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Some results in function weighted b-metric spaces 函数加权b-度量空间中的一些结果
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023417
B. Nurwahyu, N. Aris, Firman
{"title":"Some results in function weighted b-metric spaces","authors":"B. Nurwahyu, N. Aris, Firman","doi":"10.3934/math.2023417","DOIUrl":"https://doi.org/10.3934/math.2023417","url":null,"abstract":"<abstract> <p>In this paper, we introduce <italic>F</italic>-<italic>b</italic>-metric space (function weighted <italic>b</italic>-metric space) as a generalization of the <italic>F</italic>-metric space (the function weighted metric space). We also propose and prove some topological properties of the <italic>F</italic>-<italic>b</italic>-metric space, the theorems of fixed point and the common fixed point for the generalized expansive mappings, and an application on dynamic programing.</p> </abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Orbital stability of periodic standing waves of the coupled Klein-Gordon-Zakharov equations 耦合Klein-Gordon-Zakharov方程周期驻波的轨道稳定性
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023430
Qiuying Li, Xiaoxiao Zheng, Zhenguo Wang
{"title":"Orbital stability of periodic standing waves of the coupled Klein-Gordon-Zakharov equations","authors":"Qiuying Li, Xiaoxiao Zheng, Zhenguo Wang","doi":"10.3934/math.2023430","DOIUrl":"https://doi.org/10.3934/math.2023430","url":null,"abstract":"This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document} $ begin{equation*} left{ begin{aligned} &u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*} $ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lam'{e} equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms 带源项的浅水方程两步预测校正方法的稳定性分析和收敛速度
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023465
R. T. Alqahtani, J. Ntonga, E. Ngondiep
{"title":"Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms","authors":"R. T. Alqahtani, J. Ntonga, E. Ngondiep","doi":"10.3934/math.2023465","DOIUrl":"https://doi.org/10.3934/math.2023465","url":null,"abstract":"This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Double total domination number of Cartesian product of paths 路径笛卡尔积的双总支配数
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023479
Linyu Li, Jun Yue, Xia Zhang
{"title":"Double total domination number of Cartesian product of paths","authors":"Linyu Li, Jun Yue, Xia Zhang","doi":"10.3934/math.2023479","DOIUrl":"https://doi.org/10.3934/math.2023479","url":null,"abstract":"A vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ gamma_{times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i geq 4 $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Cubic B-Spline method for the solution of the quadratic Riccati differential equation 三次b样条法求解二次Riccati微分方程
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023483
O. Ala'yed, B. Batiha, Diala Alghazo, F. Ghanim
{"title":"Cubic B-Spline method for the solution of the quadratic Riccati differential equation","authors":"O. Ala'yed, B. Batiha, Diala Alghazo, F. Ghanim","doi":"10.3934/math.2023483","DOIUrl":"https://doi.org/10.3934/math.2023483","url":null,"abstract":"The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70187140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
A space-time model for analyzing contagious people based on geolocation data using inverse graphs 一种基于地理位置数据的时空模型，利用逆图分析传染性人群
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023516
S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara
{"title":"A space-time model for analyzing contagious people based on geolocation data using inverse graphs","authors":"S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara","doi":"10.3934/math.2023516","DOIUrl":"https://doi.org/10.3934/math.2023516","url":null,"abstract":"Mobile devices provide us with an important source of data that capture spatial movements of individuals and allow us to derive general mobility patterns for a population over time. In this article, we present a mathematical foundation that allows us to harmonize mobile geolocation data using differential geometry and graph theory to identify spatial behavior patterns. In particular, we focus on models programmed using Computer Algebra Systems and based on a space-time model that allows for describing the patterns of contagion through spatial movement patterns. In addition, we show how the approach can be used to develop algorithms for finding \"patient zero\" or, respectively, for identifying the selection of candidates that are most likely to be contagious. The approach can be applied by information systems to evaluate data on complex population movements, such as those captured by mobile geolocation data, in a way that analytically identifies, e.g., critical spatial areas, critical temporal segments, and potentially vulnerable individuals with respect to contact events.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Discrete Erlang-2 distribution and its application to leukemia and COVID-19 离散Erlang-2分布及其在白血病和COVID-19中的应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023520
Mohamed Ahmed Mosilhy
{"title":"Discrete Erlang-2 distribution and its application to leukemia and COVID-19","authors":"Mohamed Ahmed Mosilhy","doi":"10.3934/math.2023520","DOIUrl":"https://doi.org/10.3934/math.2023520","url":null,"abstract":"Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 review on portfolio optimization models for Islamic finance 伊斯兰金融投资组合优化模型综述
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023523
Doong Toong Lim, K. Goh, Y. Sim
{"title":"A review on portfolio optimization models for Islamic finance","authors":"Doong Toong Lim, K. Goh, Y. Sim","doi":"10.3934/math.2023523","DOIUrl":"https://doi.org/10.3934/math.2023523","url":null,"abstract":"The era of modern portfolio theory began with the revolutionary approach by Harry Markowitz in 1952. However, several drawbacks of the model have rendered it impractical to be used in reality. Thus, various modifications have been done to refine the classical model, including concerns about risk measures, trading practices and computational efficiency. On the other hand, Islamic finance is proven to be a viable alternative to the conventional system following its outstanding performance during the financial crisis in 2008. This emerging sector has gained a lot of attention from investors and economists due to its significantly increasing impact on today's economy, corresponding to globalization and a demand for a sustainable investment strategy. A comprehensive literature review of the notable conventional and Islamic models is done to aid future research and development of portfolio optimization, particularly for Islamic investment. Additionally, the study provides a concisely detailed overview of the principles of Islamic finance to prepare for the future development of an Islamic finance model. Generally, this study outlines the comprehensive features of portfolio optimization models over the decades, with an attempt to classify and categorize the advantages and drawbacks of the existing models. The trend of portfolio optimization modelling can be captured by gathering and recording the problems and solutions of the reviewed models.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70189076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application 新非扩张映射不动点数值推算的迭代格式及其应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023543
K. Ullah, Junaid Ahmad, H. Hammad, R. George
{"title":"Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application","authors":"K. Ullah, Junaid Ahmad, H. Hammad, R. George","doi":"10.3934/math.2023543","DOIUrl":"https://doi.org/10.3934/math.2023543","url":null,"abstract":"The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called $ (alpha, beta, gamma) $-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the $ K $-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the $ K $-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the $ K $-type iterative method to solve a variational inequality problem on a Hilbert space.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"31 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70189874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Pricing of vulnerable options based on an uncertain CIR interest rate model 基于不确定CIR利率模型的脆弱期权定价
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.2023563
Guiwen Lv, Ping Xu, Yanxue Zhang
{"title":"Pricing of vulnerable options based on an uncertain CIR interest rate model","authors":"Guiwen Lv, Ping Xu, Yanxue Zhang","doi":"10.3934/math.2023563","DOIUrl":"https://doi.org/10.3934/math.2023563","url":null,"abstract":"The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70190904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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