Journal of Applied Mathematics and Computing最新文献

We study single-machine scheduling problems with Generalized due-dates (GDD), learning effect, and optional job rejection. For the GDD setting, the due dates are assigned to the jobs according to their position in the sequence rather than their identity. Thus, assuming that due dates are numbered in non-decreasing order, the jth due date refers to the job assigned to the jth position. The learning effect is a model where completing former jobs decreases the completion time of latter jobs. The processing time is still part of the input, depending on how many jobs have already been scheduled. Allowing the option of job rejection means that not all jobs must be processed. In this case, the scheduler is penalized for each rejected job, and an input parameter bounds the total rejection cost. Two objective functions are considered with the above-mentioned settings: minimizing total tardiness and minimizing maximal tardiness. The problems are polynomially solvable when there is no option for job rejection. Otherwise, both are shown to be NP-hard, pseudo-polynomial dynamic programming solutions are proposed, and numerical experiments are provided.

This paper investigates the relationship between fuzzy median graphs and blocks, which are important concepts in fuzzy graph theory, particularly in terms of connectivity. The main focus is on the fuzzy median property of a block that has at least four vertices and does not have any fuzzy bridges. The paper also examines the fuzzy median property of isomorphic images of median graphs and explores the median behavior of isometric subgraphs of a fuzzy median graph. Furthermore, the paper investigates the median property of fuzzy median graphs under graph operations. The main concern of the paper is to determine whether the union of two fuzzy median graphs retains fuzzy median behavior. The paper studies the connection between fully strong gated fuzzy graphs and fuzzy median graphs. It also explores whether the gate of an induced subgraph can also be in the median set of any triple of vertices. Additionally, the paper introduces a novel centrality measure called median centrality to identify the influential nodes in a network. The sum of the median centrality of all vertices in a fuzzy median graph will always be one.

Benefiting from the development of Internet technology, online social networks with multilingual communication function are in a booming stage, greatly contributing to the convenience, extensiveness and diversity of information exchange. To explore the rumor diffusion mechanism and efficient control strategies in multilingual online environments, a novel stochastic rumor-spreading model with the generalized nonlinear diffusion form is proposed. Firstly, we strictly prove the positive and existence uniqueness of the model solution to ensure that it corresponds to the realistic meaning. Then, the asymptotic behavior around the rumor-free equilibrium is acquired by using graph theorey and stochastic stability theory. Besides, we obtain conditions for the stationary distribution of stochastic rumor-spreading model based on the Kasminskii’s theory. Moreover, an event-triggered discontinuous feedback (ETDF) control strategy that can be applied to online networks is proposed, which initiates control only when an alert threshold is exceeded and updates the control intensity when an event-triggered condition is reached. Finally, numerical simulations verify the correctness of the theoretical results, and an actual multilingual Internet rumor case shows the applicability of the model.

Carbon nanotube Y-shaped junctions (normally called as Y-junctions) are constructed by inserting heptagons into the graphene sheet. The design requires the inclusion of at least 6 heptagons at the junction where 3 carbon nanotubes joined. With the growing focus on carbon nanotubes, their junctions have garnered increased attention for their applications in various scientific fields. Chemical structures can be expressed in graphs, where atoms represent vertices, and the bonds between the atoms are called edges. To obtain the exact position of an atom, which is unique from all the atoms, several atoms are selected, this is called resolving set. The minimum number of atoms in the resolving set is called the metric dimension. In this paper, we have computed the metric dimension of carbon nanotube Y-junctions, assigning each atom a unique identifier to facilitate precise location. The metric dimension is constant for all the values of the 3 parameters included to develop a Y-junction. It resulted in 3 metric dimensions for the entire Y-junction. It means that whatever the order and quantity of nanotubes attached to it, the metric dimension will remain constant with number 3.

As a classical concept of graph theory, single-source shortest paths (SSSPs) plays a crucial role in numerous practical applications. Presently, the time complexity of existing SSSPs algorithms is at least ({O}(m + nlogn)). Therefore, it is still significant to design SSSPs algorithms with higher computational efficiency. In our former works, the efficiency of computing strongly connected components (SCCs) has enhanced through utilizing rough sets theory (RST). Thus, this paper also attempts to compute SSSPs more efficiently based on RST. Firstly, the graph concept of SSSPs is analyzed in the framework of RST, to provide the theoretical basis of computing SSSPs through RST method. Secondly, k-step R-related set (one RST operator) is utilized for traversing those vertices which are reachable from the source vertex. Thirdly, a marking strategy is introduced to narrow the search scope of SSSPs, which can further promote the efficiency of computing SSSPs. Finally, based on RST and marking strategy, an algorithm named 3SP@RM is put forward for finding SSSPs of unweighted directed graphs. The comparative experiment is conducted over 14 datasets. Related results display that 3SP@RM algorithm can correctly compute SSSPs of unweighted directed graphs, and the efficiency of 3SP@RM algorithm exceeds that of two existing similar methods. Even the larger scale of dataset is, more efficiency advantage 3SP@RM algorithm has.

In this paper, based on the reproducing kernel functions and iterative technique, a new sixth order iterative numerical scheme is presented for nonlinear fourth order boundary value problems(FOBVPs). Compared with the existing reproducing kernel functions based numerical techniques for boundary value problems, the present approach is implemented by using the reproducing kernel functions of the reproducing kernel Hilbert space with lower regularity. This leads to good stability of the proposed technique. The results of numerical examples also demonstrate that our approach has higher accuracy for nonlinear FOBVPs.

Blockchain technology is a digital ledger technology that is used to store and manage data in a decentralized and secure way. It is essentially a database that is distributed across a network of computers, and every block of data is connected to the prior block, forming a chain of blocks (hence the name "blockchain"). Blockchain technology can transform the way multinational companies operate, enabling them to operate more efficiently, securely, and transparently in a globalized business environment. The selection of the best and finest blockchain technology for any multinational company is not an easy task. Thus, in this script, we generate primary operations relying on Yager t-norm and t-conorm for bipolar fuzzy information and then generate aggregation operators under bipolar fuzzy information such as bipolar fuzzy Yager weighted averaging, bipolar fuzzy Yager ordered weighted averaging, bipolar fuzzy Yager weighted geometric and bipolar fuzzy Yager ordered weighted geometric operators based on initiated operations. Moreover, we generate an approach to decision-making by employing the generated operators to tackle real-life decision-making dilemmas. Afterward, we initiate a case study i.e., ordering blockchain technology for Multinational companies. Towards the end of this script, to reveal the superior qualities and benefits of the generated work, we conduct a comparative analysis between the current and generated work.

We consider a class of generalized linear multiplicative problems (GLMP), which have a wide range of applications and are known to be NP-hard. In this paper, we first transform it into an equivalent problem (EP) by introducing p new variables and applying logarithmic transformation. Secondly, in order to calculate the lower bound, we derived the linear relaxation problem (LRP) of EP by constructing a novel relaxation strategy. Additionally, a rectangular region reduction technique is proposed to accelerate the convergence speed of the algorithm. Based on the output-space search, we propose a new branch-and-bound algorithm for tackling the GLMP or EP. The global convergence of the algorithm is proved, and its computational complexity is analyzed to estimate the maximum number of iterations. Especially on the basis of LRP, we also propose another new convex relaxation based branch-and-bound algorithm for GLMP. Some experimental examples demonstrate the feasibility and effectiveness of these two algorithms.

In recent years, the fractals (Hausdorff) derivatives with fractional order under various types kernel have gained attention from researchers. The aforesaid area has many applications in the description of intricate and irregular geometry of various processes. Numerous studies utilizing the fractional derivatives (HFDs) for initial value problems have been carried out. But the boundary value problems using the said concepts have been very rarely studied. Thus, a coupled system with non-homogenous boundary conditions (BCs) is examined in this study by using fractals fractional derivative in Caputo Fabrizio sense. To establish the required conditions for the existence and uniqueness of solution to the considered problem, we apply the Banach and Krasnoselskii’s fixed point theorems. Furthermore, some results related to Hyers-Ulam (H-U) stability have also deduced. We have included two pertinent examples to verify our results.

In this article, we introduce an enriched (omega )-Reich–Suzuki type nonexpansive mapping and provide a couple of numerical examples to verify the existence of enriched (omega )-Reich–Suzuki type nonexpansive maps. Notably, the Z-iteration method has been shown to have faster convergence rates than some well-known iteration approaches. We establish both strong and weak convergence of enriched (omega )-Reich–Suzuki type nonexpansive mapping using the powerful Z-iteration technique. Also, we provide an application to approximate the solution of a delay differential equation and presenting an illustrative numerical example to validate our findings.