American journal of applied mathematics and statistics最新文献

{"title":"An Axiomatic Approach to Gröbner Basis Theory by Examining Several Reduction Principles","authors":"G. Landsmann, Christoph Fürst","doi":"10.11648/J.AJAM.20210904.14","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210904.14","url":null,"abstract":"Several variants of the classical theory of Grobner bases can be found in the literature. They come, depending on the structure they operate on, with their own specific peculiarity. Setting up an expedient reduction concept depends on the arithmetic equipment that is provided by the structure in question. Often it is necessary to introduce a term order that can be used for determining the orientation of the reduction, the choice of which might be a delicate task. But there are other situations where a different type of structure might give the appropriate basis for formulating adequate rewrite rules. In this paper we have tried to find a unified concept for dealing with such situations. We develop a global theory of Grobner bases for modules over a large class of rings. The method is axiomatic in that we demand properties that should be satisfied by a reduction process. Reduction concepts obeying the principles formulated in the axioms are then guaranteed to terminate. The class of rings we consider is large enough to subsume interesting candidates. Among others this class contains rings of differential operators, Ore-algebras and rings of difference-differential operators. The theory is general enough to embrace the well-known classical Grobner basis concepts of commutative algebra as well as several modern approaches for modules over relevant noncommutative rings. We start with introducing the appropriate axioms step by step, derive consequences from them and end up with the Buchberger Algorithm, that makes it possible to compute a Grobner basis. At the end of the paper we provide a few examples to illustrate the abstract concepts in concrete situations.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75920158","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}

{"title":"Modelling a Multilevel Data Structure Using a Composite Index","authors":"Prabath Badullahewage, D. Attygalle","doi":"10.12691/AJAMS-9-3-1","DOIUrl":"https://doi.org/10.12691/AJAMS-9-3-1","url":null,"abstract":"When modelling complexed data structures related to a certain social aspect, there could be various hierarchical levels where data units are nested within each other. There could also be several variables in each level, and those variables may not be unique for each case or record, making the data structure even more complexed. Multilevel modelling has been used for decades, to handle such data structures, but may not be effective at all times to capture the structure fully, due to the extent of complexities of the data structure and the inherent issues of the procedure. On the contrary, ignoring the multilevel data structure when modelling, can lead to incorrect estimations and thereby may not achieve acceptable accuracies from the model. This research explains a simple approach where a complexed multilevel structure is compressed to a single level by combining higher level variables to form a composite index. Moreover, this composite index, also reduces the number of variables considered in the entire modelling process, substantially. The process is exemplified, using a primary data set gathered on household education expenditure using a systematic sampling survey. Several variables are collected on each household and another set of variables relating to each school going child in the household, creating a multilevel data structure. The composite index, named as, i°Household Level Education Indexi± is developed through a factor analysis where the detailed process of its construction is explained. The LASSO regression was performed to illustrate the use of the proposed composite index by predicting the monthly household education expenditure through a single level regression model. Finally, a Random Forest model was used to examine the feature importance, where the proposed composite index i°Household level education indexi± was the most important feature in predicting the monthly household educational expenditure.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"18 1","pages":"75-82"},"PeriodicalIF":0.0,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89412967","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}

{"title":"Common Fixed Point of Generalized αs-ψ-Geraghty Contractive Mappings on b-metric Spaces","authors":"Jianju Li, H. Guan","doi":"10.12691/AJAMS-9-2-5","DOIUrl":"https://doi.org/10.12691/AJAMS-9-2-5","url":null,"abstract":"In this paper, we study the existence and uniqueness of common fixed point of generalized αs-ψ-Geraghty contractive mapping in the framework of b-metric spaces. We give an example to prove the validity of our conclusion.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82365662","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}

{"title":"Post Hoc Analysis of Life Expectancy in West Africa","authors":"Jonathan Iworiso","doi":"10.12691/AJAMS-9-2-4","DOIUrl":"https://doi.org/10.12691/AJAMS-9-2-4","url":null,"abstract":"This paper investigates the effect of country, gender and the associated interaction term on life expectancy in West African countries. The empirical analysis revealed that country and gender have statistically significant effect on life expectancy in West Africa, while the associated interaction term has no significant effect on life expectancy. Thus the removal of the nuisance interaction term seems to improve the predictive task of the statistical model. The empirical findings in this paper revealed that Cape Verde has the highest average life expectancy among all the West African countries, which also ranks highest in the United Nations index of West Africa. The Tukey HSD tests provide statistically significant differences between countries with higher life expectancy and countries with lower life expectancy. This accounts for the variation in life expectancy between the West African countries. Contrary to the notion in some previous reports which believed that countries with higher GDP tend to have a higher life expectancy, and that the difference in life expectancy per difference in GDP per capita is higher for poorer than for richer countries; this paper reveals that most West African countries endowed with natural resources resulting to higher GDP tend to have lower life expectancy.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91016015","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}

{"title":"Pressure Control Design of High-Pressure Fuel Pipe","authors":"Shih-Shan Wei, Chunyong Wang, Tailin Cen, Yuhua Su","doi":"10.11648/J.AJAM.20210904.11","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210904.11","url":null,"abstract":"In order to ensure the normal operation of the engine, the stability of the fuel supply system must be ensured. The fuel supply system needs to obtain fuel from the outside, and then pressurized into the high-pressure oil pipe, and then input into the engine cylinder. Therefore, the fuel parameters in the components of the fuel supply system affect each other. In this paper, a mathematical model is established to describe the relationship between the fuel parameters of each part of the fuel supply system, and then the stability of the fuel supply system can be controlled by controlling some parameters under given conditions. We intercept a very short time, analyze the mutual transfer of fuel in the fuel supply system through the micro element method, and establish the differential equations. Because some differential equations are more complex, it is difficult to find the formula solution, so we discretize the differential equations and get a group of recurrence relations. After calculating the initial state and related parameters, the fuel pressure parameters and fuel density parameters of each part of the fuel supply system at each time can be obtained recursively. Because the pressure and density of the fuel can express each other, we focus on the density parameter of the fuel, and do the conversion when the pressure is needed. On the basis of this group of recursive relations, we established an optimization model of fuel pressure control in high-pressure oil pipe: Taking the fuel supply time of one-way valve as decision variables, minimizing the difference between fuel pressure and standard value at each time as optimization objective, taking the practical significance of each physical quantity as constraint condition, and gave a discrete algorithm.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88750699","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}

{"title":"A Maximization Problem Involving a Fractional Laplace Type Operator","authors":"C. Qiu","doi":"10.11648/j.ajam.20210903.14","DOIUrl":"https://doi.org/10.11648/j.ajam.20210903.14","url":null,"abstract":"Fractional Laplacian is an important nonlocal operator which has many applications in different kinds of differential equations. Recently, optimization problems involving the fractional Laplacian have been studied a lot by many authors. However, most of these papers are focusing on the optimization problems related to the first eigenvalue of the equation. Optimization problems related to the energy functional of the equation have not been investigated well enough. In this paper, we are going to study a maximization problem related to the energy functional of an equation involving a fractional Laplace type operator. Firstly, by using suitable variational framework in a fractional Sobolev space, we can show that a fractional equation has a solution which is in fact the global minimum of the corresponding energy functional. Moreover, by using reduction to absurdity we can obtain the uniqueness of the solution of the fractional equation. Then, we focus on a maximization problem related to the equation which takes the energy functional as the objective functional. Finally, by carefully analysing the properties of an arbitrarily choosen minimizing sequence and the tools of the rearrangement theory, we can prove that the maximization problem is solvable.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85667222","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}

{"title":"Modelling Chlamydia Trachomatis Infection Among Young Women in Ghana: A Case Study at Tarkwa Nsuaem Municipality","authors":"C. Nyarko, Nicholas Nicodemus Nana Nsowa-Nuamah, P. Nyarko, E. N. Wiah, A. Buabeng","doi":"10.11648/j.ajam.20210903.13","DOIUrl":"https://doi.org/10.11648/j.ajam.20210903.13","url":null,"abstract":"Chlamydia Genital infection has been a global health issue especially among most developing countries. Although, a lot of researchers have modelled CT infection to determine the impact of different intervals between Chlamydia infection and the development of Pelvic Inflammatory Disease (PID) on the cost-effectiveness of screening and the use of Chlamydia vaccine. This paper seeks to model the dynamics of Chlamydia Trachomatis (CT) infection among females who were diagnosed of vaginal discharge and the likelihood of developing PID complications. The model was formulated using a sexual network to explore the relationship between Chlamydia infection through diagnosed vaginal infection and PID. A sample of 147 females were diagnosed and screened of Chlamydia related symptoms on a routine check-up in the Tarkwa Nsuaem Municipality in the Western part of Ghana. Lyapunov functions was used to prove the necessary and sufficient conditions for Stability State of the system while Next Generation Method was also used to calculate the basic reproduction number (R0). The Stability Analysis of the Modified SIRS model shows that the system is locally and asymptotically stable at the Disease-Free Equilibrium (DFE) E0, when R0 1, the Endemic Equilibrium (EE) E*, was found to be locally and asymptotically stable at certain conditions. It was observed that, as the distribution increases sharply at a given contact rate (β) of 0.05, many of the patients were infected within the first three days as compared to when the contact rate was 0.001. Moreover, at contact rates (β) of 0.5, R0 was greater than one, this shows how CT infection spreads in the population using parameter values in Table 1. Thus, the effects of change in the various initial conditions of the parameters (λ) and (β) on vaginal discharge and PID infections, turn to increase sharply at a higher infection rate for the first ten days of infection especially with vaginal discharge and then become stable over a period of time. This confirms the incubation period which is usually 7 to 10 days of infection. The paper concludes that, young women aged 18-24 years are more at risk of Chlamydia Trachomatis infection if diagnosed of vaginal discharge or PID and suggest early medication which is highly subsidised will help curb the spread of CT infection in the Municipality.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88596940","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}

{"title":"The Problem of Setting Traffic Signal Cycles at Crossroads","authors":"D. Alexiou, Leonidas Bakouros","doi":"10.11648/J.AJAM.20210903.12","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210903.12","url":null,"abstract":"In this paper, the problem of setting traffic light cycles at crossroads and intersections is considered in order to reduce traffic congestion by minimizing total vehicle waiting time. A method to determine the family ℘ of all discrete cycle phasing systems with the minimum number of phases is presented. The aim is to detect the most appropriate phasing sequence for traffic control corresponding to a current traffic situation from among all the components of ℘. The method is applied at a complex multi-cross intersection. The problem, dealing with traffic movements and the conflicting relations that arise, is stated within the framework of graph theory. There are several methods for setting traffic signal cycles at traffic light intersections. In this paper and in the context of graph theory, we develop a method which aims to determine the family of all discrete phases of phase systems with the smallest number of phases. The aim is to select from the elements of the the appropriate phase system that corresponds to the current traffic situation.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78895377","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}

{"title":"The Cauchy Operator and the Homogeneous Hahn Polynomials","authors":"Qiuxia Hu, Xinhao Huang, Zhizheng Zhang","doi":"10.11648/J.AJAM.20210903.11","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210903.11","url":null,"abstract":"The Cauchy operator plays important roles in the theory of basic hypergeometric series. As some applications, our purpose is mainly to show new proofs of the Mehler’s formula, the Rogers formula and the generating function for the homogeneous Hahn polynomials Φ(α)n(x,y|q)) by making use of the Cauchy operator and its properties. In addition, some interesting results are also obtained, which include a formal extension of the generating function for Φ(α)n(x,y|q)).","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73998511","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}

{"title":"On the Applications of Ricatti Differential Equations to Some Special Cases of the Two-Body Problem with Variable Masses","authors":"Ilhan M. Izmirli","doi":"10.12691/AJAMS-9-2-3","DOIUrl":"https://doi.org/10.12691/AJAMS-9-2-3","url":null,"abstract":"In this paper, we obtain the solution of the two-body problem with variable masses by posing some assumptions on the classical equation and thereby reducing the solution of the problem to investigating the solutions of some Ricatti type differential equations. Along this process, we also give a simple proof of the well-known Mestscherskii Theorem and establish some related formal relations under these assumptions.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"81 1","pages":"53-56"},"PeriodicalIF":0.0,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89004257","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}