Applied Mathematics-A Journal of Chinese Universities Series B最新文献

In that paper, we new study has been carried out on previous studies of one of the most important mathematical models that describe the global economic movement, and that is described as a non-linear fractional financial model of awareness, where the studies are represented at the steps following: One: The schematic of the model is suggested. Two: The disease-free equilibrium point (DFE) and the stability of the equilibrium point are discussed. Three: The stability of the model is fulfilled by drawing the Lyapunov exponents and Poincare map. Fourth: The existence of uniformly stable solutions have discussed. Five: The Caputo is described as the fractional derivative. Six: Fractional optimal control for NFFMA is discussed by clarifying the fractional optimal control through drawing before and after control. Seven: Reduced differential transform method (RDTM) and Sumudu Decomposition Method (SDM) are used to take the resolution of an NFFMA. Finally, we display that SDM and RDTM are highly identical.

The Estrada index of a graph G on n vertices is defined by (EE(G) = sumnolimits_{i = 1}^n {{e^{{lambda _i}}}} ), where λ₁, λ₂, ⋯, λ_n are the adjacency eigenvalues of G. We define two general types of dynamic graphs evolving according to continuous-time Markov processes with their stationary distributions matching the Erdös-Rényi random graph and the random graph with given expected degrees, respectively. We formulate some new estimates and upper and lower bounds for the Estrada indices of these dynamic graphs.

In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying generalized contractive conditions are obtained, without appealing to completeness of X or normality of the cone. The continuity of the mapping is relaxed. Furthermore, we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X. These results greatly generalize several well-known comparable results in the literature.

In this paper, we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalized Φ-hemicontractive mappings in the intermediate sense. We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalized Φ-hemicontractive mappings in the intermediate sense. Our results extends, improves and complements several known results in literature.

A 2-dimension linguistic lattice implication algebra (2DL-LIA) can build a bridge between logical algebra and 2-dimension fuzzy linguistic information. In this paper, the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed. Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated. Moreover, it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation (PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.

This paper is concerned with the spreading speed of a food-limited population model with delay. First, the existence of the solution of Cauchy problem is proved. Then, the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality. Finally, we present some numerical simulations and investigate the dynamical behavior of the solution.

This paper extends the criterion of the misclassification ratio of discriminant model and presents a new selection method of discriminant model. For selecting the discriminant model, this method establishes the rule of misclassification degree ratio through misclassification ratio of the discriminant model and misclassification degree of the samples. To test the effect of this method, this work uses seven UCI data sets. Numerical experiments on these examples indicate that this method has certain rationality and has a better effect to select a discriminant model.

To pursue the outperformance of deep nets in learning, we construct a deep net with three hidden layers and prove that, implementing the empirical risk minimization (ERM) on this deep net, the estimator can theoretically realize the optimal learning rates without the classical saturation problem. In other words, deepening the networks with only three hidden layers can overcome the saturation and not degrade the optimal learning rates. The obtained results underlie the success of deep nets and provide a theoretical guidance for deep learning.

In this work, stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated. Some effective sufficient conditions of stability, uniform stability, asymptotic uniform stability and Mittag Leffler stability. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. Furthermore, some numerical examples are given to show the effectiveness of our obtained theoretical results.