Journal of Applied Mathematics and Computing最新文献

In this paper, to further enhance the efficiency of the improved alternating positive semi-definite splitting (IAPSS) preconditioner proposed by Ren et al. (Numer Algorithms 91:1363–1379, 2022. https://doi.org/10.1007/s11075-022-01305-y), the modified IAPSS preconditioner is established, which can be applied to GMRES method to solve the double saddle point problems. The construction idea of the preconditioner is to modify several sub-matrices in the IAPSS preconditioner. Theoretically, the iteration method generated by the proposed preconditioner is unconditionally convergent for all positive parameters. Furthermore, the selection of the parameters is discussed in detail. Finally, the performance of the preconditioner is verified by the two examples of the liquid crystal director model and the mixed Stokes/Darcy model.

In this paper, we propose an efficient numerical algorithm for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel. In time direction, we use second-order finite difference schemes to discretize the Caputo fractional derivative and also singular integral term. To achieve fully discrete scheme, we apply Galerkin method using generalized Jacobi polynomials as basis, which satisfy essentially all the underlying homogeneous boundary conditions. The proposed method is fast and efficient due to the resulting sparse coefficient matrices. We investigate the error estimate and prove that the method is convergent. Numerical results show the high accuracy and low CPU time of proposed method and confirmed the theoretical ones. Second-order accuracy in time direction and spectral accuracy in space component are also numerically demonstrated by some test problems. Finally we compare the numerical results with the results of other recently methods developed in literature.

For a given graph G, the second Zagreb eccentricity index (xi _2 (G)) is defined as the product of the eccentricities of two adjacent vertex pairs in G. This paper mainly studies the problem of determining the graphs that minimize the second Zagreb eccentricity index among n-vertex bipartite graphs with a fixed number of edges and diameter. To be specific, we determine the sharp lower bound on the second Zagreb eccentricity index over the bipartite graphs of order n in terms of fixed edges and diameter. The extremal graphs attaining these lower bounds are fully characterized.

In this manuscript, a general class of Jacobian-free iterative schemes for solving systems of nonlinear equations is presented. Once its fourth-order convergence is proven, the most efficient sub-family is selected in order to make a qualitative study. It is proven that the most of elements of this family are very stable, and this is checked by means on numerical tests on several problems of different sizes. Their performance is compared with other known Jacobian-free iterative procedure, being better in the most of results.

Smog is a thick haze of air pollution that harms human health and the environment. If we can control the factors of smog, then we can reduce it. A well-organized and valuable tool is a picture fuzzy influence graph (left( {PFIG} right)) for managing ambiguity in practical challenges, including uncertain data, figures, facts, and discoveries. A (PFIG) provides membership, non-membership, and neutral degree values of vertices, edges, and influence pairs. Using the picture fuzzy influence pairs, we can get information regarding the effect of one vertex on another vertex or edge of the same or another graph, which is a key feature as this can connect two disconnected graphs. This article represents some basic concepts such as strongest, strong, and weak picture fuzzy influence pairs, which help to propose the idea of domination in a (PFIG). Finally, we present a helpful, applicable, and practical application to control smog using the concept of domination in a (PFIG). The proposed work is cross-verified by some multi-criteria decision-making methods such as TOPSIS, VIKOR, and EDAS, as well as with some picture fuzzy entropies.

In this paper, we derive a quantum analogue of Hermite–Hadamard-type inequalities for twice differentiable convex functions whose second derivatives in absolute value are strongly ((alpha ,m ))-convex. We obtain new bounds using the H(ddot{o})lder and power mean inequalities. Moreover, we provide suitable examples in support of our theoretical results. We correlate our findings with comparable results in the literature and show that the obtained results are refinements and improvements.

Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including rotations requires sampling the whole space of rotations, repeating the computation of the correlation each time.This article develops an alternative mathematical theory to handle efficiently, at the same time, rotations and translations. Our proposal has a reduced computational complexity because it does not require to repeatedly sample the space of rotations. To do so, we integrate the information relative to all rotated versions of the template into a unique symmetric tensor template -which is computed only once per template-. Afterward, we demonstrate that the correlation between the image to be processed with the independent tensor components of the tensorial template contains enough information to recover template instance positions and rotations. Our proposed method has the potential to speed up conventional template matching computations by a factor of several magnitude orders for the case of 3D images.

In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and sufficient condition for a pair of codes (C, D) to be LCP of codes over finite non-commutative Frobenius rings. The minimum distances d(C) and (d(D^perp )) are defined as the security parameter for an LCP of codes (C, D). It was recently demonstrated that if C and D are both 2-sided LCP of group codes over a finite commutative Frobenius rings, (D^perp ) and C are permutation equivalent in Liu and Liu (Des Codes Cryptogr 91:695–708, 2023). As a result, the security parameter for a 2-sided group LCP (C, D) of codes is simply d(C). Towards this, we deliver an elementary proof of the fact that for a linear complementary pair of codes (C, D), where C and D are linear codes over finite non-commutative Frobenius rings, under certain conditions, the dual code (D^perp ) is equivalent to C.

The primary goal of this study is to investigate the necessary conditions for the Hilfer–Langevin dynamical system with initial circumstances to be controllable. Using a sequencing technique, we have employed the concept of a bounded integral contractor to reach our results. Unlike previous studies, we do not need to specify the induced inverse of the controllability operator, and the relevant nonlinear function does not have to satisfy a Lipschitz condition to prove our accurate controllability conclusions. We have obtained a theoretical result that is shown to be critically important through an example.