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An Algorithmic Approach to Solve Continuum Hypothesis 求解连续统假设的一种算法
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-11-25 DOI: 10.2139/ssrn.3318201
Lam Kai Shun
{"title":"An Algorithmic Approach to Solve Continuum Hypothesis","authors":"Lam Kai Shun","doi":"10.2139/ssrn.3318201","DOIUrl":"https://doi.org/10.2139/ssrn.3318201","url":null,"abstract":"The continuum hypothesis has been unsolved for hundreds of years. In other words, can I answer it completely? By refuting the culturally responsible continuum [1], one can link the problem to the mathematical continuum, and it is possible to disproof the continuum hypothesis [2] . To go ahead a step, one may extend our mathematical system (by employing a more powerful set theory) and solve the continuum problem by three conditional cases. This event is sim-ilar to the status cases in the discriminant of solving a quadratic equation. Hence, my proposed al-gorithmic flowchart can best settle and depict the problem. From the above, one can further con-clude that when people extend mathematics (like set theory — ZFC) into new systems (such as Force Axioms), experts can solve important mathematical problems (CH). Indeed, there are differ-ent types of such mathematical systems, similar to ancient mathematical notation. Hence, different cultures have different ways of representation, which is similar to a Chinese saying: “different vil-lages have different laws.” However, the primary purpose of mathematical notation was initially to remember and communicate. This event indicates that the basic purpose of developing any new mathematical system is to help solve a natural phenomenon in our universe.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127171532","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}
引用次数: 1
The Critics and Contributions of Mathematical Philosophy in Hong Kong Secondary Education 数学哲学在香港中学教育中的批判与贡献
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-11-16 DOI: 10.32861/ajams.71.16.26
Lam Kai Shun
{"title":"The Critics and Contributions of Mathematical Philosophy in Hong Kong Secondary Education","authors":"Lam Kai Shun","doi":"10.32861/ajams.71.16.26","DOIUrl":"https://doi.org/10.32861/ajams.71.16.26","url":null,"abstract":"There are various schools of mathematical philosophy. However, none of them can be founded on mathematics alone. At the same time, there are two types of mathematical proof styles: Dialectic and algorithm mathematical proof. The relationship between proof and philosophy is to study philosophical problems with mathematical models. This type of proof is important to Hong Kong Secondary education. In addition, teachers should explain the connection between mathematics-based subjects, such as physics, so that lessons are more interesting rather than technical. Mathematics relates to nearly all other subjects, and as such has the role of a ‘public servant’ when it comes to serving them. One role of mathematics is to act as a ‘rational’ instrument for various subjects. This can be shown in many ancient human activities, such as Daoism and Liu Hiu, together with their symbolic representations. These examples are similar to Jewish culture; when discussing confidence, Abraham is often mentioned due to being the “Father of Confidence”. Thus, it may be said that mathematics is more than just a servant—it is also a cultural subject that has been recorded throughout history. To conclude, other than mathematical proof, Hong Kong teachers should also allow students to learn the cultural context behind various topics and subjects.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127415424","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}
引用次数: 0
The Gompertz Gumbel II Distribution: Properties and Applications Gompertz Gumbel II分布:性质与应用
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-11-16 DOI: 10.32861/ajams.71.1.15
A. A. Ogunde, G. A. Olalude, D. Omosigho
{"title":"The Gompertz Gumbel II Distribution: Properties and Applications","authors":"A. A. Ogunde, G. A. Olalude, D. Omosigho","doi":"10.32861/ajams.71.1.15","DOIUrl":"https://doi.org/10.32861/ajams.71.1.15","url":null,"abstract":"In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122266819","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}
引用次数: 2
Handling Outliers and Missing Data in Regression Models Using R: Simulation Examples 使用R处理回归模型中的异常值和缺失数据:模拟示例
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-09-10 DOI: 10.32861/ajams.68.187.203
M. Abonazel
{"title":"Handling Outliers and Missing Data in Regression Models Using R: Simulation Examples","authors":"M. Abonazel","doi":"10.32861/ajams.68.187.203","DOIUrl":"https://doi.org/10.32861/ajams.68.187.203","url":null,"abstract":"This paper has reviewed two important problems in regression analysis (outliers and missing data), as well as some handling methods for these problems. Moreover, two applications have been introduced to understand and study these methods by R-codes. Practical evidence was provided to researchers to deal with those problems in regression modeling with R. Finally, we created a Monte Carlo simulation study to compare different handling methods of missing data in the regression model. Simulation results indicate that, under our simulation factors, the k-nearest neighbors method is the best method to estimate the missing values in regression models.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124519048","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}
引用次数: 8
Annotations on the Relationship Among Discriminant Functions 判别函数间关系的注解
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-09-10 DOI: 10.32861/ajams.68.161.165
Awogbemi, Clement Adeyeye
{"title":"Annotations on the Relationship Among Discriminant Functions","authors":"Awogbemi, Clement Adeyeye","doi":"10.32861/ajams.68.161.165","DOIUrl":"https://doi.org/10.32861/ajams.68.161.165","url":null,"abstract":"Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). The relationships among the classification statistics examined were established: The Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification statistics.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129172807","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}
引用次数: 0
A Note on Different Types of Probabilities of Misclassification 关于不同类型的误分类概率的说明
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-09-10 DOI: 10.32861/ajams.68.181.186
Awogbemi, Clement Adeyeye
{"title":"A Note on Different Types of Probabilities of Misclassification","authors":"Awogbemi, Clement Adeyeye","doi":"10.32861/ajams.68.181.186","DOIUrl":"https://doi.org/10.32861/ajams.68.181.186","url":null,"abstract":"Whenever a discriminant function is constructed, the attention of a researcher is often focused on classification. The underlined interest is how well does a discriminant function perform in classifying future observations correctly. In order to assess the performance of any classification rule, probabilities of misclassification of a discriminant function serves as a basis for the procedure. Different forms of probabilities of misclassification and their associated properties were considered in this study. The misclassification probabilities were defined in terms of probability density functions (pdf) and classification regions. Apparent probability of misclassification is expressed as the proportion of observations in the initial sample which are misclassified by the sample discriminant function. Different methods of estimating probabilities of misclassification were related to each other using their individual shortcomings. The status of degrees of uncertainties associated with probabilities of misclassification and their implications were also specified.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"234 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114197797","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}
引用次数: 0
Forecasting of COVID-19 Cases in Kurdistan Region Using Some Statistical Models 基于几种统计模型的库尔德斯坦地区新冠肺炎病例预测
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-09-10 DOI: 10.32861/ajams.68.172.180
S. Hussen
{"title":"Forecasting of COVID-19 Cases in Kurdistan Region Using Some Statistical Models","authors":"S. Hussen","doi":"10.32861/ajams.68.172.180","DOIUrl":"https://doi.org/10.32861/ajams.68.172.180","url":null,"abstract":"Nowadays the new universal disease of the coronavirus that is called the epidemic COVID-19 is spread as geometric progression among the people around the world, so, such pathogen considered the most dangerous threat facing humanity. This study aimed to derive the best forecasting models for the close future cases of infected, recovered, and deaths in the four provinces of Kurdistan Region-Iraq to avoid more loss of human lives by applying more health care in certain province. Two forecasting methods were used including Exponential Smoothing and ARIMA models. The results indicate that both ARIMA and Exponential Smoothing models were close to each other for predicting the infected cases of COVID-19 in Kurdistan Region provinces, and the predicting models show that the pandemic might not be under control unless the people apply the government instructions for health care and keep social distances.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134343594","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}
引用次数: 1
A Peer Search on Integer Solutions to Quadratic Diophantine Equation with Three Unknowns (Equation) 三未知数二次Diophantine方程(方程)整数解的对等搜索
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-09-10 DOI: 10.32861/ajams.68.166.171
A. Vijayasankar, Sharadha Kumar, M. Gopalan
{"title":"A Peer Search on Integer Solutions to Quadratic Diophantine Equation with Three Unknowns (Equation)","authors":"A. Vijayasankar, Sharadha Kumar, M. Gopalan","doi":"10.32861/ajams.68.166.171","DOIUrl":"https://doi.org/10.32861/ajams.68.166.171","url":null,"abstract":"The non- homogeneous ternary quadratic diophantine (Equation) is analyzed for its patterns of non-zero distinct integral solutions. Various interesting relations between the solutions and special numbers namely polygonal, Pronic and Gnomonic numbers are exhibited.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133234368","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}
引用次数: 0
Response Triggered Architecture for E-Payment Examined for General Purpose Transaction 一般用途交易的电子支付响应触发体系结构研究
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-08-25 DOI: 10.32861/ajams.68.153.160
Akomolafe Dipo Theophilus, A. Stephen
{"title":"Response Triggered Architecture for E-Payment Examined for General Purpose Transaction","authors":"Akomolafe Dipo Theophilus, A. Stephen","doi":"10.32861/ajams.68.153.160","DOIUrl":"https://doi.org/10.32861/ajams.68.153.160","url":null,"abstract":"The explosive growth in internet coupled with advancement in Information and Communication Technology (ICT) has made business transactions much easier than it used to be in the past. For example, e-commerce has particularly benefited from the introduction of GSM system. One of the major challenges, however, is how to isolate fraudulent transactions from genuine businesses. This becomes more imperative as the advancement in ICT has brought with it fraud and related scams. In this work, we examined different types of e-commerce as well as the challenges being encountered in the course of daily transactions. We took advantage of the current trends in mobile communication networks, particularly GSM and proposed a system based on Response Triggered Architecture for electronic transaction. Our proposed system is platform independent which means only little modification is needed when switching from one platform to another. We used Visual.basic.net and knowledge in fraud for our system prototype and presented the results in the body of this work.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124723842","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}
引用次数: 0
Study of MHD Heat and Mass Transfer Flow for Hall and Ion-Slip Currents Effects in High Porosity Medium and Revolving System 高孔隙率介质和旋转系统中霍尔效应和离子滑移效应的MHD传热传质流研究
Academic Journal of Applied Mathematical Sciences Pub Date : 2020-07-04 DOI: 10.32861/ajams.67.100.125
M. Hossain, M. A. Samad, M. Alam
{"title":"Study of MHD Heat and Mass Transfer Flow for Hall and Ion-Slip Currents Effects in High Porosity Medium and Revolving System","authors":"M. Hossain, M. A. Samad, M. Alam","doi":"10.32861/ajams.67.100.125","DOIUrl":"https://doi.org/10.32861/ajams.67.100.125","url":null,"abstract":"In high porosity medium and revolving system the effects of ion-slip and Hall currents are studied on MHD heat and mass transfer flow. The non-linear coupled partial differential equations are determined using byl transformations and solve these equations employing finite difference method. Velocity, temperature as well as concentration profiles are studied for the concerned physical parameters and results are presented graphically. Due to the Hall and ion-slip parameters, Eckert number, and porosity parameter the velocity profiles are pronounced while it is declined for the effects of magnetic parameter, Prandtl number. Also the magnetic parameter enhances the temperature profiles. On the other hand, the temperature (concentration) profile decreases (increases) for the increasing effect of Prandtl number (Soret number). The rate of changes of velocity, temperature and concentration profiles are also presented graphically.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124386490","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}
引用次数: 0
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