Computational and Applied Mathematics最新文献

A graph invariant, in the sense of graph automorphism, is a mapping from the set of graphs to the reals. Numerous topological indices have been proposed to characterize the topological properties of graphs, and they are widely recognized as graph invariants. Some sufficient conditions in terms of certain topological indices have been suggested to describe hamiltonian properties of graphs, such as Hamiltonicity, traceability, Hamiltonian-connectedness, k-leaf-connectedness, as well as (beta )-deficiency. For a graph G, the first and second Zagreb indices are defined as (M_1(G)= sum nolimits _{uin V(G)} {d_u^2}) and (M_2(G)= sum nolimits _{uvin E(G)} {d_u}{d_v}), where (d_u) denotes the degree of vertex u in G. The difference of Zagreb indices of G is defined as (Delta M(G) = {M_2}(G) - {M_1}(G)). In this paper, we suggest some sufficient conditions in terms of (Delta M(G)) for graphs to be Hamiltonian, Hamiltonian-connected and (beta )-deficient, respectively.

This article presents a numerical solution for a specific class of 2D parabolic singularly perturbed convection-diffusion problems with a special interior line source. The proposed approach employs the alternating direction implicit type operator splitting streamline-diffusion finite element method (SDFEM), offering a viable solution to alleviate computational complexity and high storage requirements encountered in higher-dimensional problems. The overall stability of the two-step method is established, while a piecewise-uniform Shishkin mesh is employed for spatial domain discretization. By carefully selecting the stabilization parameter, an (varepsilon )-uniform error estimate is derived, accounting for the influence of the time step-interval which is essential to maintain the method’s stability. To validate the theoretical error estimate, numerical investigation are conducted, showcasing the effectiveness of the proposed method. This research contributes to advancing the understanding and numerical treatment of this specific class of 2D parabolic singularly perturbed convection-diffusion problems, shedding light on the intricate dynamics and behavior of the system in the presence of a special interior line source.

The concept of alpha-order has been recently introduced as a binary relation that allows ranking fuzzy sets with bounded support and whose (beta )-cuts are closed subsets with a finite number of connected components. This paper explores some key properties of such alpha-order. Specifically, we will focus on admissibility, a fundamental property for any ranking method defined for fuzzy numbers since it guarantees that such a ranking method is consistent with the usual order on the real line.

In the current intelligent era, with the increasing complexity and diversification of productive practices, it is usually necessary to get a balanced consideration of many aspects of the decision-making problem. One of the most important and popular methods to solve decision problems is multi-attribute decision making (MADM). Traditional MADM problems in q-rung orthopair fuzzy (q-ROF) environment aggregate evaluation information by means of aggregation operators. However, aggregation operators are improper to effectively solve some complicated problems. To settle this problem, we come up with a new method based on neighborhood-related q-ROF covering-based rough set (NRq-ROFCRS) models for MADM problem in this paper. To define these models, several q-ROF logical operators are firstly defined. Next the concepts of q-ROF neighborhood systems of an object, q-ROF minimal and maximal description of an object and q-ROF covering are defined. On this basis, four t-norm-based q-ROF neighborhood operators (Tq-ROFNOs) and four overlap function-based q-ROF neighborhood operators (Oq-ROFNOs) are proposed. For a finite q-ROF covering, combining four Tq-ROFNOs and six q-ROF coverings results in 24 Tq-ROFNOs and only sixteen groups of Tq-ROFNOs are obtained. We also combine four Oq-ROFNOs and six q-ROF coverings and prove that only seventeen groups of Oq-ROFNOs are obtained. Then partial order relations among 16 groups of Tq-ROFNOs and 17 groups of Oq-ROFNOs are discussed, respectively. Moreover, four types of NRq-ROFCRS models are defined based on q-ROF neighborhood operators and the groups and partial order relations of neighborhood-related q-ROF approximate operators are discussed. Finally, a novel method for MADM problems by integrating NRq-ROFCRS models with TOPSIS method is put forward and the effectiveness and the reasonableness of our method are verified by experiments.

In this paper, an approximate descent three-term derivative-free algorithm is developed for a large-scale system of nonlinear symmetric equations where the gradients and the difference of the gradients are computed approximately in order to avoid computing and storing the corresponding Jacobian matrices or their approximate matrices. The new method enjoys the sufficient descent property independent of the accuracy of line search strategies and the error bounds of these approximations are established. Under some mild conditions and a nonmonotone line search technique, the global and local convergence properties are established respectively. Numerical results indicate that the proposed algorithm outperforms the other similar ones available in the literature.

In this study, we explore a new robust compact difference method (CDM) on graded meshes for the time-fractional nonlinear Kuramoto–Sivashinsky (KS) equation. This equation exemplifies a fourth-order sub-diffusion equation marked by nonlinearity. Considering the weak singularity often exhibited by exact solutions of time-fractional partial differential equations (TFPDEs) near the initial time, we introduce the L2-1(_{sigma }) scheme on graded meshes to discretize the Caputo derivatives. By employing a novel double reduction order approach, we obtain a triple-coupled nonlinear system of equations. To address the nonlinear term (uu_{x}), we use a fourth-order nonlinear CDM, while the second and fourth derivatives in space are treated using the fourth-order linear CDM. We prove the solvability through Browder theorem. Additionally, (alpha )-robust stability and convergence are demonstrated by introducing a modified discrete Grönwall inequality. Finally, we present numerical examples to corroborate the findings of our theoretical analysis.

In this article, we develop innovative models of multigranulation rough fuzzy sets, utilizing fuzzy (beta )-covering and incorporating a range of techniques such as fuzzy (beta )-neighborhood, fuzzy complementary (beta )-neighborhood, fuzzy (beta )-minimal description, and fuzzy (beta )-maximal description. The axiomatic characteristics of fuzzy (beta )-neighborhoods within the context of fuzzy (beta )-covering based multigranulation rough fuzzy sets (F(beta )CMGRFS) are analyzed. Thus, we introduce seven new classes of F(beta )CMGRFS and investigate their relevant properties. Furthermore, the connections and associations between these techniques are established. Thus, we provide a set of observations and propositions that highlight the value and dissimilarities of our proposed models compared to others. A test example is produced to verify the applicability of the presented strategies and treat MCGDM issues. Finally, we compare the outcomes of our approaches and the existing studies to check the reliability and the validity of our work.

In this paper, we consider the steps to be followed in the analysis and interpretation of the quantization problem related to the (C_{2,8}) channel, where the Fuchsian differential equations, the generators of the Fuchsian groups, and the tessellations associated with the cases (g=2) and (g=3), related to the hyperbolic case, are determined. In order to obtain these results, it is necessary to determine the genus g of each surface on which this channel may be embedded. After that, the procedure is to determine the algebraic structure (Fuchsian group generators) associated with the fundamental region of each surface. To achieve this goal, an associated linear second-order Fuchsian differential equation whose linearly independent solutions provide the generators of this Fuchsian group is devised. In addition, the tessellations associated with each analyzed case are identified. These structures are identified in four situations, divided into two cases ((g=2) and (g=3)), obtaining, therefore, both algebraic and geometric characterizations associated with quantizing the (C_{2,8}) channel.

The impurity segregation in diluted transition-metal bimetallic alloys is a subject of study in many fields of interest and still deserves more understanding. Using a tight-binding model for the case of a single substitutional metal impurity the segregation is investigated analysing the segregation energy. Different impurity positions are considered from the (001) top surface to a number of planes below it on a simple cubic lattice. With only one orbital per site, the impurity potentials are determined in order to satisfy charge neutrality through the Friedel sum rule. In particular, our attention will be mainly directed to the substitutional impurity located in the surface and in the bulk. Temperature effects are considered through the Sommerfeld Expansion. Interesting effects on the segregation energy are pointed out such as the appearance of a quantum interference on the electronic states due to the surface itself. The obtained trend of the segregation energy profile is in good agreement with the surface concentration experimental data.

This paper is concerned with developing an iterative tensor Krylov subspace method to solve linear discrete ill-posed systems of equations with a particular tensor product structure. We use the well-known Frobenius inner product for two tensors and the n-mode matrix-product of a tensor with a matrix to define tensor QR decomposition and alternative Arnoldi algorithms. Moreover, we illustrate how the tensor alternative Arnoldi process can be exploited to solve ill-posed problems by recovering blurry color images and videos in conjunction with the Tikhonov regularization technique, to derive approximate regularized solutions. We also review a generalized cross-validation technique for selecting the regularization parameter in the Tikhonov regularization. Theoretical properties of this method are demonstrated and applications including image deblurring and video processing are investigated. Numerical examples compare the proposed method with several other methods and illustrate the potential superiority of mentioned methods.