Applied Mathematics and Computation最新文献

In the past few years, tensor robust principal component analysis (TRPCA) which is based on tensor singular value decomposition (t-SVD) has got a lot of attention in recovering low-rank tensor corrupted by sparse noise. However, most TRPCA methods only consider the global structure of the image, ignoring the local details and sharp edge information of the image, resulting in the unsatisfactory restoration results. In this paper, to fully preserve the local details and edge information of the image, we propose a new TRPCA method by introducing a total generalized variation (TGV) regularization. The proposed method can simultaneously explore the global and local prior information of high-dimensional data. Specifically, the tensor nuclear norm (TNN) is employed to develop the global structure feature. Moreover, we introduce the TGV, a higher-order generalization of total variation (TV), to preserve the local details and edges of the underlying image. Subsequently, the alternating direction method of multiplier (ADMM) algorithm is introduced to solve the proposed model. Sufficient experiments on color images and videos have demonstrated that our method is superior to other comparison methods.

The paper addresses the issue of the finite-time energy-to-peak quantized filtering for Takagi-Sugeno (T-S) fuzzy systems under event-triggered-based weighted try-once-discard (WTOD) protocol, considering deception attacks in the network. To process the measurement output and schedule the transmission sequence for relieving the communication burden, a dynamic quantizer and an event-triggered-based WTOD protocol are synthesized to determine whether the quantified measurement value of the sensor should be sent and which ones to be delivered. The main intention of this paper is to construct a mode-dependent filter such that the filtering error system is stochastically stable under the finite-time bounded and meets an energy-to-peak performance levels. The sufficient conditions for the existence of the admissible filter criterion are formulated, and the specific filter gains are obtained through solving a convex optimization problem. Finally, a practical example is used to evaluate the theoretical design and analysis.

In the context of an edge-coloured graph G, a path within the graph is deemed conflict-free when a colour is exclusively applied to one of its edges. The presence of a conflict-free path connecting any two unique vertices of an edge-coloured graph is what defines it as conflict-free connected. The conflict-free connection number, indicated by $cfc\left(G\right)$, is the fewest number of colours necessary to make G conflict-free connected. Consider the subgraph $C\left(G\right)$ of a connected graph G, which is constructed from the cut-edges of G. Let ${\sigma }_3\left(G\right)$ be the minimum degree-sum of any 3 independent vertices in G. In this study, we establish that for a connected graph G with an order of $n\ge 8$ and ${\sigma }_3\left(G\right)\ge n-1$, the following conditions hold: (1) $cfc\left(G\right)=3$ when $C\left(G\right)\cong K_{1,3}$; (2) $cfc\left(G\right)=2$ when $C\left(G\right)$ forms a linear forest. Moreover, we will now demonstrate that if G is a connected, non-complete graph with n vertices, where $n\ge 43$, $C\left(G\right)$ is a linear forest, $\delta \left(G\right)\ge 3$, and ${\sigma }_3\left(G\right)\ge \frac{3n-14}{5}$, then $cfc\left(G\right)=2$. Moreover, we also determine the upper bound of the number of cut-edges of a connected graph depending on the degree-sum of any three independent vertices.

In López, Pagola and Perez (2009) [9] we introduced a modification of the Laplace's method for deriving asymptotic expansions of Laplace integrals which simplifies the computations, giving explicit formulas for the coefficients of the expansion. On the other hand, motivated by the approximation of special functions with two asymptotic parameters, Nemes has generalized Laplace's method by considering Laplace integrals with two asymptotic parameters of a different asymptotic order. Nemes considers a linear dependence of the phase function on the two asymptotic parameters. In this paper, we investigate if the simplifying ideas introduced in López, Pagola and Perez (2009) [9] for Laplace integrals with one large parameter may be also applied to the more general Laplace integrals considered in Nemes's theory. We show in this paper that the answer is yes, but moreover, we show that those simplifying ideas can be applied to more general Laplace integrals where the phase function depends on the large variable in a more general way, not necessarily in a linear form. We derive new asymptotic expansions for this more general kind of integrals with simple and explicit formulas for the coefficients of the expansion. Our theory can be applied to special functions with two or more large parameters of a different asymptotic order. We give some examples of special functions that illustrate the theory.

A graph G is called k-extendable if for any matching M of size k in G, there exists a perfect matching of G containing M. Let $D\left(G\right)$ and $A\left(G\right)$ be the degree diagonal matrix and the adjacency matrix of G, respectively. For $0\le \alpha <1$, the spectral radius of $A_{\alpha }\left(G\right)=\alpha D\left(G\right)+(1-\alpha )A\left(G\right)$ is called the α-spectral radius of G. In this paper, we give a sufficient condition for a graph G to be k-extendable in terms of the α-spectral radius of G and characterize the corresponding extremal graphs. Moreover, we determine the spectral and signless Laplacian spectral radius conditions for a balanced bipartite graph to be k-extendable.

One of the crucial problems in combinatorics and graph theory is characterizing extremal structures with respect to graph invariants from the family of chemical trees. Cruz et al. (2020) [7] presented a unified approach to identify extremal chemical trees for degree-based graph invariants in terms of graph order. The exponential augmented Zagreb index (EAZ) is a well-established graph invariant formulated for a graph G as$EAZ\left(G\right)=\sum _{v_i{v}_j\in E\left(G\right)}{e}^{{\left(\frac{d_i{d}_j}{d_i+d_j-2}\right)}^3},$ where $d_i$ signifies the degree of vertex $v_i$, and $E\left(G\right)$ is the edge set. Due to some special counting features of EAZ, it was not covered by the aforementioned unified approach. As a result, the exploration of extremal chemical trees for this invariant was posed as an open problem in the same article. The present work focuses on generating a complete solution to this problem. Our findings offer maximal and minimal chemical trees of EAZ in terms of the graph order n.

The interaction between strategy and environment widely exists in nature and society. Traditionally, evolutionary dynamics in finite populations are described by the Moran process, where the environment is constant. Therefore, we model the Moran process with environmental feedbacks. Our results show that the selection intensity, which is closely related to the population size, exerts varying influences on evolutionary dynamics. In the case of the specific payoff matrix, cooperation cannot be favored by selection in extremely small-sized populations. The medium-sized populations are beneficial for the evolution of cooperation under intermediate selection intensities. For weak or strong selection intensities, the larger the population size, the more favorable it is for the evolution of cooperation. In the case of the generalized payoff matrix, the low incentives for the defector to cooperate in the degraded state cannot promote the emergence of cooperation. As the incentive for the defector to cooperate in the degraded state increases, selection favors cooperation or defection depending on the population size and selection intensity. For large values of the incentive for the defector facing the cooperative opponent to cooperate in the degraded state, selection always favors cooperation. We further investigate the impact of the time-scale on the fixation probability of cooperation.

Binarization for degraded text images has always been a very challenging issue due to the variety and complexity of degradations. In this paper, we first construct a thresholding function for the input image in a local manner and then present an anisotropic diffusion equation with a source involving dynamic thresholding function. This dynamic thresholding function is governed by an auxiliary evolution equation, taking the constructed thresholding function as the initial condition. In the diffusion equation, the diffusion term achieves the edge preserving smoothing, while the source term is response for designating dynamically the text and background pixels as two dominant modes separated by the final dynamic thresholding function. To evaluate the proposed model solely, we only utilize the simplest finite differencing rather than more elaborated scheme to solve it numerically. Experiments show that the proposed model has generally achieved the superior binarization results to other nine compared models.

The transmission of a vertex in a connected graph is the sum of distances from that vertex to all other vertices. A graph is transmission-irregular (TI) if no two of its vertices have the same transmission. Xu et al. (2023) [3] recently asked to establish methods for constructing new TI graphs from the existing ones and also about the existence of chemical TI graphs on every even order. We show that, under certain conditions, new TI graphs can be obtained from the existing TI graph G either by attaching pendent paths of equal length to every vertex of G or by attaching two pendent paths of consecutive lengths to one vertex of G. We also show the existence of chemical TI graphs for almost all even orders.

Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish this without relying on some extreme constraints, which are usually necessary in stability analysis. Then, with the aid of the integral form of the method coefficients, we provide a simple stability criterion that can be easily verified. We also present a theorem on the order barrier for the proposed methods, stating that there is no method of order five or higher that satisfies the simple criterion. Numerical tests are carried out to validate the theoretical results.