The closed Cohen class time-frequency resolution obtained by the linear canonical transformation free parameter embedding method depends on the parameter selection, and the lower bound described by the uncertainty principle can represent the time-frequency resolution limit. Therefore, studying the uncertainty principle of the closed Cohen class time-frequency distribution plays an important part in guiding significance for the optimal parameter selection. In this paper, by constructing the relationship of two-dimensional separable linear canonical transform between the N-dimensional free metaplectic transformation and the closed Cohen class time-frequency distribution, we studied the uncertainty principle of closed Cohen class time-frequency distributions, including types of Heisenberg, Hardy, Donoho, Nazarov, Beurling, Logarithmic, Entropic, and etc. For the first four categories, except for the closed Cohen class time-frequency distribution uncertainty principle based on free metaplectic transformation, there are also expressions generalized from the traditional Cohen class time-frequency distribution. Finally, the equivalence of the uncertainty principle obtained by the two methods is proved.

The least square method and SPSS 22.0 are used to obtain three common parameter estimation formulas of the tumor growth model whether the maximum environmental capacity of tumor cells is known or unknown. Through the parameter estimation formula and the published data, the growth rates of 8 different types of cancers are calculated. The original data are fitted through Matlab. Furthermore, the fitting effect is verified by taking the first three quarters of the initial data of tumor cell growths as the fitting data and by taking the last quarter of the experimental data as the prediction data. The optimal mathematical models for describing various tumor growths are determined. According to the characteristics and the fitting effects of tumor growths, as well as the function characteristics of the organs where tumors are located, the growth situations of 8 types of cancer cells in different organs are classified from a mathematical perspective. Further, this study provides a theoretical reference for further research on the anti-tumor

immunity mechanism and the improvement of mathematical models for immune cells inhibiting tumor growths.

In this paper, the pressure stabilization method of the stochastic Navier-Stokes equation with multiplicative noise is studied, and the velocity pressure space is approximated by first-order finite elements. This method solves the problem of finite element space pair selection by introducing stabilization parameters and decoupling velocity pressure variables. The stability and convergence of the pressure stabilization method are proved theoretically. Finally, it is proved that the convergence order of space discreteness can reach the optimal when the stabilization parameters meet certain conditions.

The stability problem of T-S fuzzy systems with random time-varying delay is investigated in this article. First, a new random variable dependent system model is established by considering the stochastic time-varying characteristics of time-varying delay, and the original systems can be implied by it. Based on the new system model, a suitable Lyapunov functional is constructed that can utilize the information of membership function, random time-varying delay and its derivative. The fuzzy reciprocally convex integral inequality is used to estimate the quadratic integral term from the derivative of the Lyapunov functional, and a new membership function and derivative of delay function dependent system stability criterion is proposed. For both known and unknown cases of system random time-varying delay function, the obtained stability criterion is applicable, and has less conservatism. Finally, the effectiveness of the proposed stability criterion is verified through two numerical examples.

The paper establishes a competitive trading model based on heterogeneous attentions, referring to the analytical framework of Kyle model in 1985. The model considers that there are three types of risk neutral traders in the financial market with only one risk asset: two attentive traders with different attentions, liquidity trader and market maker. According to the different levels of attention, three scenarios were mainly considered: homogeneous attention, one limited attention while the other completely neglected, and one complete attention while the other limited attention. The mechanism of the impact of attention on trading behavior and returns in heterogeneous attention scenarios was revealed. By solving the linear equilibrium solutions under the three scenarios, it is found that in all three scenarios, the expected returns of limited attentive trader increase with attention. The expected returns of completely negligent trader have an inverted U-shaped relationship with attention, while the expected returns of fully attentive trader decrease with increasing attention. In the case of the first and second scenarios, the impact of attention on the trading intensity of limited trader is related to the noise in the signal. In the third scenario, the attention of limited trader reduces the trading intensity of attentive trader, while it has an inverted U-shaped relationship with his own trading intensity.

In this paper, the problem of aperiodic intermittent control for nonlinear stochastic time-delay systems based on discrete-time observations is studied. Combining the discrete feedback control strategy with the intermittent control strategy, an aperiodic intermittent feedback controller for observing the state of the system in discrete time is designed, which makes the controlled system reach mean square exponential stability. The conditions for system stability are established through M-matrix theory and intermittent control strategy, and the mean square exponential stability of nonlinear stochastic time-delay systems is proved by Lyapunov function and It\^{o} formula. Finally, a numerical example was provided to demonstrate the correctness of the theoretical derivation.

In this paper, a compact difference scheme which is fourth-order in space and third-order in time for the Boussinesq equation is proposed by using the three-point fourth-order compact finite difference method in space and the third-order strong-stability-preserving implicit and explicit Runge-Kutta method (SSP-IMEXRK3) in time.~The stability of the proposed scheme is verified by Fourier analysis. Based on several numerical examples, the result analysis and comparisons with other schemes verify the effectiveness of the proposed scheme.

In this paper, a new inverse-free dynamical model is developed for a class of absolute value equation with symmetric positive definite matrix. It is also shown that the equilibrium point of this kinetic model is globally asymptotically stable. Based on the numerical experiments, the proposed inverse-free dynamical model is feasible. Meanwhile, by comparing it with the five existing kinetic models, the analysis in terms of computational time and error shows that the inverse-free dynamical model proposed in this paper is competitive.

High-dimensional data modeling in the fields of machine learning and pattern recognition is ubiquitous and of great value. The ``curse of dimensionality" problem that exists in the high-dimensional data analysis process constrains the effective intervention of many machine learning models. Many effective methods for subspace and non-negative matrix reconstruction have been proposed. Non-negative matrix reconstruction can improve algorithm construction in unsupervised and semi-supervised learning by improving the loss function and adding priors. This paper proposes a non-negative matrix factorization loss function based on adaptive dual-weight learning. The proposed loss-function learns based on the class structure information of the data set in high-dimensional space and low-dimensional space, uses weighted $L_{2,1}$ norm to improve model robustness, and uses weighted learning strategies to learn approximation in low-dimensional space. This results in better algorithmic robustness. Experimental results on some benchmark datasets and hyperspectral images demonstrate the superiority of the new algorithm.

The researches on the alternating direction method of multipliers (ADMM) for solving two-block optimization have been gradually perfect. However, the studies on ADMM for solving nonconvex multi-block optimization are relatively few. In this paper, we propose a symmetric proximal ADMM with relaxation stepsize parameter for nonconvex multi-block optimization. Under some suitable conditions, the global convergence of the algorithm is established. Subsequently, the strong convergence of the algorithm is established when the benefit function satisfies the Kurdyka-{\L}ojasiewicz (KL) property. Finally, numerical experiments verify the effectiveness of the proposed method.

Formal concept analysis and rough set theory are two effective data analysis methods, which merge with each other. Through introducing fuzzy rough sets into fuzzy formal concept analysis, based on generalized fuzzy rough approximations, a crisp-fuzzy concept lattice is proposed. Subsequently, the attribute reduction of the corresponding concept lattice is studied. The study involves the definition of attribute reduction to keep the lattice structure of the concept lattice unchanged, the judgement of consistent attribute sets, the feature characterization of different types of attributes, and a method of reduction computation based on discernibility matrix.

Relationship extraction is an important natural language processing task that involves extracting relationships between entities. Recent research has shown that the pre-trained BERT model achieves very good results in natural language processing tasks. Since then, many methods using pre-trained BERT model for relationship extraction have been developed, with R-BERT being a representative example. However, this method does not consider the semantic differences between the subject and object entities or the impact of global semantic information on the accuracy of relationship extraction tasks. This paper addresses this by setting up two separate fully connected layers to extract information for the subject and object entities, thereby incorporating the semantic differences between them into the model's learning process. Additionally, a new fully connected layer with an activation function is added after the existing information fusion module to fully integrate high-dimensional global semantic information with entity pairs. The proposed model, which integrates semantic differences and global semantic information, is referred to as GR-BERT. Experiments on a Chinese entity relationship extraction dataset show that GR-BERT significantly improves the original R-BERT, thereby validating its effectiveness.

In this paper, by using the Moore-Penrose generalized inverse of the covariance matrix, for the mean-variance selection problem of any finite kinds of risk assets portfolio, the expression of the optimal strategies and the variance for the minimum variance portfolio under the given portfolio expected return are given. By proceeding the generalized inverse analysis, we further deduced the geometric characterization of the efficient frontier of the portfolio under two different circumstances, respectively. The conclusions not only include the results of the covariance matrix under the positive definite condition in the literature, but also include the classical results of the geometric characterization of the effective frontier of the portfolio when $n=2$ and the two risky assets are completely negatively correlated.

In this paper, we study a continuous review $M/M/1$ queueing-inventory system with customer batch demand, lost sales and multiple working vacations, where the server takes multiple working vacations when the inventory is zero. Customers arrive according to a Poisson process. The service time, the lead time and the working vacation time are assumed to follow exponential distributions, and the batch size of demands is assumed to follow a general distribution. The steady-state condition and the steady-state probability distribution of the system are derived by using quasi-birth-and-death process and matrix geometry solution method, and then the computational formulae for the steady-state performance indicators of the system are obtained. The long-term average cost function of the system is established based on the performance measures, and the optimal inventory strategy and the optimal cost of the system are analyzed by numerical examples.