This paper solves the problem of boundary feedback stabilization of a class of coupled ordinary differential equations-hyperbolic equations with boundary, trace, and integral nonlocal terms. Using ...the backstepping approach, the controller is designed by formulating an integral operator, whose kernel is required to satisfy a coupled hyperbolic partial integral differential equation. By applying the method of successive approximations, the kernel's well-posedness is given. We prove the exponential stability of the origin of the system in a suitable Hilbert space. Moreover, a wave system with nonlocal terms is stabilized by applying the above result.
Significant advancements have been made in hyperspectral image (HSI) super-resolution with the development of deep-learning techniques. However, the current application of deep neural network ...architectures to HSI super-resolution heavily relies on empirical design strategies, which can potentially impede the improvement of image reconstruction performance and introduce distortions in the results. To address this, we propose an innovative HSI super-resolution network called dual ordinary differential equations (Dual ODEs). Drawing inspiration from ordinary differential equations (ODEs), our approach offers reliable guidelines for the design of HSI super-resolution networks. The Dual ODE model leverages a spatial ODE block to extract spatial information and a spectral ODE block to capture internal spectral features. This is accomplished by redefining the conventional residual module using the multiple ODE functions method. To evaluate the performance of our model, we conducted extensive experiments on four benchmark HSI datasets. The results conclusively demonstrate the superiority of our Dual ODE approach over state-of-the-art models. Moreover, our approach incorporates a small number of parameters while maintaining an interpretable model design, thereby reducing model complexity.
In this article, the flow of ternary nanofluid is analysed past a stretching sheet subjected to Thomson and Troian slip condition along with the temperature jump. The ternary nanofluid is formed by ...suspending three different types of nanoparticles namely Formula: see text and Formula: see text into water which acts as a base fluid and leads to the motion of nanoparticles. The high thermal conductivity and chemical stability of silver was the main cause for its suspension as the third nanoparticle into the hybrid nanofluid Formula: see text. Thus, forming the ternary nanofluid Formula: see text. The sheet is assumed to be vertically stretching where the gravitational force will have its impact in the form of free convection. Furthermore, the presence of radiation and heat source/sink is assumed so that the energy equation thus formed will be similar to most of the real life applications. The assumption mentioned here leads to the mathematical model framed using partial differential equations (PDE) which are further transformed to ordinary differential equations (ODE) using suitable similarity transformations. Thus, obtained system of equations is solved by incorporating the RKF-45 numerical technique. The results indicated that the increase in the suspension of silver nanoparticles enhanced the temperature and due to density, the velocity of the flow is reduced. The slip in the velocity decreased the flow speed while the temperature of the nanofluid was observed to be increasing.
We prove that there exists at least one positive Einstein metric on $\mathbb {HP}^{m+1}\sharp \overline {\mathbb {HP}}^{m+1}$ for $m\geq ~2$ . Based on the existence of the first Einstein metric, we ...give a criterion to check the existence of a second Einstein metric on $\mathbb {HP}^{m+1}\sharp \overline {\mathbb {HP}}^{m+1}$ . We also investigate the existence of cohomogeneity-one positive Einstein metrics on $\mathbb {S}^{4m+4}$ and prove the existence of a non-standard Einstein metric on $\mathbb {S}^8$ .
A small-gain approach is presented for analyzing exponential stability of a class of (dynamical) hybrid systems. The systems considered in the paper are composed of finite-dimensional dynamics, ...represented by a linear ordinary differential equation (ODE), and infinite-dimensional dynamics described by a parabolic partial differential equation (PDE). Exponential stability is established under conditions involving the maximum allowable sampling period (MASP). This new stability result is shown to be useful in the design of sampled-output exponentially convergent observers for linear systems that are described by an ODE-PDE cascade. The new stability result also proves to be useful in designing practical approximate observers involving no PDEs.
In this book, the authors present the elements of a general theory for flows on three-dimensional compact boundaryless manifolds, encompassing flows with equilibria accumulated by regular orbits. The ...book aims to provide a global perspective of this theory and make it easier for the reader to digest the growing literature on this subject. This is not the first book on the subject of dynamical systems, but there are distinct aspects which together make this book unique.Firstly, this book treats mostly continuous time dynamical systems, instead of its discrete counterpart, exhaustively treated in some other texts. Secondly, this book treats all the subjects from a mathematical perspective with proofs of most of the results included. Thirdly, this book is meant to be an advanced graduate textbook and not just a reference book or monograph on the subject. This aspect is reflected in the way the cover material is presented, with careful and complete proofs, and precise references to topics in the book.
In these lectures I present a review of non‐perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. I first consider the structure of these ...effects in the case of ordinary differential equations, which provide a model for more complicated theories, and I introduce in a pedagogical way some technology from resurgent analysis, like trans‐series and the resurgent version of the Stokes phenomenon. After reviewing instanton effects in quantum mechanics and quantum field theory, I address general aspects of large N instantons, and then present a detailed review of non‐perturbative effects in matrix models. Finally, I consider two applications of these techniques in string theory.
These lectures review non‐perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. First the structure of these effects in the case of ordinary differential equations is considered providing a model for more complicated theories and leading to a pedagogical approach to some technology from resurgent analysis like trans‐series and the resurgent version of the Stokes phenomenon. After reviewing instanton effects in quantum mechanics and quantum field theory, general aspects of large N instantons are addressed. A detailed review of non‐perturbative effects in matrix models including two applications of these techniques in string theory is presented.
The thermal management of the flow of the hybrid nanofluid within the conical gap between a cone and a disk is analyzed. Four different cases of flow are examined, including (1) stationary cone ...rotating disk (2) rotating cone stationary disk (3) rotating cone and disk in the same direction and (4) rotating cone and disk in the opposite directions. The magnetic field of strength Formula: see text is added to the modeled problem that is applied along the z-direction. This work actually explores the role of the heat transfer, which performs in a plate-cone viscometer. A special type of hybrid nanoliquid containing copper Cu and magnetic ferrite Fe
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nanoparticles are considered. The similarity transformations have been used to alter the modeled from partial differential equations (PDEs) to the ordinary differential equations (ODEs). The modeled problem is analytically treated with the Homotopy analysis method HAM and the numerical ND-solve method has been used for the comparison. The numerical outputs for the temperature gradient are tabulated against physical pertinent variables. In particular, it is concluded that increment in volume fraction of both nanoparticles Formula: see text effectively enhanced the thermal transmission rate and velocity of base fluid. The desired cooling of disk-cone instruments can be gained for a rotating disk with a fixed cone, while the surface temperature remains constant.
Abstract
Discovering the governing laws underpinning physical and chemical phenomena entirely from data is a key step towards understanding and ultimately controlling systems in science and ...engineering. Noisy measurements and complex, highly nonlinear underlying dynamics hinder the identification of such governing laws. In this work, we introduce a machine learning framework rooted in moving horizon nonlinear optimization for identifying governing equations in the form of ordinary differential equations from noisy experimental data sets. Our approach evaluates sequential subsets of measurement data, and exploits statistical arguments to learn truly parsimonious governing equations from a large dictionary of basis functions. The proposed framework reduces gradient approximation errors by implicitly embedding an advanced numerical discretization scheme, which improves robustness to noise as well as to model stiffness. Canonical nonlinear dynamical system examples are used to demonstrate that our approach can accurately recover parsimonious governing laws under increasing levels of measurement noise, and outperform state of the art frameworks in the literature. Further, we consider a non-isothermal chemical reactor example to demonstrate that the proposed framework can cope with basis functions that have nonlinear (unknown) parameterizations.
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