Ashpazzadeh, ElmiraChu, Yu-MingHashemi, Mir SajjadMoharrami, Mahsa...
16页
查看更多>>摘要：In this research , we study the numerical solution of the singular Abel's equation of the second kind. Solving this equation is challengeable, because of the nonlinear and singularity. For this purpose, we present an efficient algorithm based on the Galerkin method using biorthogonal Hermite cubic spline multiwavelets (BHCSMWs). Because of the sparse multiscale representations of functions and operators by these wavelets, the CPU time and computer memory are reduced by the proposed algorithm. Also, the convergence analysis of the method is discussed. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, a Bessel-type inequality in semi-inner produce (s.i.p.) spaces is presented to deal with the problem of stability analysis for a class of discrete-time systems with distributed delays. The main purpose of this paper is to obtain less conservative stability conditions for the investigated systems. For this purpose, a novel inequality (which is re-ferred to as Bessel-type inequality in s.i.p. spaces) is constructed by combining the Bessel inequality and a set of polynomials which is pairwise orthogonal in a s.i.p. space. The pro-posed inequality is more general than the conventional Jensen-type inequality, which is, to the best of our knowledge, the only inequality to deal with the problem of stability anal-ysis for discrete-time systems with distributed delays up to now. Based on the proposed inequality and the Lyapunov-Krasovskii stability theory, a stability condition is presented. Finally, a numerical example is given to indicate that the proposed method is able to ef-fectively reduce the conservatism. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Image denoising is to recover true image from noisy image. Many image deonising models are proposed during the last decades. Some models preserve the margin of tissue, i.e., TV model, while the others, i.e., LLT model, prefer smooth solutions. By decomposing true image into cartoon part and texture part, we propose a fractional image denoising model with two-component regularization terms. Setting some appropriate parameters, the proposed model can deal with both smooth and non-smooth image denosing problems. The existence and uniqueness of solution for the variational model are proved. Moreover, a Split-Bregman(S-B) based numerical algorithm to solve this model is also proposed to validate the theoretical results. Numerical tests show that the proposed model can produce competitive denoising result to the other three published models.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, a finite-time optimal consensus control strategy is presented for unknown multi-agent systems (MASs) with the time-varying asymmetric output constraint. Different from existing results, the output constraint problem investigated here eliminates the requirements that constraint boundary functions must be strictly non-zero and have different signs, which is successfully handled by introducing special barrier functions. Moreover, to deal with disturbances well, a reinforcement learning (RL) with the critic-actor disturbance structure is introduced. Meanwhile, the weights of neural networks are adjusted online by applying the gradient descent method to positive functions newly constructed, which not only significantly simplifies the algorithm but also eliminates the persistent excitation condition. For obtaining a fast convergence rate, the finite-time control technique is embedded into the RL algorithm, and an effective finite-time optimal control scheme is proposed to achieve the consistency of multi-agent system in a finite time. Finally, the effectiveness of the proposed protocol is demonstrated by two simulation examples. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The distribution of eigenvalues for Seidel matrices of threshold graphs is investigated in this paper. We show that there is no eigenvalue of Seidel matrices of threshold graphs in the interval (-root 2, / root 2,) except for -1 and 1. We also determine the inertia of the Seidel matrix of a threshold graph in terms of its binary string. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we investigate steady states of shallow water moment equations including bottom topographies. We derive a new hyperbolic shallow water moment model based on linearized moment equations that allows for a simple assessment of the steady states. After proving hyperbolicity of the new model, the steady states are fully identified. A wellbalanced scheme is adopted to the specific structure of the new model and allows to preserve the steady states in numerical simulations. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we consider the unsteady flow of a micropolar fluid through a thin pipe with the nonzero boundary condition for microrotation. We first prove the well-posedness of the corresponding initial-boundary value problem governing the flow. Then, using asymptotic analysis with respect to the pipe's thickness, we construct the higher-order approximation of the solution. The proposed approximation is given in explicit form, taking into account the effects of the boundary conditions, the micropolar nature of the fluid as well as the time derivative. A detailed study of the boundary layers in the vicinity of the pipe's ends is also provided along with a numerical example illustrating the behaviour of the derived asymptotic solution. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：A direct analytical treatment on singularities in the 3D TD-BEM formulation is proposed, where the wavefront singularity and the dual singularity are analytically expressed. In the process of the solution of the spatial singularity, the integration domain is divided into the regular part and the singular part. The singularities in the singular part are analytically eliminated by the direct method of the concept of the finite part of an integral (Hadamard principal integral), while the singular integrals in the regular part are solved by the conve-nient Gaussian integration. Due to the increase of the dimension and the additional causal-ity relevant function, the 3D TD-BEM formulation is further more intricate than the 2D one. In order to reduce the complexity, in the process of the solution of the boundary in-tegral equation in the 3D TD-BEM formulation, a new coordinate transformation method is proposed to analytically transform the coefficient integrals on the spatial surface element into the 2D plane element. The 3D TD-BEM formulation based on the proposed analytical treatment on singularities is verified to be correct by three examples. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper concerns a new generalized inverse for matrices of an arbitrary index. It is proved that every complex square matrix A possesses a {1 , 2 , 3}-inverse X such that XA(m+1) = A(m) for some integer m . We shall call such X a { 1 , 2 , 3 , 1 m }-inverse of A . A notable result is that A has a unique {1 , 2 , 3 , 1(m)}-inverse if and only if it has index 0 or 1, in which case A* is exactly its unique {1 , 2 , 3 , 1 (m)}-inverse. For a matrix with an arbitrary index, the set of all its {1 , 2 , 3 , 1(m)}-inverses is completely determined. Some new characterizations of EP matrices, generalized EP matrices and m-EP matrices are established by using their {1 , 2 , 3 , 1(m)}-inverses. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：It is now well known that the magnetic resonance imaging (MRI) signal decay deviates from the classical mono-exponential relaxation. This deviation is referred to in the literature as anomalous relaxation. The modelling of this anomalous relaxation can provide a better understanding of MRI magnetization. The purpose of this work is to investigate the utility of the distributed-order time fractional Bloch equations to describe anomalous relaxation processes in human brain MRI data. Two choices of continuous distribution weight functions, which are parameterised by their mean mu and standard deviation sigma, are studied to investigate their impact on the model solution behaviour. An implicit numerical method implemented on a graded mesh is proposed to solve the model and the stability and convergence analysis are presented. We also derive semi-analytical solutions of the fully coupled Bloch equations using the Laplace transform technique to assess the accuracy of the numerical scheme. Furthermore, three different voxel models of continuous distribution weight functions, namely a single continuous probability distribution (model 1), two distinct continuous probability distributions (model 2) and a mixture of two continuous probability distributions (model 3), are applied to the in vivo human brain MRI data, and a feasible and reliable parameter estimation method based on a modified hybrid Nelder-Mead simplex search and particle swarm optimization is presented to perform the voxel-level temporal fitting of the MRI data. The application of these distributed-order time fractional Bloch models highlights the validity of the proposed models, and based on the mean square error we conclude that models 2 and 3 might be more suitable than model 1 to characterize anomalous relaxation processes in human brain MRI data. (c) 2022 Elsevier Inc. All rights reserved.
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