Pub Date : 2024-02-15DOI: 10.37745/ijmss.13/vol12n1924
I.U. Amadi, L.C. Nnoka, C.P Amadi
This paper investigated system of stochastic differential equations with prominence on disparities of drift parameters. These problems were solved analytical by adopting the Ito’s method of solution and three different investment solutions were obtained consequently. The necessary conditions were achieved which govern various drift parameters in assessing financial markets. Therefore, the impressions on each solution of investors in financial markets were analyzed graphically. Secondly, stock price data of Transco, LTD were analyzed which covariance matrix were considered and analysis were logically extended to stochastic vector differential equation where control measures were incorporated that would help in predicting different stock price processes, and the result obtained by exploring the properties of the fundamental matrix solution where asymptotic null controllability results were obtained by the singularity of the controllability matrix a function of the drift. Finally, the effects of the significant parameters of stochastic variables were successfully discussed.
{"title":"Application of Non-Linear Evolution Stochastic Equations with Asymptotic Null Controllability Analysis","authors":"I.U. Amadi, L.C. Nnoka, C.P Amadi","doi":"10.37745/ijmss.13/vol12n1924","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol12n1924","url":null,"abstract":"This paper investigated system of stochastic differential equations with prominence on disparities of drift parameters. These problems were solved analytical by adopting the Ito’s method of solution and three different investment solutions were obtained consequently. The necessary conditions were achieved which govern various drift parameters in assessing financial markets. Therefore, the impressions on each solution of investors in financial markets were analyzed graphically. Secondly, stock price data of Transco, LTD were analyzed which covariance matrix were considered and analysis were logically extended to stochastic vector differential equation where control measures were incorporated that would help in predicting different stock price processes, and the result obtained by exploring the properties of the fundamental matrix solution where asymptotic null controllability results were obtained by the singularity of the controllability matrix a function of the drift. Finally, the effects of the significant parameters of stochastic variables were successfully discussed.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"220 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140456035","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 : 2024-02-15DOI: 10.37745/ijmss.13/vol12n118
J. T. Otobong, Eno John, M. U. Udeme, Michael N. John
This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups 𝐺. By delving into three distinct forms of full transitivity within the endomorphism ring of 𝐺, specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphisms, we aim to provide a comprehensive understanding of the totally projective groups exhibiting these properties. The Ulm function of 𝐺 emerges as a key tool in solving this problem and related inquiries, leading to a precise characterization of the groups involved.
{"title":"Ulm Function Analysis of Full Transitivity in Primary Abelian Groups","authors":"J. T. Otobong, Eno John, M. U. Udeme, Michael N. John","doi":"10.37745/ijmss.13/vol12n118","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol12n118","url":null,"abstract":"This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups 𝐺. By delving into three distinct forms of full transitivity within the endomorphism ring of 𝐺, specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphisms, we aim to provide a comprehensive understanding of the totally projective groups exhibiting these properties. The Ulm function of 𝐺 emerges as a key tool in solving this problem and related inquiries, leading to a precise characterization of the groups involved.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"345 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140455413","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 : 2024-02-15DOI: 10.37745/ijmss.13/vol12n14755
Kai Shun Lam
There were many mathematicians who tried to prove or disprove the statement of Riemann Hypothe-sis. However, none of them have been successfully approved by the Clay Mathematical Institute. In addition, to the best of this author’s knowledge, these mathematicians haven’t employed the technique of logical truth table during their proofs. With reference to this author’s previous proof in [1], this author have employed the method of multiplicative telescope together with the prime boundary gaps. In this extended version of my proof to the Riemann Hypothesis, this author tries to show that RH statement is true through the four cases of the conditional statements in the truth table. Three of the cases (I, II, IV) are found to be true for the conditional statement in the Riemann Hypothesis while only one (case III) is found to be false (and acts as the disproof by a counter-example). Moreover, there are also three sub-cases (i, ii, iii) [1] among these four tabled cases. The main idea is that the we may disproof the hypothesis statement that is similar to the RH one by first find a counter-example which is obviously a disproof (case III) to the (Riemann) hypothesis. But it is NOT compatible with the GÖdel’s Incompleteness Theorem. Otherwise either the disproof to the statement or the Gödel is incorrect which is impossible. Hence, the disproof is said to be incompatible with the Gödel. On the other hand, all of the other truth cases (I, II, IV) for the statement are indeed the examples for the pos-itive results to the Riemann Hypothesis statement and are compatible with the Gödel. Therefore, the only way to make a conclusion is to say or force the Riemann Hypothesis statement to be correct.In general, for any hypothesis with the conditional statements structure like the Riemann one, we may also prove them by the similar techniqe and the arguments of the truth table for their conditional statements together with the Gödel’s Incompleteness theorem to force the positive result for the hy-pothesis statement. Actually, there are many applications for the truth tables especially in the fields like language (structure & modeling) or in engineering (logic gates & programming) etc during our everyday usage.
{"title":"An Extension Proof of Riemann Hypothesis by a Logical Entails Truth Table","authors":"Kai Shun Lam","doi":"10.37745/ijmss.13/vol12n14755","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol12n14755","url":null,"abstract":"There were many mathematicians who tried to prove or disprove the statement of Riemann Hypothe-sis. However, none of them have been successfully approved by the Clay Mathematical Institute. In addition, to the best of this author’s knowledge, these mathematicians haven’t employed the technique of logical truth table during their proofs. With reference to this author’s previous proof in [1], this author have employed the method of multiplicative telescope together with the prime boundary gaps. In this extended version of my proof to the Riemann Hypothesis, this author tries to show that RH statement is true through the four cases of the conditional statements in the truth table. Three of the cases (I, II, IV) are found to be true for the conditional statement in the Riemann Hypothesis while only one (case III) is found to be false (and acts as the disproof by a counter-example). Moreover, there are also three sub-cases (i, ii, iii) [1] among these four tabled cases. The main idea is that the we may disproof the hypothesis statement that is similar to the RH one by first find a counter-example which is obviously a disproof (case III) to the (Riemann) hypothesis. But it is NOT compatible with the GÖdel’s Incompleteness Theorem. Otherwise either the disproof to the statement or the Gödel is incorrect which is impossible. Hence, the disproof is said to be incompatible with the Gödel. On the other hand, all of the other truth cases (I, II, IV) for the statement are indeed the examples for the pos-itive results to the Riemann Hypothesis statement and are compatible with the Gödel. Therefore, the only way to make a conclusion is to say or force the Riemann Hypothesis statement to be correct.In general, for any hypothesis with the conditional statements structure like the Riemann one, we may also prove them by the similar techniqe and the arguments of the truth table for their conditional statements together with the Gödel’s Incompleteness theorem to force the positive result for the hy-pothesis statement. Actually, there are many applications for the truth tables especially in the fields like language (structure & modeling) or in engineering (logic gates & programming) etc during our everyday usage.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"109 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140456335","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 : 2024-02-15DOI: 10.37745/ijmss.13/vol12n12546
M. Alabi, M. S. Olaleye, K. S. Adewoye
The numerical computation of fourth order ordinary differential equations cannot be gloss over easily due to its significant and importance. There have been glowing needs to find an appropriate numerical method that will handle effectively fourth order ordinary differential equations without resolving such an equation to a system of first order ordinary differential equations. To this end, this presentation focuses on direct numerical computation to fourth order ordinary differential equations without resolving such equations to a system of first order ordinary differential equations. The method is not predictor – corrector one due to its limitation in the level of accuracy. The method is order wise christened “Block Method” which is a self-starting method. In order to achieve this objective, Chebyshev polynomial is hereby used as basis function.
{"title":"Initial Value Solvers for Direct Solution of Fourth Order Ordinary Differential Equations in a Block from Using Chebyshev Polynomial as Basis Function","authors":"M. Alabi, M. S. Olaleye, K. S. Adewoye","doi":"10.37745/ijmss.13/vol12n12546","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol12n12546","url":null,"abstract":"The numerical computation of fourth order ordinary differential equations cannot be gloss over easily due to its significant and importance. There have been glowing needs to find an appropriate numerical method that will handle effectively fourth order ordinary differential equations without resolving such an equation to a system of first order ordinary differential equations. To this end, this presentation focuses on direct numerical computation to fourth order ordinary differential equations without resolving such equations to a system of first order ordinary differential equations. The method is not predictor – corrector one due to its limitation in the level of accuracy. The method is order wise christened “Block Method” which is a self-starting method. In order to achieve this objective, Chebyshev polynomial is hereby used as basis function.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"30 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140455793","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 : 2024-02-15DOI: 10.37745/ijmss.13/vol12n15670
Victor Yokoso, Davidson Teye Kabutey, Susan Ansah, Yvonne Mawusi Ntow, Sylvia Ofotsu
This study aimed to investigate the different errors and misconceptions made by students when dealing with linear inequalities. The goal was to uncover the nature and causes of these errors and misconceptions among students in Senior High Schools within the Mfantseman Municipality in the Central Region of Ghana. The research employed an explanatory sequential mixed methods design and was conducted in two public Senior High Schools selected from the Municipality. A total of 180 Senior High School students and teachers participated in the study, including 10 teachers. The sample was selected using a random sampling technique, which yielded 170 students from the two chosen public Senior High Schools. Data collection encompassed results from students' tests on linear inequalities, interviews with students, and questionnaires given to mathematics teachers. The collected data was coded and analyzed using descriptive statistics. The study's findings revealed common errors made by students, such as multiplying/dividing by a negative number, substituting inequality symbols with "equal to" symbols, performing operations on only one side or different numbers on the two sides of a compound inequality, as well as errors in algebraic operations, simplification, and arithmetic. Misconceptions observed included confusion between equality and inequality, misconceptions when dividing or multiplying through an inequality by a negative number, and struggles with compound inequalities. Students' difficulties arose from an inadequate understanding of basic inequality concepts, overgeneralization, limited mastery of inequality rules, and insufficient exposure to compound inequalities. Translating word problems into algebraic symbols posed a significant challenge. The study also highlighted that mathematics teachers were aware of the errors made by students. Consequently, teachers made efforts to address these errors during linear inequality classes. The findings suggest that teachers not only need assistance in identifying errors but also in understanding how errors can emerge during the learning process. One of the recommendations is to enhance teacher education by emphasizing diverse teacher-student interactions that thoroughly consider students' mathematical ideas. This approach aims to support teachers in effectively utilizing students' experiences in the learning process.
{"title":"Errors and Misconceptions in Linear Inequalities Among Senior High Students in Mfantseman Municipality","authors":"Victor Yokoso, Davidson Teye Kabutey, Susan Ansah, Yvonne Mawusi Ntow, Sylvia Ofotsu","doi":"10.37745/ijmss.13/vol12n15670","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol12n15670","url":null,"abstract":"This study aimed to investigate the different errors and misconceptions made by students when dealing with linear inequalities. The goal was to uncover the nature and causes of these errors and misconceptions among students in Senior High Schools within the Mfantseman Municipality in the Central Region of Ghana. The research employed an explanatory sequential mixed methods design and was conducted in two public Senior High Schools selected from the Municipality. A total of 180 Senior High School students and teachers participated in the study, including 10 teachers. The sample was selected using a random sampling technique, which yielded 170 students from the two chosen public Senior High Schools. Data collection encompassed results from students' tests on linear inequalities, interviews with students, and questionnaires given to mathematics teachers. The collected data was coded and analyzed using descriptive statistics. The study's findings revealed common errors made by students, such as multiplying/dividing by a negative number, substituting inequality symbols with \"equal to\" symbols, performing operations on only one side or different numbers on the two sides of a compound inequality, as well as errors in algebraic operations, simplification, and arithmetic. Misconceptions observed included confusion between equality and inequality, misconceptions when dividing or multiplying through an inequality by a negative number, and struggles with compound inequalities. Students' difficulties arose from an inadequate understanding of basic inequality concepts, overgeneralization, limited mastery of inequality rules, and insufficient exposure to compound inequalities. Translating word problems into algebraic symbols posed a significant challenge. The study also highlighted that mathematics teachers were aware of the errors made by students. Consequently, teachers made efforts to address these errors during linear inequality classes. The findings suggest that teachers not only need assistance in identifying errors but also in understanding how errors can emerge during the learning process. One of the recommendations is to enhance teacher education by emphasizing diverse teacher-student interactions that thoroughly consider students' mathematical ideas. This approach aims to support teachers in effectively utilizing students' experiences in the learning process.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"37 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140456226","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 : 2023-03-15DOI: 10.37745/ijmss.13/vol11n34352
Desire E Edeminam, Anthony E Usoro
The study aimed at analyzing the profiles of academic staff in the Akwa State University. The categories of staff included Professors/Associate Professors, Senior Lecturers and Lecturer1/Below with a total number of 26, 73 and 289 respectively. Hotelling’s T2 was adopted for the pair wise analysis between Professors/Associate Professors and Senior Lecturers, Professors/Associate Professors and Lecturer1/Below and Senior Lecturer and Lecturer1/Below. The results of the analysis revealed that there is a significant difference between the profiles of Professors/Associate Professors and Senior Lecturer, Professors/Associate Professors and Lecturer1/Below and Senior Lecturers and Lecturer1/Below respectively. This research appraises the average productivity of each category of academic staff in Akwa Ibom State University. This will serve as reference document for further research.
{"title":"Hotelling’s T2 Analysis of Academic Staff Profiles: A Case Study of the Akwa Ibom State University, Nigeria","authors":"Desire E Edeminam, Anthony E Usoro","doi":"10.37745/ijmss.13/vol11n34352","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol11n34352","url":null,"abstract":"The study aimed at analyzing the profiles of academic staff in the Akwa State University. The categories of staff included Professors/Associate Professors, Senior Lecturers and Lecturer1/Below with a total number of 26, 73 and 289 respectively. Hotelling’s T2 was adopted for the pair wise analysis between Professors/Associate Professors and Senior Lecturers, Professors/Associate Professors and Lecturer1/Below and Senior Lecturer and Lecturer1/Below. The results of the analysis revealed that there is a significant difference between the profiles of Professors/Associate Professors and Senior Lecturer, Professors/Associate Professors and Lecturer1/Below and Senior Lecturers and Lecturer1/Below respectively. This research appraises the average productivity of each category of academic staff in Akwa Ibom State University. This will serve as reference document for further research.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135748055","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 : 2023-03-15DOI: 10.37745/ijmss.13/vol11n3110
Lam Kai Shun
As in my previous two papers [2] & [3] about the boundary of the prime gap still cause some misunderstanding, I here in this paper tries to clarify those detailed steps in proving such boundary of the prime gap for a contradiction. Indeed, the general idea of my designed proof is to make all of the feasible case of the Riemann Zeta function with exponents ranged from 1 to s = u + v*I becomes nonsense (where u, v are real numbers with I is imaginary equals to (-1)1/2 except that u = 0.5 with some real numbers v as the expected zeta roots. Once if we can exclude all other possibilies unless u = 0.5 with some real numbers v in the Riemann Zeta function’s exponent “s”, then the Riemann Hypothesis will be proved immediately. The truth of the hypothesis further implies that there is a need for the shift from the line x = 0 to the line x = 0.5 as all of the zeta roots lie on it. However, NOT all of the points on x = 0.5 are zeros as we may find from the model equation that has been well established in [2]. One of my application is in the quantum filtering for an elimination of noise in a quantum system but NOT used to filter human beings like the political counter-parts.In general, this author suggests that for all of the proof or disproof to any cases of hypothesis, one may need to point out those logical contradictions [14] among them. Actually, my proposition works very well for the cases in my disproof of Continuum Hypothesis [15] together with the proof in Riemann Hypothesis
{"title":"A Full and Detailed Proof for the Riemann Hypothesis & the Simple Inductive proof of Goldbach’s Conjecture","authors":"Lam Kai Shun","doi":"10.37745/ijmss.13/vol11n3110","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol11n3110","url":null,"abstract":"As in my previous two papers [2] & [3] about the boundary of the prime gap still cause some misunderstanding, I here in this paper tries to clarify those detailed steps in proving such boundary of the prime gap for a contradiction. Indeed, the general idea of my designed proof is to make all of the feasible case of the Riemann Zeta function with exponents ranged from 1 to s = u + v*I becomes nonsense (where u, v are real numbers with I is imaginary equals to (-1)1/2 except that u = 0.5 with some real numbers v as the expected zeta roots. Once if we can exclude all other possibilies unless u = 0.5 with some real numbers v in the Riemann Zeta function’s exponent “s”, then the Riemann Hypothesis will be proved immediately. The truth of the hypothesis further implies that there is a need for the shift from the line x = 0 to the line x = 0.5 as all of the zeta roots lie on it. However, NOT all of the points on x = 0.5 are zeros as we may find from the model equation that has been well established in [2]. One of my application is in the quantum filtering for an elimination of noise in a quantum system but NOT used to filter human beings like the political counter-parts.In general, this author suggests that for all of the proof or disproof to any cases of hypothesis, one may need to point out those logical contradictions [14] among them. Actually, my proposition works very well for the cases in my disproof of Continuum Hypothesis [15] together with the proof in Riemann Hypothesis","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135748054","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 : 2023-03-15DOI: 10.37745/ijmss.13/vol11n31126
I. C. Eli, A. B. Okrinya
Tuberculosis (TB) is a dangerous contagious disease which can even lead to death if no control measure is applied. The disease is caused by mycobacterium which generally affects lungs and other related organs such as lymph gland, intestine, kidneys, uterus, bone and brain. The spread of TB occurs via the bacteria contaminated air which is inhaled into the lungs. Cough, chest pain, shortness of breath, appetite loss, weight loss, fever, cold and fatigue are some of the symptoms of TB. However, we proposed a mathematical model to investigate the transmission dynamics of tuberculosis and it is investigated analytically that the endemic equilibrium point is stable with the help of Routh-Hurwitz criteria. The sensitivity analysis shows that there would be an epidemic if and only if β≈β^1, where β^1≤0.1. Finally, using Matlab, it is shown that the disease free equilibrium is unstable which the endemic equilibrium becomes stable beyond 60 days. In addition, the recovered population increased rapidly while the exposed population decreased steeply in the disease-free equilibrium. It is an indication that there will be no outbreak of the tuberculosis infection. Besides, an increased in the effective contact rate increases both the infected population and recovered population. It is equally inferred that the recovered population do not show a trend pattern as ∝ increases while the susceptible and infected populations increased and decreased respectively as ∝ is increased. The recovered population showed no response pattern for ∝ since recovered individuals do not obtain permanent immunity.
{"title":"Sensitivity and Stability Analysis of Tuberculosis Disease with Infectious Latent","authors":"I. C. Eli, A. B. Okrinya","doi":"10.37745/ijmss.13/vol11n31126","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol11n31126","url":null,"abstract":"Tuberculosis (TB) is a dangerous contagious disease which can even lead to death if no control measure is applied. The disease is caused by mycobacterium which generally affects lungs and other related organs such as lymph gland, intestine, kidneys, uterus, bone and brain. The spread of TB occurs via the bacteria contaminated air which is inhaled into the lungs. Cough, chest pain, shortness of breath, appetite loss, weight loss, fever, cold and fatigue are some of the symptoms of TB. However, we proposed a mathematical model to investigate the transmission dynamics of tuberculosis and it is investigated analytically that the endemic equilibrium point is stable with the help of Routh-Hurwitz criteria. The sensitivity analysis shows that there would be an epidemic if and only if β≈β^1, where β^1≤0.1. Finally, using Matlab, it is shown that the disease free equilibrium is unstable which the endemic equilibrium becomes stable beyond 60 days. In addition, the recovered population increased rapidly while the exposed population decreased steeply in the disease-free equilibrium. It is an indication that there will be no outbreak of the tuberculosis infection. Besides, an increased in the effective contact rate increases both the infected population and recovered population. It is equally inferred that the recovered population do not show a trend pattern as ∝ increases while the susceptible and infected populations increased and decreased respectively as ∝ is increased. The recovered population showed no response pattern for ∝ since recovered individuals do not obtain permanent immunity.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"421 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135748062","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 : 2023-03-15DOI: 10.37745/ijmss.13/vol11n32742
Mohammad M R Sheikh
Categorical principal component analysis (CATPCA) technique was applied in the road killed or seriously injured (KSI) car accidents in England based on STATS19 data so that the categorical variables of KSI car accidents can be transferred into few components with reduction of dimensionality. Finally selected 20 variables in KSI car accident database were divided to create four principal components by applying “optimal scaling CATPCA” procedure in SPSS. The statistically significant KSI car accident variables, particularly the most accountable categorical variables, were identified and quantified for developing models as well as leading to aims to reduce as well as to prevent the car accidents, particularly the KSI car accidents. It also leads to map out the possible safety improvement strategies as well as to inform the policymakers on how best to reduce the number and severity of car crashes.
{"title":"Optimal Scaling Categorical Principal Components Analysis: Road Traffic KSI Car Accidents in England (STATS19)","authors":"Mohammad M R Sheikh","doi":"10.37745/ijmss.13/vol11n32742","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol11n32742","url":null,"abstract":"Categorical principal component analysis (CATPCA) technique was applied in the road killed or seriously injured (KSI) car accidents in England based on STATS19 data so that the categorical variables of KSI car accidents can be transferred into few components with reduction of dimensionality. Finally selected 20 variables in KSI car accident database were divided to create four principal components by applying “optimal scaling CATPCA” procedure in SPSS. The statistically significant KSI car accident variables, particularly the most accountable categorical variables, were identified and quantified for developing models as well as leading to aims to reduce as well as to prevent the car accidents, particularly the KSI car accidents. It also leads to map out the possible safety improvement strategies as well as to inform the policymakers on how best to reduce the number and severity of car crashes.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135748061","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 : 2023-02-15DOI: 10.37745/ijmss.13/vol11n2112
Orok Udofia David, Uwem Daniel Udom
The crux of this study investigated “cultural variable and functional probability learning: An Ethnomathematics perspectives”. Nsa Isong game was used as major independent variable and functional probability learning as dependent variable. Two (2) purpose of the study was used to generate two (2) research questions and two (2) null hypotheses were formulated for the study. The Quasi-experimental design of pretest and posttest was adopted for the study with a proportionate stratified sampling technique used to obtain a sample size of 320 students from a population of 3,610 students. Probability Achievement Test (PAT) was the instrument used for data collection with a reliability coefficient of 0.87 using split half reliability test. Data collected from the study were subjected to analysis of covariance (ANCOVA) for analysis. The results indicated that; there is significant effect of Nsa Isong game on students’ functional probability learning, there is significant effect of Nsa Isong game and gender on students’ functional probability learning. Based on this result obtained it was recommended amongst others that workshops and seminars should be organize for teachers at primary and secondary level of education on how to use the Nsa Isong game in the teaching and learning of probability.
{"title":"Cultural Variable and Functional Probability Learning: An Ethnomathematics Perspectives","authors":"Orok Udofia David, Uwem Daniel Udom","doi":"10.37745/ijmss.13/vol11n2112","DOIUrl":"https://doi.org/10.37745/ijmss.13/vol11n2112","url":null,"abstract":"The crux of this study investigated “cultural variable and functional probability learning: An Ethnomathematics perspectives”. Nsa Isong game was used as major independent variable and functional probability learning as dependent variable. Two (2) purpose of the study was used to generate two (2) research questions and two (2) null hypotheses were formulated for the study. The Quasi-experimental design of pretest and posttest was adopted for the study with a proportionate stratified sampling technique used to obtain a sample size of 320 students from a population of 3,610 students. Probability Achievement Test (PAT) was the instrument used for data collection with a reliability coefficient of 0.87 using split half reliability test. Data collected from the study were subjected to analysis of covariance (ANCOVA) for analysis. The results indicated that; there is significant effect of Nsa Isong game on students’ functional probability learning, there is significant effect of Nsa Isong game and gender on students’ functional probability learning. Based on this result obtained it was recommended amongst others that workshops and seminars should be organize for teachers at primary and secondary level of education on how to use the Nsa Isong game in the teaching and learning of probability.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"356 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135683440","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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