Based on the fact that epidemics are affected by environmental noise and psychological effects, a stochastic SIRS epidemic model with Logistic growth and psychological effects is established to discuss the effects of Logistic growth and psychological effects on the global dynamics of the model. Firstly, by constructing the Lyapunov function and using the It$\hat{\rm o}$ formula, the existence and uniqueness of the global positive solution of the model are proved, and then, under appropriate conditions, by using the random Lyapunov function method, the sufficient conditions for the existence of ergodic stationary distribution of the positive solution of the model are obtained by using the LaSalle invariance principle. The results show that environmental and psychological change can inhibit the disease under certain conditions. Finally, the correctness of the theoretical results is verified by numerical simulation.

The numerical algorithm of continuous Sylvester matrix equation is studied deeply, and a parameterized single step HSS iteration method is proposed innovatively. This method has a unique solution idea and its convergence is proved. In order to improve the performance, quasi-optimal parameters are found by minimizing the upper bound of the spectral radius of the iterative matrix. Numerical experiments verify the effectiveness and robustness of the new method, and demonstrate its high efficiency and stability in solving continuous Sylvester matrix equations, which provides a new tool for relevant numerical calculation.

The filled function method, as an effective approach for solving global optimization problems involving multivariable and multimodal functions, finds the global optimal solution or approximate global optimal solution by alternately minimizing the objective function and the filled function. Its optimization performance is directly related to the properties of the filled function employed. Consequently, constructing novel filled functions with good mathematical properties has always been a significant hot research. However, existing filled functions present the following issues: they with discontinuity and non-differentiability are not easily solvable; they contain many parameters that are difficult to control and adjust; they include exponential or logarithmic terms affecting the efficiency of the algorithm. To address these shortcomings, the F-C function for solving unconstrained global optimization problems is introduced by combining the filled function with the cross function. Based on this definition, a new single-parameter F-C function is constructed, and the parameter is easily adjustable during the iterative process. By the theoretical properties analysis, a new global optimization F-C function method using the F-C function is proposed, which breaks the solving framework of traditional filled function algorithms, reduces the numbers of solving the objective function, and improves computational efficiency. The effectiveness and feasibility of the F-C function algorithm are verified through several numerical computations. Finally, the F-C function algorithm is applied to optimize parameters in cutting temperature experiments. The numerical experiment results showed that the proposed algorithm has better fitting effect compared with previous findings.

In this paper, we considered a class of matrix trace function minimization problem under orthogonal constraints which arise in multivariate statistical analysis. Serval special forms of the considered problem model are widely used in the least square fitting of DEDICOM model and orthogonal INDSCAL model in multidimensional scaling analysis. Combining with orthogonal splitting techniques, several classical unfeasible iterative algorithms for solving manifold optimization problems are constructed to solve the underlying problem, and the iterative framework of these algorithms and the specific solution scheme of the generated subproblems are given. Some numerical tests are given to show the efficiency of the proposed methods.

In view of the multi-attribute decision problem in which attribute weights are completely unknown or partially known and attribute values are in the form of interval-valued Pythagorean hesitant fuzzy numbers, ELECTRE II decision making method is proposed based on interval-valued Pythagorean hesitant fuzzy entropy and cross entropy. Firstly, new interval score function and interval accuracy function of interval-valued Pythagorean hesitant fuzzy number are defined, and a new distance measure is defined. Secondly, the entropy and cross entropy formula are given based on the fuzzy factor, intuitive factor and amplitude factor of interval-valued Pythagorean hesitant fuzzy number, and their properties are proved. A method to determine attribute weights based on entropy and cross entropy is proposed. Finally, interval-valued Pythagorean hesitation fuzzy ELECTRE II method is proposed, and comprehensive precedence value is used to rank alternatives. The feasibility and effectiveness of the proposed method are verified by numerical example and comparative analysis.

The paper proposes a coordinated iterative learning control protocol for a class of second-order leader-follower nonlinear multi-agent system under the different states communication graphs, a sufficient condition of the exact consensus on a finite time interval for the multi-agent system is also given. Furthermore, the proposed scheme is extended to solve the exact formation control problem on a finite time interval for the multi-agent system. The protocols can reduce the communication cost. The efficiency of the proposed methods are illustrated by two simulation examples. The results show that the MAS could obtain the exact consensus and form a desired formation on the finite-time interval under the conditions that the topology of the velocity is connected although the topology of the position is not necessary connected, the communication requirement is relaxed. It provides an efficient approach in the unmanned aerial vehicles formation problem.

This paper discusses the robust asset-liability management problem of maximizing the expected utility of the terminal wealth under partial information with delay, that is, the investors can observe the risky asset price with random drift which is not directly observable in the financial market. It is reduced to a partially observed stochastic differential game problem. This paper tries to an effort to find the equilibrium strategies by maximizing the expected utility of the insurer's terminal wealth with delay under the worst-case scenario of the alternative measures. By using the idea of filtering theory and the dynamic programming approach, we derive the robust equilibrium strategies and value functions explicitly. Finally, some numerical examples are presented. Obviously, the value function is higher in the full information case than it in the partial information case. Therefore, investors should collect more information related to investment as much as possible in order to make more informed decisions.

Unbounded block operator matrix widely appears in the fields of system theory, nonlinear analysis and evolution equation problems, and has been widely concerned in both theory and practical application. Firstly, the decomposability of unbounded block operator matrix is characterized by using local spectrum theory. Secondly, the condition that the decomposability of operator matrix remains diagonally stable is given, and some local spectral properties of block operator matrix are generalized and obtained. Finally, as an application, the decomposability of Hamilton operator is investigated and illustrated with examples.

Considering the self-oscillating system evolved from Andronov-Hopf bifurcation and the corresponding linearized system no longer share the same differential manifold, but would exhibit multi-dimensional nonlinear coupling characteristics. Previous study adopts Washout filter to stabilize the oscillatory system, while, the number of filters needed for a particular system is still unsolved. Based on normal form analysis of the Andronov-Hopf bifurcation system, this work explores to connect two filters on the dual-unstable eigenspace, however, feedback design based on state-space method may cause the results being high ordered, which cannot be realized by a Washout filter compartment physically. Through transient dynamics analysis on the Laplace transfer function, we propose to decouple the feedback loop and reduce the Washout algorithm to 1-ordered, which is able to be realized by stable Washout filters physically. A simulation example of the self-oscillation reaction process further verifies the fea-sibility and effectiveness of the obtained control scheme.

Quadratic matrix equation is an important kind of equations in scientific and engineering computations, and it is a meaningful work to explore some effective numerical methods. A special class of quadratic matrix equations derived from quasi-birth-death processes is studied. The quasi-birth-death process has important applications in many fields such as stock price simulation, inventory control, queuing theory, etc. Under the assumption that the minimum non-negative solution exists and is unique, the Newton iteration method is proposed and its convergence is proved. When the initial matrix is zero matrix, the matrix sequence generated by Newton iteration method converges to the unique minimum non-negative solution. Finally, numerical examples are used to verify the effectiveness and feasibility of the algorithm.