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Applied Mathematics-A Journal of Chinese Universities Series B最新文献

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On the Lanzhou Indices of Trees under Graph Decoration 图形装饰下兰州树木指数研究
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-01-01 DOI: 10.4236/AM.2021.122007
Xiaolin Zeng, Tingzeng Wu
{"title":"On the Lanzhou Indices of Trees under Graph Decoration","authors":"Xiaolin Zeng, Tingzeng Wu","doi":"10.4236/AM.2021.122007","DOIUrl":"https://doi.org/10.4236/AM.2021.122007","url":null,"abstract":"The Lanzhou index of a graph G is defined as the sum of the product between and square of du over all vertices u of G, where du and are respectively the degree of u in G and the degree of u in the complement graph of G. R(G) is obtained from G by adding a new vertex corresponding to each edge of G, then joining each new vertex to the end vertices of the corresponding edge. Lanzhou index is an important topological index. It is closely related to the forgotten index and first Zagreb index of graphs. In this note, we characterize the bound of Lanzhou index of R(T) of a tree T. And the corresponding extremal graphs are also determined.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74933428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function 具有变符号格林函数的四阶三点BVP正解的存在性
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-01-01 DOI: 10.4236/AM.2021.124022
A. Mohamed
{"title":"Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function","authors":"A. Mohamed","doi":"10.4236/AM.2021.124022","DOIUrl":"https://doi.org/10.4236/AM.2021.124022","url":null,"abstract":"","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78377155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Stochastic Strategy for Optimizing the Cost of Systematic Screening of Some Diseases in a Situation of Insufficient Equipment 设备不足情况下某些疾病系统筛查成本优化的随机策略
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-12-08 DOI: 10.4236/am.2020.1112086
Lucien Zihindula Biguru
{"title":"A Stochastic Strategy for Optimizing the Cost of Systematic Screening of Some Diseases in a Situation of Insufficient Equipment","authors":"Lucien Zihindula Biguru","doi":"10.4236/am.2020.1112086","DOIUrl":"https://doi.org/10.4236/am.2020.1112086","url":null,"abstract":"In this work, we show that when there is insufficient equipment for detecting a disease whose prevalence is t% in a sub-population of size N, it is optimal to divide the N samples into n groups of size r each and then, the value allows systematic screening of all N individuals by performing less than N tests (In this expression, represents the floor function1 of x ∈ R). Based on this result and on certain functions of the R software, we subsequently propose a probabilistic strategy capable of optimizing the screening tests under certain conditions.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87686819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems 求解椭圆型Neumann边界控制问题的有限体积元法
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-12-08 DOI: 10.4236/am.2020.1112085
Quanxiang Wang
{"title":"Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems","authors":"Quanxiang Wang","doi":"10.4236/am.2020.1112085","DOIUrl":"https://doi.org/10.4236/am.2020.1112085","url":null,"abstract":"Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L2 (Γ) and L∞ (Γ) norm. For state and adjoint state, optimal convergence order in the L2 (Ω) and H1 (Ω) can also be obtained.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91223892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Credit Card Fraud Detection Using Weighted Support Vector Machine 基于加权支持向量机的信用卡欺诈检测
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-12-08 DOI: 10.4236/am.2020.1112087
Dongfang Zhang, B. Bhandari, Dennis Black
{"title":"Credit Card Fraud Detection Using Weighted Support Vector Machine","authors":"Dongfang Zhang, B. Bhandari, Dennis Black","doi":"10.4236/am.2020.1112087","DOIUrl":"https://doi.org/10.4236/am.2020.1112087","url":null,"abstract":"Credit card fraudulent data is highly imbalanced, and it has presented an overwhelmingly large portion of nonfraudulent transactions and a small portion of fraudulent transactions. The measures used to judge the veracity of the detection algorithms become critical to the deployment of a model that accurately scores fraudulent transactions taking into account case imbalance, and the cost of identifying a case as genuine when, in fact, the case is a fraudulent transaction. In this paper, a new criterion to judge classification algorithms, which considers the cost of misclassification, is proposed, and several undersampling techniques are compared by this new criterion. At the same time, a weighted support vector machine (SVM) algorithm considering the financial cost of misclassification is introduced, proving to be more practical for credit card fraud detection than traditional methodologies. This weighted SVM uses transaction balances as weights for fraudulent transactions, and a uniformed weight for nonfraudulent transactions. The results show this strategy greatly improve performance of credit card fraud detection.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74609141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
The Application of Linear Ordinary Differential Equations 线性常微分方程的应用
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-12-08 DOI: 10.4236/am.2020.1112088
Haoyang Cui
{"title":"The Application of Linear Ordinary Differential Equations","authors":"Haoyang Cui","doi":"10.4236/am.2020.1112088","DOIUrl":"https://doi.org/10.4236/am.2020.1112088","url":null,"abstract":"In this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although linear ODEs have a comparatively easy form, they are effective in solving certain physical and geometrical problems. We will begin by introducing fundamental knowledge in Linear Algebra and proving the existence and uniqueness of solution for ODEs. Then, we will concentrate on finding the solutions for ODEs and introducing the matrix method for solving linear ODEs. Eventually, we will apply the conclusions we’ve gathered from the previous parts into solving problems concerning Physics and differential curves. The matrix method is of great importance in doing higher dimensional computations, as it allows multiple variables to be calculated at the same time, thus reducing the complexity.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73111401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 Ball Proximinality 关于球的近端性的注释
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-11-02 DOI: 10.4236/am.2020.1111081
Bo Wang, Xiaoyan Liu
{"title":"A Note on Ball Proximinality","authors":"Bo Wang, Xiaoyan Liu","doi":"10.4236/am.2020.1111081","DOIUrl":"https://doi.org/10.4236/am.2020.1111081","url":null,"abstract":"In this paper, we prove when these x ∈ l2 with , they have the common δ for strongly ball proximinal. By using this property, we can prove the strong ball proximinality of l∞(l2). Also, we show that equable subspace Y of a Banach space X is actually uniform ball proximinality.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80098987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients 系数不连续SPDEs的随机粘度解
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-11-02 DOI: 10.4236/am.2020.1111083
Yidong Zhang
{"title":"Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients","authors":"Yidong Zhang","doi":"10.4236/am.2020.1111083","DOIUrl":"https://doi.org/10.4236/am.2020.1111083","url":null,"abstract":"In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function fn to the coefficient f, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78781511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Iterating with Fuzzy Parameters to Produce Exact Results 用模糊参数迭代产生精确结果
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-11-02 DOI: 10.4236/am.2020.1111072
E. Klingman
{"title":"Iterating with Fuzzy Parameters to Produce Exact Results","authors":"E. Klingman","doi":"10.4236/am.2020.1111072","DOIUrl":"https://doi.org/10.4236/am.2020.1111072","url":null,"abstract":"Iteration problems such as compound interest calculations have well-specified parameters and aim to derive an exact value. Not all problems offer well-specified parameters, even for well-defined dynamic equations; the linear “weak field approximation” of general relativity is iteratively equivalent to Einstein’s non-linear field equation, but the exact parameters involved in some applications are unknown. This paper develops a theory based on “fuzzy” parameters that must produce exact results. The problem is analyzed and example calculations are produced.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78510152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Multiplicative Generators of n-Dimensional Overlap Functions 关于n维重叠函数的乘法生成
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-11-02 DOI: 10.4236/am.2020.1111071
Hai Xie
{"title":"On Multiplicative Generators of n-Dimensional Overlap Functions","authors":"Hai Xie","doi":"10.4236/am.2020.1111071","DOIUrl":"https://doi.org/10.4236/am.2020.1111071","url":null,"abstract":"In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80342986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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