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Excess profit relative to the benchmark asset under the $ alpha $-confidence level 在$ alpha $-置信水平下相对于基准资产的超额利润
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231553
Dong Ma, Peibiao Zhao, Minghan Lyu, Jun Zhao
{"title":"Excess profit relative to the benchmark asset under the $ alpha $-confidence level","authors":"Dong Ma, Peibiao Zhao, Minghan Lyu, Jun Zhao","doi":"10.3934/math.20231553","DOIUrl":"https://doi.org/10.3934/math.20231553","url":null,"abstract":"<abstract><p>We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ alpha $-confidence level, $ alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ alpha $-REP.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135562870","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
On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations Petryshyn不动点定理的推广及其在n -非线性积分方程积中的应用
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231562
Ateq Alsaadi, Manochehr Kazemi, Mohamed M. A. Metwali
{"title":"On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations","authors":"Ateq Alsaadi, Manochehr Kazemi, Mohamed M. A. Metwali","doi":"10.3934/math.20231562","DOIUrl":"https://doi.org/10.3934/math.20231562","url":null,"abstract":"<abstract><p>Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135610499","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
Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators 基于分段分数阶算子的SARS-COVID-19 seir型数学模型分析
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231382
Nadiyah Hussain Alharthi, Mdi Begum Jeelani
{"title":"Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators","authors":"Nadiyah Hussain Alharthi, Mdi Begum Jeelani","doi":"10.3934/math.20231382","DOIUrl":"https://doi.org/10.3934/math.20231382","url":null,"abstract":"<abstract><p>Recently, the area devoted to mathematical epidemiology has attracted much attention. Mathematical formulations have served as models for various infectious diseases. In this regard, mathematical models have also been used to study COVID-19, a threatening disease in present time. This research work is devoted to consider a SEIR (susceptible-exposed-infectious-removed) type mathematical model for investigating COVID-19 alongside a new scenario of fractional calculus. We consider piece-wise fractional order derivatives to investigate the proposed model for qualitative and computational analysis. The results related to the qualitative analysis are studied via using the tools of fixed point approach. In addition, the computational analysis is performed due to a significance of simulation to understand the transmission dynamics of COVID-19 infection in the community. In addition, a numerical scheme based on Newton's polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Additionally, some real data results are also shown in comparison to the numerical results.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135653429","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
Mathematical modeling for the development of traffic based on the theory of system dynamics 基于系统动力学理论的交通发展数学建模
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231413
Juan Manuel Sánchez, Adrián Valverde, Juan L. G. Guirao, Huatao Chen
{"title":"Mathematical modeling for the development of traffic based on the theory of system dynamics","authors":"Juan Manuel Sánchez, Adrián Valverde, Juan L. G. Guirao, Huatao Chen","doi":"10.3934/math.20231413","DOIUrl":"https://doi.org/10.3934/math.20231413","url":null,"abstract":"<abstract><p>This paper is concerned with mathematical modeling for the development of Shandong traffic. The system dynamics model of the development of traffic in Shandong is established. In terms of this model, it is shown that highway operation as well as rail transit promotes the development of traffic, while traffic accidents inhibit traffic development. Moreover, the maximum error between the output data and the statistics bureau, based on which some forecasts for the development of traffic in the future are given, is obtained, some suggestions and optimization schemes for traffic development are given. Finally, a neural network model of the development of Shandong traffic is also derived.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053176","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
Double sequences with ideal convergence in fuzzy metric spaces 模糊度量空间中具有理想收敛性的二重序列
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231437
Aykut Or
{"title":"Double sequences with ideal convergence in fuzzy metric spaces","authors":"Aykut Or","doi":"10.3934/math.20231437","DOIUrl":"https://doi.org/10.3934/math.20231437","url":null,"abstract":"<abstract><p>We show ideal convergence ($ I $-convergence), ideal Cauchy ($ I $-Cauchy) sequences, $ I^* $-convergence and $ I^* $-Cauchy sequences for double sequences in fuzzy metric spaces. We define the $ I $-limit and $ I $-cluster points of a double sequence in these spaces. Afterward, we provide certain fundamental properties of the aspects. Lastly, we discuss whether the phenomena should be further investigated.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136303908","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
Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions 具有不同幂哈密顿函数的非线性时滞系统的自适应预定义时间鲁棒控制
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231441
Shutong Liu, Renming Yang
{"title":"Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions","authors":"Shutong Liu, Renming Yang","doi":"10.3934/math.20231441","DOIUrl":"https://doi.org/10.3934/math.20231441","url":null,"abstract":"<abstract><p>The article studies $ H_infty $ control as well as adaptive robust control issues on the predefined time of nonlinear time-delay systems with different power Hamiltonian functions. First, for such Hamiltonian systems with external disturbance and delay phenomenon, we construct the appropriate Lyapunov function and Hamiltonian function of different powers. Then, a predefined-time $ H_infty $ control approach is presented to stabilize the systems within a predefined time. Furthermore, when considering nonlinear Hamiltonian system with unidentified disturbance, parameter uncertainty and delay, we devise a predefined-time adaptive robust strategy to ensure that the systems reach equilibrium within one predefined time and have better resistance to disturbance and uncertainty. Finally, the validity of the results is verified with a river pollution control system example.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136307206","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
An estimate for the numerical radius of the Hilbert space operators and a numerical radius inequality 希尔伯特空间算子的数值半径估计和数值半径不等式
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231347
Mohammad H. M. Rashid, Feras Bani-Ahmad
{"title":"An estimate for the numerical radius of the Hilbert space operators and a numerical radius inequality","authors":"Mohammad H. M. Rashid, Feras Bani-Ahmad","doi":"10.3934/math.20231347","DOIUrl":"https://doi.org/10.3934/math.20231347","url":null,"abstract":"<abstract><p>We provide a number of sharp inequalities involving the usual operator norms of Hilbert space operators and powers of the numerical radii. Based on the traditional convexity inequalities for nonnegative real numbers and some generalize earlier numerical radius inequalities, operator. Precisely, we prove that if $ {bf A}_i, {bf B}_i, {bf X}_iin mathcal{B}(mathcal{H}) $ ($ i = 1, 2, cdots, n $), $ min mathbb N $, $ p, q &amp;gt; 1 $ with $ frac{1}{p}+frac{1}{q} = 1 $ and $ phi $ and $ psi $ are non-negative functions on $ [0, infty) $ which are continuous such that $ phi(t)psi(t) = t $ for all $ t in [0, infty) $, then</p> <p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ begin{equation*} w^{2r}left({sumlimits_{i = 1}^{n} {bf X}_i {bf A}_i^m {bf B}_i}right)leq frac{n^{2r-1}}{m}sumlimits_{j = 1}^{m}leftVert{sumlimits_{i = 1}^{n}frac{1}{p}S_{i, j}^{pr}+frac{1}{q}T_{i, j}^{qr}}rightVert-r_0inflimits_{leftVert{xi}rightVert = 1}rho(xi), end{equation*} $end{document} </tex-math></disp-formula></p> <p>where $ r_0 = min{frac{1}{p}, frac{1}{q}} $, $ S_{i, j} = {bf X}_iphi^2left({leftvert{ {bf A}_i^{j*}}rightvert}right) {bf X}_i^* $, $ T_{i, j} = left({ {bf A}_i^{m-j} {bf B}_i}right)^*psi^2left({leftvert{ {bf A}_i^j}rightvert}right) {bf A}_i^{m-j} {bf B}_i $ and</p> <p><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ rho(xi) = frac{n^{2r-1}}{m}sumlimits_{j = 1}^{m}sumlimits_{i = 1}^{n}left({left&amp;lt;{S_{i, j}^rxi, xi}right&amp;gt;^{frac{p}{2}}-left&amp;lt;{T_{i, j}^rxi, xi}right&amp;gt;^{frac{q}{2}}}right)^2. $end{document} </tex-math></disp-formula></p> </abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135496215","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
Symmetric $ n $-derivations on prime ideals with applications 素数理想上的对称n -导数及其应用
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231410
Shakir Ali, Amal S. Alali, Sharifah K. Said Husain, Vaishali Varshney
{"title":"Symmetric $ n $-derivations on prime ideals with applications","authors":"Shakir Ali, Amal S. Alali, Sharifah K. Said Husain, Vaishali Varshney","doi":"10.3934/math.20231410","DOIUrl":"https://doi.org/10.3934/math.20231410","url":null,"abstract":"<abstract><p>Let $ mathfrak{S} $ be a ring. The main objective of this paper is to analyze the structure of quotient rings, which are represented as $ mathfrak{S}/mathfrak{P} $, where $ mathfrak{S} $ is an arbitrary ring and $ mathfrak{P} $ is a prime ideal of $ mathfrak{S} $. The paper aims to establish a link between the structure of these rings and the behaviour of traces of symmetric $ n $-derivations satisfying some algebraic identities involving prime ideals of an arbitrary ring $ mathfrak{S} $. Moreover, as an application of the main result, we investigate the structure of the quotient ring $ mathfrak{S}/mathfrak{P} $ and traces of symmetric $ n $-derivations.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784234","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
A quaternion Sylvester equation solver through noise-resilient zeroing neural networks with application to control the SFM chaotic system 基于噪声弹性归零神经网络的四元数Sylvester方程求解器在SFM混沌系统控制中的应用
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231401
Sondess B. Aoun, Nabil Derbel, Houssem Jerbi, Theodore E. Simos, Spyridon D. Mourtas, Vasilios N. Katsikis
{"title":"A quaternion Sylvester equation solver through noise-resilient zeroing neural networks with application to control the SFM chaotic system","authors":"Sondess B. Aoun, Nabil Derbel, Houssem Jerbi, Theodore E. Simos, Spyridon D. Mourtas, Vasilios N. Katsikis","doi":"10.3934/math.20231401","DOIUrl":"https://doi.org/10.3934/math.20231401","url":null,"abstract":"<abstract><p>Dynamic Sylvester equation (DSE) problems have drawn a lot of interest from academics due to its importance in science and engineering. Due to this, the quest for the quaternion DSE (QDSE) solution is the subject of this work. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. Keeping in mind that the original ZNN can handle QDSE successfully in a noise-free environment, but it might not work in a noisy one, and the noise-resilient ZNN (NZNN) technique is also utilized. In light of that, one new ZNN model is introduced to solve the QDSE problem and one new NZNN model is introduced to solve the QDSE problem under different types of noises. Two simulation experiments and one application to control of the sine function memristor (SFM) chaotic system show that the models function superbly.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"60 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135798311","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
Global existence and energy decay for a transmission problem under a boundary fractional derivative type 一类边界分数阶导数型传输问题的整体存在性和能量衰减
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231412
Noureddine Bahri, Abderrahmane Beniani, Abdelkader Braik, Svetlin G. Georgiev, Zayd Hajjej, Khaled Zennir
{"title":"Global existence and energy decay for a transmission problem under a boundary fractional derivative type","authors":"Noureddine Bahri, Abderrahmane Beniani, Abdelkader Braik, Svetlin G. Georgiev, Zayd Hajjej, Khaled Zennir","doi":"10.3934/math.20231412","DOIUrl":"https://doi.org/10.3934/math.20231412","url":null,"abstract":"<abstract><p>The paper considers the effects of fractional derivative with a high degree of accuracy in the boundary conditions for the transmission problem. It is shown that the existence and uniqueness of the solutions for the transmission problem in a bounded domain with a boundary condition given by a fractional term in the second equation are guaranteed by using the semigroup theory. Under an appropriate assumptions on the transmission conditions and boundary conditions, we also discuss the exponential and strong stability of solution by also introducing the theory of semigroups.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800132","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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