AIMS Mathematics最新文献

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.

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.

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 > 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

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}

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

begin{document}$ rho(xi) = frac{n^{2r-1}}{m}sumlimits_{j = 1}^{m}sumlimits_{i = 1}^{n}left({left<{S_{i, j}^rxi, xi}right>^{frac{p}{2}}-left<{T_{i, j}^rxi, xi}right>^{frac{q}{2}}}right)^2. $end{document}

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.

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.

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.

This paper introduces the Lagrange collocation method with radial basis functions (LRBF) as a novel approach to solving 1D partial differential equations. Our method addresses the trade-off principle, which is a key challenge in standard RBF collocation methods, by maintaining the accuracy and convergence of the numerical solution, while improving the stability and efficiency. We prove the existence and uniqueness of the numerical solution for specific differential operators, such as the Laplacian operator, and for positive definite RBFs. Additionally, we introduce a perturbation into the main matrix, thereby developing the perturbed LRBF method (PLRBF); this allows for the application of Cholesky decomposition, which significantly reduces the condition number of the matrix to its square root, resulting in the CPLRBF method. In return, this enables us to choose a large value for the shape parameter without compromising stability and accuracy, provided that the perturbation is carefully selected. By doing so, highly accurate solutions can be achieved at an early level, significantly reducing central processing unit (CPU) time. Furthermore, to overcome stagnation issues in the RBF collocation method, we combine LRBF and CPLRBF with multilevel techniques and obtain the Multilevel PLRBF (MuCPLRBF) technique. We illustrate the stability, accuracy, convergence, and efficiency of the presented methods in numerical experiments with a 1D Poisson equation. Although our approach is presented for 1D, we expect to be able to extend it to higher dimensions in future work.