In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations: P1 = 1 + 6 * n (n > 0, n is an integer) P5 = 5 + 6 * m (m ≥ 0, m is an integer) Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Twin prime numbers can only be formed between P1 and P5 prime numbers, n must be 1 greater than m. The largest prime number is known at the moment 2^(82,589,933) – 1 is a P1 prime number.
{"title":"Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers","authors":"H. Pan","doi":"10.32861/ajams.84.69.77","DOIUrl":"https://doi.org/10.32861/ajams.84.69.77","url":null,"abstract":"In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations:\u0000P1 = 1 + 6 * n (n > 0, n is an integer)\u0000P5 = 5 + 6 * m (m ≥ 0, m is an integer)\u0000Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Twin prime numbers can only be formed between P1 and P5 prime numbers, n must be 1 greater than m. The largest prime number is known at the moment 2^(82,589,933) – 1 is a P1 prime number.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122413836","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}
This manuscript presents a new univariate six parameters type I half-logistic inverse Weibull distribution. Explicit expressions for the quantile function, the moments, the moment generating function and the maximum likelihood esti-mators are formulated. Simulation is employed to investigate the goodness of fit and to discuss the behaviour of the new model. Competitive models are compared via real data. The univariate one is used as a base line to construct a bivariate one named bivariate six parameters type I half-logistic inverse Weibull distribution. Mathematical properties of the new bivariate distrib-ution are investigated. The goodness of fit and the model performance are discussed via simulation. COVID-19 mortality data for Italy and Canada are treated as a bivariate random variable to prove the applicability of the new bivariate distribution.
{"title":"On Bivariate Modeling of the COVID-19 Data with a New Type I Half-Logistic Inverse Weibull Distribution","authors":"A. Elhassanein","doi":"10.32861/ajams.83.42.68","DOIUrl":"https://doi.org/10.32861/ajams.83.42.68","url":null,"abstract":"This manuscript presents a new univariate six parameters type I half-logistic inverse Weibull distribution. Explicit expressions for the quantile function, the moments, the moment generating function and the maximum likelihood esti-mators are formulated. Simulation is employed to investigate the goodness of fit and to discuss the behaviour of the new model. Competitive models are compared via real data. The univariate one is used as a base line to construct a bivariate one named bivariate six parameters type I half-logistic inverse Weibull distribution. Mathematical properties of the new bivariate distrib-ution are investigated. The goodness of fit and the model performance are discussed via simulation. COVID-19 mortality data for Italy and Canada are treated as a bivariate random variable to prove the applicability of the new bivariate distribution.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115545579","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}
A class of stable numerical differential algorithms is constructed based on the Fourier transform. The instability of the numerical differentiation problem is overcome by modifying the integral “kernel” in the frequency domain. The convergence of the approximate derivatives is ensured based on some reasonable assumptions of the modified “kernel” function. The a-posteriori choice strategy of the regularization parameter is considered. Moreover, the convergence analysis and error estimate of the approximate derivatives are also given.
{"title":"Stable Numerical Differentiation Algorithms Based on the Fourier Transform in Frequency Domain","authors":"Yan He, Huilin Xu, Xiaoyan Xiang","doi":"10.32861/ajams.82.34.41","DOIUrl":"https://doi.org/10.32861/ajams.82.34.41","url":null,"abstract":"A class of stable numerical differential algorithms is constructed based on the Fourier transform. The instability of the numerical differentiation problem is overcome by modifying the integral “kernel” in the frequency domain. The convergence of the approximate derivatives is ensured based on some reasonable assumptions of the modified “kernel” function. The a-posteriori choice strategy of the regularization parameter is considered. Moreover, the convergence analysis and error estimate of the approximate derivatives are also given.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126339998","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}
Operator ∇ inner products on both sides of Combination of Boyles’ law and Chares law (“B-C law” in short), we got the “Wind Speed Equation of a Point in Air” (“Wind Speed Equation” in short). It suits for describing straight-line motion, and It states that mu ̇ is in proportion to ∇•T. Operator ∇ outer products on both sides of “Wind Speed Equation” (where T is replaced by T), we get the “Rotation Equation of a Point in Air” (“Rotation Equation” in short). It is a vector partial differential equation (PDE), suits for describing circular motion. It states that (mu ̇ ) is in proportion to T. Its solution is found by the method of separating variables. The existence of vector T is proved by the existence of rotation in the atmosphere and the solution of the “Rotation Equation”. It reveals that the vector form of B-C law holds in rotating air. Examples of up-side-down vertical rotation and horizontal rotation are given.
{"title":"Rotation Equation of a Point in Air and its Solution","authors":"Tian-quan Yun","doi":"10.32861/ajams.82.30.33","DOIUrl":"https://doi.org/10.32861/ajams.82.30.33","url":null,"abstract":"Operator ∇ inner products on both sides of Combination of Boyles’ law and Chares law (“B-C law” in short), we got the “Wind Speed Equation of a Point in Air” (“Wind Speed Equation” in short). It suits for describing straight-line motion, and It states that mu ̇ is in proportion to ∇•T. Operator ∇ outer products on both sides of “Wind Speed Equation” (where T is replaced by T), we get the “Rotation Equation of a Point in Air” (“Rotation Equation” in short). It is a vector partial differential equation (PDE), suits for describing circular motion. It states that (mu ̇ ) is in proportion to T. Its solution is found by the method of separating variables. The existence of vector T is proved by the existence of rotation in the atmosphere and the solution of the “Rotation Equation”. It reveals that the vector form of B-C law holds in rotating air. Examples of up-side-down vertical rotation and horizontal rotation are given.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132169034","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}
Linear programming is applied to bread production and the raw materials for the research were collected from the bakery industry in Lokoja which were clearly identified. The paper took into account three types of bread with estimated profits and the problem was formulated from the collected data. The formulated problem was parameterized into parametric linear programming and run using the developed algorithm of linear programming The result obtained indicates that profit is made at d different values of the parameter,t, leaving the company the choice of any profit it wants to get.
{"title":"Linear Programming on Bread Production Using Uncertainty Approach","authors":"Adamu Wakili","doi":"10.32861/ajams.82.27.29","DOIUrl":"https://doi.org/10.32861/ajams.82.27.29","url":null,"abstract":"Linear programming is applied to bread production and the raw materials for the research were collected from the bakery industry in Lokoja which were clearly identified. The paper took into account three types of bread with estimated profits and the problem was formulated from the collected data. The formulated problem was parameterized into parametric linear programming and run using the developed algorithm of linear programming The result obtained indicates that profit is made at d different values of the parameter,t, leaving the company the choice of any profit it wants to get.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116794696","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}
A forbidden zone theorem, hypothesis, and applied mathematical method and model are introduced in the present article. The method and model are based on the forbidden zones and hypothesis. The article is initiated by the well-known generic problems concerned with the mathematical description of the behavior of a man. The essence of the problems consists in biases of preferences and decisions of a man in comparison with predictions of the probability theory. The model is uniformly and successfully applied for different domains. The ultimate goal of the research is to solve some generic problems of behavioral economics, decision theories, and the social sciences.
{"title":"Forbidden Zones for the Expectations of Data: New Mathematical Methods and Models for Behavioral Economics","authors":"A. Harin","doi":"10.32861/ajams.81.12.26","DOIUrl":"https://doi.org/10.32861/ajams.81.12.26","url":null,"abstract":"A forbidden zone theorem, hypothesis, and applied mathematical method and model are introduced in the present article. The method and model are based on the forbidden zones and hypothesis. The article is initiated by the well-known generic problems concerned with the mathematical description of the behavior of a man. The essence of the problems consists in biases of preferences and decisions of a man in comparison with predictions of the probability theory. The model is uniformly and successfully applied for different domains. The ultimate goal of the research is to solve some generic problems of behavioral economics, decision theories, and the social sciences.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126970451","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}
This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.
{"title":"Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application","authors":"Oseghale O. I., Akomolafe A. A., Gayawan E.","doi":"10.32861/ajams.81.1.11","DOIUrl":"https://doi.org/10.32861/ajams.81.1.11","url":null,"abstract":"This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121511664","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 : 2021-09-13DOI: 10.32861/ajams.74.192.197
Faisal F Alamri, Ezz H. Abdelfattah, K. Sait, N. Anfinan, H. Sait
The four levels of data analytics techniques (descriptive, diagnostic, predictive, and perspective) were used as a methodology. We also used data mining techniques to predict Gynecologic cancer before any lab test or surgical intervention. Influencing and associating between factors are used to cover hidden relationships or unknown patterns. We focused on three types of Gynecologic cancer (cervical, endometrial, and ovarian cancer). We collected an initial examination of 513 (228 benign and 285 malignant) patients from King Abdulaziz University Hospital (Saudi Arabia). Data were collected during the period of 16 years (2000-2016). After examining many models, we found that the classification trees C5 and CHAID beside the Support Vector Machine (SVM) algorithm give the highest accuracy, with the values of 87.33 %, 79.53%, and 78.36 % respectively. The sensitivity and specificity were found to be 86.18 % and 89.00 % for C5. The corresponding values for CHAID were found to be to equals to 82.20 % and 76.72 % while for support vector machine (SVM) the values were found to be 83.74 % and 77.10 %.
{"title":"Building a Predictive Model for Gynecologic Cancer Using Levels of Data Analytics","authors":"Faisal F Alamri, Ezz H. Abdelfattah, K. Sait, N. Anfinan, H. Sait","doi":"10.32861/ajams.74.192.197","DOIUrl":"https://doi.org/10.32861/ajams.74.192.197","url":null,"abstract":"The four levels of data analytics techniques (descriptive, diagnostic, predictive, and perspective) were used as a methodology. We also used data mining techniques to predict Gynecologic cancer before any lab test or surgical intervention. Influencing and associating between factors are used to cover hidden relationships or unknown patterns. We focused on three types of Gynecologic cancer (cervical, endometrial, and ovarian cancer). We collected an initial examination of 513 (228 benign and 285 malignant) patients from King Abdulaziz University Hospital (Saudi Arabia). Data were collected during the period of 16 years (2000-2016). After examining many models, we found that the classification trees C5 and CHAID beside the Support Vector Machine (SVM) algorithm give the highest accuracy, with the values of 87.33 %, 79.53%, and 78.36 % respectively. The sensitivity and specificity were found to be 86.18 % and 89.00 % for C5. The corresponding values for CHAID were found to be to equals to 82.20 % and 76.72 % while for support vector machine (SVM) the values were found to be 83.74 % and 77.10 %.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128382942","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 : 2021-08-13DOI: 10.32861/ajams.74.187.191
C. Wei, Jian Wang
Eigenspace is a convenient way to represent sets of observations with widespread applications, so it is necessary to accurately calculate the eigenspace of data. With the advent of the era of big data, the increasing and updating of data bring great challenges to the solution of eigenspace. Hall, et al. [1], proposed that the incremental method could update the eigenspace of data online, which reduces computational costs and storage space. In this paper, the updating coefficient of the sample covariance matrix in an incremental method is modified. Numerical analysis shows that the modified updating form has better performance.
{"title":"The Modified Increment Method for Eigenspace Model","authors":"C. Wei, Jian Wang","doi":"10.32861/ajams.74.187.191","DOIUrl":"https://doi.org/10.32861/ajams.74.187.191","url":null,"abstract":"Eigenspace is a convenient way to represent sets of observations with widespread applications, so it is necessary to accurately calculate the eigenspace of data. With the advent of the era of big data, the increasing and updating of data bring great challenges to the solution of eigenspace. Hall, et al. [1], proposed that the incremental method could update the eigenspace of data online, which reduces computational costs and storage space. In this paper, the updating coefficient of the sample covariance matrix in an incremental method is modified. Numerical analysis shows that the modified updating form has better performance.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"543 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123914334","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 : 2021-07-29DOI: 10.32861/ajams.73.179.186
N. V. Toàn, Pham Ngoc Van, N. T. Tung, Nguyen Ngoc Dien
The article presents a method for designing the trajectory of the UAV in space, taking into account the restriction on control. The chosen optimal controls are namely normal overload with restrictions, tangential overload with restrictions, and lateral overload. The Pontryagin maximum principle allows the transition of the optimal control problem to a boundary value problem. The parameter continuation method is applied to solve the boundary problem. The article results reveal reference trajectories in different cases of UAV landing. This result allows the design of reference trajectories for the UAV to attain the highest landing efficiency.
{"title":"Landing Trajectory Design for UAV Considering Control Restrictions and Landing Speed","authors":"N. V. Toàn, Pham Ngoc Van, N. T. Tung, Nguyen Ngoc Dien","doi":"10.32861/ajams.73.179.186","DOIUrl":"https://doi.org/10.32861/ajams.73.179.186","url":null,"abstract":"The article presents a method for designing the trajectory of the UAV in space, taking into account the restriction on control. The chosen optimal controls are namely normal overload with restrictions, tangential overload with restrictions, and lateral overload. The Pontryagin maximum principle allows the transition of the optimal control problem to a boundary value problem. The parameter continuation method is applied to solve the boundary problem. The article results reveal reference trajectories in different cases of UAV landing. This result allows the design of reference trajectories for the UAV to attain the highest landing efficiency.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121998666","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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