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Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow 沿利玛窦流的（p,q）毕谐系统特征值
Axioms Pub Date : 2024-05-17 DOI: 10.3390/axioms13050332
Lixu Yan, Yanlin Li, A. Saha, Abimbola Abolarinwa, Suraj Ghosh, Shyamal Kumar Hui
{"title":"Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow","authors":"Lixu Yan, Yanlin Li, A. Saha, Abimbola Abolarinwa, Suraj Ghosh, Shyamal Kumar Hui","doi":"10.3390/axioms13050332","DOIUrl":"https://doi.org/10.3390/axioms13050332","url":null,"abstract":"In this paper, we determine the variation formula for the first eigenvalue of (p,q)-biharmonic system on a closed Riemannian manifold. Several monotonic quantities are also derived.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"38 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140964824","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}
引用次数: 0
Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities 具有非局部特征速度的双曲系统数值解的指数稳定性
Axioms Pub Date : 2024-05-17 DOI: 10.3390/axioms13050334
Rakhmatillo Djuraevich Aloev, Abdumauvlen Suleimanovich Berdyshev, Vasila Alimova, Kymbat Slamovna Bekenayeva
{"title":"Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities","authors":"Rakhmatillo Djuraevich Aloev, Abdumauvlen Suleimanovich Berdyshev, Vasila Alimova, Kymbat Slamovna Bekenayeva","doi":"10.3390/axioms13050334","DOIUrl":"https://doi.org/10.3390/axioms13050334","url":null,"abstract":"In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary control for the specified hyperbolic system is given. A difference scheme is constructed for the numerical solution of the considered initial boundary value problem. The definition of the exponential stability of the numerical solution in ℓ2-norm with respect to a discrete perturbation of the equilibrium state of the initial boundary value difference problem is given. A discrete Lyapunov function for a numerical solution is constructed, and a theorem on the exponential stability of a stationary solution of the initial boundary value difference problem in ℓ2-norm with respect to a discrete perturbation is proved.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"48 47","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140965840","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}
引用次数: 0
Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization 通过艾森哈特提升和线性化求解非线性二阶 ODEs
Axioms Pub Date : 2024-05-16 DOI: 10.3390/axioms13050331
A. Paliathanasis
{"title":"Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization","authors":"A. Paliathanasis","doi":"10.3390/axioms13050331","DOIUrl":"https://doi.org/10.3390/axioms13050331","url":null,"abstract":"The linearization of nonlinear differential equations represents a robust approach to solution derivation, typically achieved through Lie symmetry analysis. This study adopts a geometric methodology grounded in the Eisenhart lift, revealing transformative techniques that linearize a set of second-order ordinary differential equations. The research underscores the effectiveness of this geometric approach in the linearization of a class of Newtonian systems that cannot be linearized through symmetry analysis.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"118 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140967615","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}
引用次数: 0
Extremal Bicyclic Graphs with Respect to Permanental Sums and Hosoya Indices 关于永久和与细谷指数的极值双环图
Axioms Pub Date : 2024-05-16 DOI: 10.3390/axioms13050330
Tingzeng Wu, Yinggang Bai, Shoujun Xu
{"title":"Extremal Bicyclic Graphs with Respect to Permanental Sums and Hosoya Indices","authors":"Tingzeng Wu, Yinggang Bai, Shoujun Xu","doi":"10.3390/axioms13050330","DOIUrl":"https://doi.org/10.3390/axioms13050330","url":null,"abstract":"Graph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs. The Hosoya index of a graph is the sum of the absolute value of all coefficients for the matching polynomial. And the permanental sum of a graph is the sum of the absolute value of all coefficients of the permanental polynomial. In this paper, we characterize the second to sixth minimal Hosoya indices of all bicyclic graphs. Furthermore, using the results, the second to sixth minimal permanental sums of all bicyclic graphs are also characterized.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"2 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140967495","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}
引用次数: 0
Tractability of Multivariate Approximation Problem on Euler and Wiener Integrated Processes 欧拉和维纳综合过程多变量逼近问题的可操作性
Axioms Pub Date : 2024-05-15 DOI: 10.3390/axioms13050326
Jie Zhang
{"title":"Tractability of Multivariate Approximation Problem on Euler and Wiener Integrated Processes","authors":"Jie Zhang","doi":"10.3390/axioms13050326","DOIUrl":"https://doi.org/10.3390/axioms13050326","url":null,"abstract":"This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is represented by the tensor product of one-dimensional kernels corresponding to Euler and Wiener integrated processes with non-negative and nondecreasing smoothness parameters {rd}d∈N. We give matching sufficient and necessary conditions for various concepts of tractability in terms of the asymptotic properties of the regularity parameters, except for (s, 0)-WT.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"64 47","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972220","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}
引用次数: 0
Mathematical Methods in Applied Sciences 应用科学中的数学方法
Axioms Pub Date : 2024-05-15 DOI: 10.3390/axioms13050327
Nuno R. O. Bastos, Touria Karite
{"title":"Mathematical Methods in Applied Sciences","authors":"Nuno R. O. Bastos, Touria Karite","doi":"10.3390/axioms13050327","DOIUrl":"https://doi.org/10.3390/axioms13050327","url":null,"abstract":"In this editorial, we introduce “Mathematical Methods in Applied Sciences”, a Special Issue of Axioms comprising 17 articles [...]","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"65 45","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972398","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}
引用次数: 0
Static Spherically Symmetric Perfect Fluid Solutions in Teleparallel F(T) Gravity 远距离平行 F(T) 重力下的静态球面对称完美流体解决方案
Axioms Pub Date : 2024-05-15 DOI: 10.3390/axioms13050333
Alexandre Landry
{"title":"Static Spherically Symmetric Perfect Fluid Solutions in Teleparallel F(T) Gravity","authors":"Alexandre Landry","doi":"10.3390/axioms13050333","DOIUrl":"https://doi.org/10.3390/axioms13050333","url":null,"abstract":"In this paper, we investigate static spherically symmetric teleparallel F(T) gravity containing a perfect isotropic fluid. We first write the field equations and proceed to find new teleparallel F(T) solutions for perfect isotropic and linear fluids. By using a power-law ansatz for the coframe components, we find several classes of new non-trivial teleparallel F(T) solutions. We also find a new class of teleparallel F(T) solutions for a matter dust fluid. After, we solve the field equations for a non-linear perfect fluid. Once again, there are several new exact teleparallel F(T) solutions and also some approximated teleparallel F(T) solutions. All these classes of new solutions may be relevant for future cosmological and astrophysical applications.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"4 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972837","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}
引用次数: 0
Nonuniform Sampling in Lp-Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform 与多维特殊仿射傅里叶变换相关的 Lp 子空间中的非均匀采样
Axioms Pub Date : 2024-05-15 DOI: 10.3390/axioms13050329
Yingchun Jiang, Jing Yang
{"title":"Nonuniform Sampling in Lp-Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform","authors":"Yingchun Jiang, Jing Yang","doi":"10.3390/axioms13050329","DOIUrl":"https://doi.org/10.3390/axioms13050329","url":null,"abstract":"In this paper, the sampling and reconstruction problems in function subspaces of Lp(Rn) associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval’s relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the Lp-stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a Lp-subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"35 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140974123","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}
引用次数: 0
Coercive and Noncoercive Mixed Generalized Complementarity Problems 强制性和非强制性混合广义互补问题
Axioms Pub Date : 2024-05-15 DOI: 10.3390/axioms13050328
Ram N. Mohapatra, Bijaya K. Sahu, Gayatri Pany
{"title":"Coercive and Noncoercive Mixed Generalized Complementarity Problems","authors":"Ram N. Mohapatra, Bijaya K. Sahu, Gayatri Pany","doi":"10.3390/axioms13050328","DOIUrl":"https://doi.org/10.3390/axioms13050328","url":null,"abstract":"Impressed with the very recent developments of noncoercive complementarity problems and the use of recession sets in complementarity problems, here, we discuss mixed generalized complementarity problems in Hausdorff topological vector spaces. We used the Tikhonov regularization procedure, as well as arguments from the recession analysis, to establish the existence of solutions for mixed generalized complementarity problems without coercivity assumptions in Banach spaces.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973506","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}
引用次数: 0
A Vector Representation of Multicomplex Numbers and Its Application to Radio Frequency Signals 多复数的矢量表示法及其在射频信号中的应用
Axioms Pub Date : 2024-05-14 DOI: 10.3390/axioms13050324
D. Borio
{"title":"A Vector Representation of Multicomplex Numbers and Its Application to Radio Frequency Signals","authors":"D. Borio","doi":"10.3390/axioms13050324","DOIUrl":"https://doi.org/10.3390/axioms13050324","url":null,"abstract":"Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification. We focus on multicomplex numbers, sets of hypercomplex numbers with commutative products, and introduce a vector representation allowing one to isolate the hyperbolic real and imaginary parts of a multicomplex number. The orthogonal decomposition of a multicomplex number is also discussed, and its connection with Hadamard matrices is highlighted. Finally, a multicomplex polar representation is provided. These properties are used to extend the standard complex baseband signal representation to the multi-dimensional case. It is shown that a set of 2n Radio Frequency (RF) signals can be represented as the real part of a single multicomplex signal modulated by several frequencies. The signal RFs are related through a Hadamard matrix to the modulating frequencies adopted in the multicomplex baseband representation. Moreover, an orthogonal decomposition is provided for the obtained multicomplex baseband signal as a function of the complex baseband representations of the input RF signals.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"37 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140981016","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}
引用次数: 0
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