查看更多>>摘要：The smallest cardinalities of identifying and locating codes in dihedral graphs are studied in this paper which is the first step to study these codes in general networks. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Based on the standard method of zeroing neural network (ZNN) for time-varying matrix problems, three improved ZNN models are proposed and extended to solve the time-varying Sylvester tensor equation (TV-STE) in finite-time. These presented ZNN models, which mainly use classical sign-bi-power (S-B-P) activation function and varying parameters, are S-B-P based ZNN (S-ZNN), S-B-P function based linear varying parameter ZNN (LVP-ZNN) and S-B-P function based exponential varying parameter ZNN (EVP-ZNN) models. Due to the applications of S-B-P activation function and varying parameters, the S-ZNN, LVP-ZNN and EVP-ZNN models can accomplish finite-time convergence, i.e., the state solutions generated by these models can converge to the analytical solutions of the TV-STE problem in finite-time. Further, based on the relationship between error, design parameter and convergence property, a dynamic varying parameter adapted to the error variation is designed and applied to the S-ZNN model. Then an error-adaptive dynamic varying parameter ZNN (DVP-ZNN) model is obtained for the TV-STE, which possesses faster finite-time convergence. These four models are proved to be stable and their upper bounds of convergence time are derived and analyzed. Theoretical analyses and comparison experiments demonstrate that the proposed ZNN models can solve the TV-STE in finite-time and the convergence of the DVP-ZNN model is the best. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：As molecular descriptors, topological indices based on k-eccentricity of a graph are introduced. Firstly we devise an algorithm for these indices based on 3-eccentricity and analyze the computing complexity. As their applications, we employ the topological indcies based on 2- and 3-eccentricity as the feature vectors to predict anti-HIV activity by devising machine learning predicting models with the help of Support Vector Machine (SVM), K Nearest Neighbor (KNN) and Decision Tree (DecTree), respectively. Experiment results show that the highest accuracy is 99.7%, while the lowest is 97.7% except the special cases. The special cases are that the experiments are with the single 2-CEI or 3-CEI as the feature vector, respectively. Through these experiments, we find that these topological indices based on the k -eccentricity (k = 2, 3) have good applications in predicting anti-HIV activity. But not every feature vector is generally applicable. Different feature vectors may be used to different models. Furthermore, there is no clear relationship between the dimension of feature vectors and the accuracy of prediction. (C) 2021ElsevierInc. Allrightsreserved.
查看更多>>摘要：In this paper, the problem of distributed fault-tolerant state estimation is studied for stochastic systems over sensor networks with intermittent sensor faults. Compared with the traditional state estimation algorithms, the distinct advantage of fault-tolerant state estimation is that the estimator can keep good performance whether sensor faults occur or not. Different from the previous literature concerning with distributed fault diagnosis, the distributed fault diagnosis problem is investigated in this paper for intermittent faults, whose appearing time, disappearing time and magnitude are all nondeterministic. The distributed fault-tolerant state estimation scheme is constructed, in which the appearing time and disappearing time of intermittent faults are detected, intermittent faults are estimated and compensated. By means of the matrix inequality technique, the H-infinity performance of state estimation errors is guaranteed by properly choosing the estimator parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed algorithm. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper we propose a model reduction technique to speed up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once systems from evolutionary PDEs. In particular, we use the reduced basis method to seek a low-dimensional approximation to the sequence of complex-shifted systems arising from Step(b) of the ParaDIAG preconditioning procedure. Different from the standard reduced order modeling that uses the separation of offline and online stages, we have to build the reduced order model (ROM) online for the considered systems at each iteration. Therefore, several heuristic acceleration techniques are introduced in the greedy basis generation algorithm, that is built upon a residual-based error indicator, to further boost up its computational efficiency. Several numerical experiments are conducted, which illustrate the favorable computational efficiency of our proposed ROM-accelerated ParaDIAG preconditioner, in comparison with the multigrid-based one. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Based on elementary geometry, Gutman proposed a novel graph invariants called the Sombor index SO(G), which is defined as SO(G) = Sigma(uv epsilon E(G))root d(G(u))(2) + d(G(v))(2), where d(G) (u) and d(G)(v) denote the degree of u and v in G, respectively. It has been proved that the Sombor index could predict some physicochemical properties. In this paper, we characterize the extremal graphs with respect to the Sombor index among all the n-order trees with a given diameter. Firstly, we order the trees with respect to the Sombor index among the n-vertex trees with diameter 3. Then, we determine the largest and the second largest Sombor indices of n-vertex trees with a given diameter d >= 4 and characterize the corresponding trees. Moreover, for n - d = 3, we characterize the extremal n-order trees which reach from the third to the fourth (resp. the sixth, the seventh) largest Sombor indices with d = 4 (resp. d = 5, d >= 6). For n - d >= 4, we characterize the extremal n-order trees which reach from the third to the fifth (resp. the eighth, the ninth) largest Sombor indices with d = 4 (resp. d = 5, d >= 6). As consequences, the top four n-order trees with respect to the Sombor index are characterized. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The role of rank one perturbations in transforming the eigenstructure of a matrix has long been considered in the context of applications, especially in linear control systems. Two cases are examined in this paper: First, we propose a practical method to place the system eigenvalues (poles) in desired locations via feedback control that is computed in terms of recursive rank one perturbations. Second, a choice of feedback control is proposed in order to achieve that a trajectory eventually enters the nonnegative orthant and remains therein for all time thereafter. The latter situation is achieved by imposing the strong Perron-Frobenius property and involves altering the eigenvalues, as well as left eigenvectors via rank one perturbations. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A fractional Helmholtz equation with the fractional Laplacian is investigated. Fundamental solutions of this equation and their factorized representations in terms of H-functions are constructed using Fourier and Mellin integral transforms. Multipole expansion for integral representation of the fractional Helmholtz equation's solution is derived. A technique for evaluating H-functions from the multipole expansion is proposed. A modification of the multipole method for solving considered equation is developed. Numerical results demonstrating high efficiency of the proposed approach are presented. A fractional generalization of the mathematical model for a plane polarized electromagnetic wave propagation in the inhomogeneous medium, leading to a fractional Helmholtz equation with the fractional Laplacian, is derived and investigated using the proposed algorithm. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let H be a reproducing kernel Hilbert space of analytic functions on the unit disk D. The best kernel approximation problem for His the following: given any positive integer n and any function f epsilon H find the best norm approximation of f by a linear combination of no more than n kernel functions K(z, z(k)), 1 <= k <= n. The purpose of this paper is to prove the existence of best kernel approximation for weighted Bergman spaces with standard weights. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper addresses H-infinity observer-based control issue for fractional-order uncertain Takagi-Sugeno (T-S) fuzzy model with unknown input and time-delay in the case of system order in (0,1). In order to construct the state estimation variables, reduced-order fuzzy observer is devised. By utilizing Lyapunov method of fractional-order derivative, the sufficient conditions are provided to ensure the effectiveness of proposed reduced-order unknown input observer and the stabilization of augmented T-S fuzzy model with an H-infinity-norm s. The conditions are shown in terms of linear matrix inequalities (LMIs) and the matrices of unknown input fuzzy observer are computed by relevant LMIs. Furthermore, by solving LMIs, the T-S fuzzy output feedback control is realized. Finally, a numerical example and a single-link robot arm example are simulated to illustrate the validity of the addressed strategy. (C) 2021 Published by Elsevier Inc.
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