rational expressions and establish existence and uniqueness of fixed points of Berinde type generalized (alpha) - (beta) - (psi) contractive mappings in the context of partial metric spaces. Additionally, we provide an example in support of our results.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136381590","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 : 2023-10-25DOI: 10.9734/arjom/2023/v19i11753
Emmanuel Oladayo Oduselu–Hassan, Ignatius N. Njoseh, Jonathan Tsetimi
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms and the solution are stochastic processes. Numerous studies have employed orthogonal polynomials, however most of them focus on deterministic rather than stochastic systems. This is the reason why in this study, we looked into a numerical solution for the stochastic Ito-Volterra integral equation using the explicit finite difference scheme and Bernstein polynomials as trial functions. The equidistant collocation procedure was used to calculate the unknown constant parameters in between and reach the desired approximation. The method was evaluated and contrasted with the Block Pulse method for approximate answers based on the aforementioned method, which were obtained and compared with others in the literature.
{"title":"A Numerical Approximation of the Stochastic Ito-Volterra Integral Equation","authors":"Emmanuel Oladayo Oduselu–Hassan, Ignatius N. Njoseh, Jonathan Tsetimi","doi":"10.9734/arjom/2023/v19i11753","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11753","url":null,"abstract":"A stochastic differential equation (SDE) is a differential equation in which one or more of the terms and the solution are stochastic processes. Numerous studies have employed orthogonal polynomials, however most of them focus on deterministic rather than stochastic systems. This is the reason why in this study, we looked into a numerical solution for the stochastic Ito-Volterra integral equation using the explicit finite difference scheme and Bernstein polynomials as trial functions. The equidistant collocation procedure was used to calculate the unknown constant parameters in between and reach the desired approximation. The method was evaluated and contrasted with the Block Pulse method for approximate answers based on the aforementioned method, which were obtained and compared with others in the literature.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"43 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218964","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 : 2023-10-25DOI: 10.9734/arjom/2023/v19i11752
None Atsu, J. U.
Aims: This study modelled a- and b-values of earthquakes employing the least squares regression and maximum likelihood estimate methods. Methodology: Data used in the study were obtained from the International Seismological Centre (ISC), an earthquake catalogue of the United Kingdom. The time window was from 1st January 1988 to 31st December 2010 (30 years) with earthquake focal depth of 0-700km and magnitude Mb ≥ 1.3. Ten different locations were selected and a total of 149,965 events were used. The acquired data were processed and analysed using Microsoft Excel and the hypothesis was tested using independent t-test statistics with the aid of Statistical Software for Social Sciences (SPSS) version 23.0. Results: The findings of the study revealed that the b- and a-values calculated using the least squares regression method were higher than the ones obtained using the maximum likelihood estimate method. Also, the hypothesis revealed that there is a significant difference between the use of the least squares regression method and the maximum likelihood estimate method in the determination of b- and a-value of earthquakes in a given region. Conclusion: The maximum likelihood estimate gives a better estimate of b- and -a values than the least squares regression method.
{"title":"Modelling of Earthquake b-and a-Values Using Least Squares and Maximum Likelihood Estimate Methods in Different Tectonic Regions of the World","authors":"None Atsu, J. U.","doi":"10.9734/arjom/2023/v19i11752","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i11752","url":null,"abstract":"Aims: This study modelled a- and b-values of earthquakes employing the least squares regression and maximum likelihood estimate methods. Methodology: Data used in the study were obtained from the International Seismological Centre (ISC), an earthquake catalogue of the United Kingdom. The time window was from 1st January 1988 to 31st December 2010 (30 years) with earthquake focal depth of 0-700km and magnitude Mb ≥ 1.3. Ten different locations were selected and a total of 149,965 events were used. The acquired data were processed and analysed using Microsoft Excel and the hypothesis was tested using independent t-test statistics with the aid of Statistical Software for Social Sciences (SPSS) version 23.0. Results: The findings of the study revealed that the b- and a-values calculated using the least squares regression method were higher than the ones obtained using the maximum likelihood estimate method. Also, the hypothesis revealed that there is a significant difference between the use of the least squares regression method and the maximum likelihood estimate method in the determination of b- and a-value of earthquakes in a given region. Conclusion: The maximum likelihood estimate gives a better estimate of b- and -a values than the least squares regression method.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135216622","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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