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Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101721

Abstract:
Recent advancements in artificial intelligence and machine learning have led to the development of powerful tools for use in problem solving in a wide array of scientific and technical fields
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101723

Abstract:
The free-riding behavior of companies that do not act will bring losses to companies that provide services. A market consists of two secondary supply chains: manufacturers and retailers. Each supply chain can choose to adopt promotional strategies to expand its market demand. This paper constructs the centralized decision-making in the supply chain and the Nash game competition model between supply chains and primarily studies the impact of risk aversion and the free-riding coefficient on supply chain pricing, promotion strategy selection, and expected utility. We show that the supply chain with high-risk aversion has relatively low pricing, but the demand and a total expected utility are high. We also identify that, on the premise of the same risk aversion degree of the two supply chains, when the free-riding coefficient between the chains is small and equal, the supply chain tends to implement the promotion strategy. When consumers have the same preference for the products of two retailers, the pricing of the free-riding supply chain increases with the increase in the free-riding coefficient, while the supply chain with a promotion strategy is the opposite. Based on the numerical results, we further give the optimal one-way free-riding coefficient when the two supply chains have the same degree of risk aversion; when there is a bidirectional free-riding behavior in the market, competition among supply chains gradually tends to the first two scenarios.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101731

Abstract:
Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold $\left(M,g,f,\mu \right)$ to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a $\left(\lambda ,n+m\right)$-Einstein manifold $\left(M,g,w\right)$ having harmonic Weyl tensor, $\left({\nabla }^{j}w\right)\left({\nabla }^{m}w\right){\mathcal{C}}_{jklm}=0$ and ${\nabla }_{l}w{\nabla }^{l}w<0$ reduces to a perfect fluid generalized Robertson–Walker spacetime with Einstein fibers. Finally, $\left(M,g,w\right)$ reduces to a perfect fluid manifold if $\phi =-m\nabla \left(lnw\right)$ is a $\phi \left(\mathrm{Ric}\right)$-vector field on M and to an Einstein manifold if $\psi =\nabla w$ is a $\psi \left(\mathrm{Ric}\right)$-vector field on M. Some consequences of these results are considered.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101728

Abstract:
This paper mainly considers a class of non-weight modules over the Lie algebra of the Weyl type. First, we construct the $U\left(\mathfrak{h}\right)$-free modules of rank one over the differential operator algebra. Then, we characterize the tensor products of these kind of modules and the quasi-finite highest weight modules. Finally, we undertake such research for the differential operator algebra of multi-variables.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101733

Abstract:
The remaining useful life (RUL) of the unmanned aerial vehicle (UAV) is primarily determined by the discharge state of the lithium-polymer battery and the expected flight maneuver. It needs to be accurately predicted to measure the UAV’s capacity to perform future missions. However, the existing works usually provide a one-step prediction based on a single feature, which cannot meet the reliability requirements. This paper provides a multilevel fusion transformer-network-based sequence-to-sequence model to predict the RUL of the highly maneuverable UAV. The end-to-end method is improved by introducing the external factor attention and multi-scale feature mining mechanism. Simulation experiments are conducted based on a high-fidelity quad-rotor UAV electric propulsion model. The proposed method can rapidly predict more precisely than the state-of-the-art. It can predict the future RUL sequence by four-times the observation length (32 s) with a precision of 83% within 60 ms.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101727

Abstract:
The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in 2018 by Mihai, A. and Mihai, I. who dealt with Chen-Ricci and Euler inequalities. Later on, Siddiqui, A.N., Ahmad K. and Ozel C. came with the study of Casorati inequality for statistical submanifolds in the same ambient space by using algebraic technique. Also, Chen, B.-Y., Mihai, A. and Mihai, I. obtained a Chen first inequality for such submanifolds. In 2020, Mihai, A. and Mihai, I. studied the Chen inequality for $\delta \left(2,2\right)$-invariant. In the development of this topic, we establish the generalized Wintgen inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature. Some examples are also discussed at the end.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101722

Abstract:
A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in each step. The high-order series of expanded variables bring high accuracy in the time domain, especially for the elasto-dynamic equations, which are second-order PDE in the time domain. In the present mixed MLPG5 dynamic formulation, the strains are interpolated independently, as are displacements in the local weak form, which eliminates the expensive differential of the shape function. In the traditional MLPG5, both shape function and its derivative for each node need to be calculated. By taking the Heaviside function as the test function, the local domain integration of stiffness matrix is avoided. Several numerical examples, including the comparison of our method, the MLPG5–Newmark method and FEM (ANSYS) are given to demonstrate the advantages of the presented method: (1) a large time step can be used in solving a elasto-dynamics problem; (2) computational efficiency and accuracy are improved in both space and time; (3) smaller support sizes can be used in the mixed MLPG5.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101724

Abstract:
Considering the $\omega$-distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using $\omega$-distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101725

Abstract:
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.
Published: 18 May 2022
by MDPI
Mathematics, Volume 10; https://doi.org/10.3390/math10101726

Abstract:
The idea of bipolar complex fuzzy (BCF) sets, as a genuine modification of both bipolar fuzzy sets and complex fuzzy sets, gives a massive valuable framework for representing and evaluating ambiguous information. In intelligence decision making based on BCF sets, it is a critical dilemma to compare or rank positive and negative membership grades. In this framework, we deliberated various techniques for aggregating the collection of information into a singleton set, called BCF weighted arithmetic averaging (BCFWAA), BCF ordered weighted arithmetic averaging (BCFOWAA), BCF weighted geometric averaging (BCFWGA), and BCF ordered weighted geometric averaging (BCFOWGA) operators for BCF numbers (BCFNs). To illustrate the feasibility and original worth of the diagnosed approaches, we demonstrated various properties of the diagnosed operators, in addition to their capability that the evaluated value of a set of BCF numbers is a unique BCF number. Further, multiattribute decision making (“MADM”) refers to a technique employed to compute a brief and dominant assessment of opinions with multiattributes. The main influence of this theory is implementing the diagnosed theory in the field of the MADM tool using BCF settings. Finally, a benchmark dilemma is used for comparison with various prevailing techniques to justify the cogency and dominancy of the evaluated operators.