Mixed geographically weighted regression (MGWR) models, assuming that some regression coefficients are constant and the others are spatially varying, have been a powerful tool for comprehensively exploring spatial variation characteristics of impact of the exploratory variables on the response variable. Based on the local-linear geographically weighted regression estimators of the coefficients, we propose in this paper a coefficient-average-based estimation method for the MGWR models, on which a bootstrap test is formulated to identify constant coefficients in the models. In addition, the estimation and test methods are extended to the estimation of the multi-type MGWR models and the identification of special types of the coefficients. The simulation studies show that, compared with the existing two-step estimation of the MGWR models, the proposed estimation method can yield more accurate estimators for the spatially varying coefficients and the test method is of valid size and satisfactory power. A real-life example is finally given to demonstrate the applicability of the proposed estimation and test methods.

This study investigates an ecological epidemiological model of prey harvesting and predator switching with time delay. Firstly, the linearization of the system is performed, and the method of analyzing the eigenvalues is used to show that when the predator's digestion delay exceeds a certain bifurcation threshold, the system loses stability and exhibits a Hopf bifurcation. Secondly, based on the theory of normal forms and center manifold, computational steps describing the characteristics of the Hopf bifurcation in the system are derived. Thirdly, under the influence of linear time-delayed feedback control, it is shown that the occurrence of the Hopf bifurcation can be effectively delayed while keeping the original equilibrium point of the system unchanged. Finally, numerical simulations are conducted to support the analytical results.

The improved design of warehouse layouts is an important factor affecting the operational efficiency of e-commerce warehouses and distribution centers. On the basis of the traditional warehouse layout, this paper takes the shelf placement angle as the starting point to study the Chevron warehouse layout and constructs the area utilization model of the Chevron warehouse layout under the random storage strategy to investigate the influence of the shelf placement angle and picking aisle width on the warehouse area utilization. The stochastic model of S-shape and return routing strategies in the warehouse with Chevron layout is constructed, and the approximation is verified and is compared with the simulation. The numerical experimental results show that in the Chevron layout warehouse, the change in shelf placement angle has a small impact on the effective storage area utilization, with a difference of 0.5\% (horizontal shelf placement) and 1.6\% (vertical shelf placement) compared with the traditional layout, and the routing strategy can be further studied under the Chevron layout. When the angle is close to half of the diagonal of the warehouse, the walking distance of both the return strategy and the S-shape strategy reach their respective minimum values, and the S-shape strategy has better results.

Consider a vehicle manufacturer selling the fuel vehicle and new energy vehicle during the finite selling horizon. In each period, the firm needs to decide the prices of the fuel vehicle and the new energy vehicle simultaneously. Under the dual credit policy, the firm generates negative credit when producing the fuel vehicle, and generates positive credit when producing the new energy product. Based on the stochastic dynamic programming approach, we propose the dynamic pricing decision model under dual credit policy. Through the theoretical analysis, we prove that the dual credit policy can still promote the popularization of new energy vehicle when firm adopts the dynamic pricing strategy. Besides, the credit of the firm will impact the firm's profit and optimal pricing decisions. When the credit increases, the firm will increase the price of the new energy vehicle, and decrease the price of the fuel vehicle, and the firm’s profit increases. The cost analysis reveals that under the dual credit policy, the firm can expand the sales of new energy vehicle by reducing the manufacturing cost of fuel vehicle and new energy vehicle.

As one of the most common and important financial derivatives, options are the core tools of risk management, and how to price options is naturally an important issue. In this paper, the pricing of European barrier options for discrete time scenarios under the model of Wishart multidimensional stochastic volatility is discussed. Using some stochastic analysis techniques and mathematical induction, such as the semi-martingale It\^o formula, multidimensional federated characteristic functions, Girsanov theorem and Fourier inverse transform technique are to derive the pricing formula for the European discrete barrier call option. And derive the discrete fast Fourier transform (FFT) method to implement the pricing formula for the option. Finally, numerical examples are given, and the variation of the implicit volatility curve of options under different volatility parameters is also analyzed by this numerical examples, the results show that the diffusion factor has a significant impact on the price of options.

Eikonal equations are widely used in computer vision, image processing, geometric optics, etc. This paper extends the weighted compact nonlinear scheme (WCNS) and the weighted essentially non-oscillatory (WENO) scheme for hyperbolic conservation laws and designs high-order fast sweeping WCNS and WENO schemes to solve the pseudo-time dependent Eikonal equations. Fifth-order WCNS and WENO schemes are applied to compute the left and right limit values of spatial derivatives of the unknown variable coupled with the monotone Lax-Friedrichs numerical Hamiltonians. In order to speed up the convergence of the designed algorithm and to avoid solving a nonlinear discrete system, an explicit time-marching scheme combined with a fast sweeping strategy is used for time discretization. Numerical results show that both the fast sweeping WCNS method and the fast sweeping WENO method can achieve fifth-order accuracy in smooth regions and the numerical solutions obtained with the two methods are in good agreement with the exact solutions of Eikonal equations. Compared with the classical WENO method of the same order, the fast sweeping WCNS and WENO schemes are more efficient when they obtain the same numerical errors.

The Schr\"odinger equation is an important class of mathematical physics equations, and it has significant applications in engineering. The conservative difference scheme for the coupled nonlinear Schr\"odinger equation is studied based on the high-order finite difference method, the Crank-Nicolson, and the Leap-frog method. Moreover, the proposed numerical formulation is decoupled, linear, and it satisfies the discrete mass and energy conservation laws. The existence, uniqueness, stability and convergence of the numerical formulation are discussed, and it is shown that the numerical formulation is of the accuracy $O(\tau^2+h^4)$. The numerical experiments are given, and their results verify the efficiency of the scheme.

In this paper, the novel optimization model for tensor completion by considering the bi-level optimization model with the smooth $\epsilon$-trace functions instead of nuclear norm is proposed. In the new model, it is not necessary to perform singular value decomposition for all modes of the tensor in each iteration, but only two singular value decomposition is needed at most, which effectively reduces the huge computation amount brought by all modes expansion of the tensor and greatly improves the computation efficiency. Finally, the experimental results of randomly generated tensor completion problem and color image inpainting problem show that the proposed bi-level (minimin and minimax combination) optimization models usually has less than CPU time and better precision than the traditional nuclear norm based model.

A class of function transformation with reference variables is proposed, and it is proved that the method can reduce the step ratio deviation of the sequence to a certain extent. The sufficient and necessary conditions for reducing the step ratio deviation of the monotonically increasing and monotonically decreasing sequences are given respectively. In order to ensure that the modeling accuracy is still improved after the reduction, the function characteristics of non-expanding relative error in the transformation reduction of function with reference variables are further studied. Finally, the ${\rm GM}(1,1)$ modeling method is used to build the model. The example verifies that this kind of parametric variable function transformation method has the characteristics of reducing without expanding the relative error, and can improve the short-term prediction accuracy.

In this paper, by using the potential well method, finite time blowup and global existence of solutions are studied for a class of $p$-Laplace parabolic equations with nonlinear logarithmic term and Neumann boundary conditions. Firstly, the existence of global weak solutions is proved by the Galerkin method and the compactness principle. Then, the decay estimation of the global weak solution is derived by an energy integration and ODE inequality technique. Secondly, through constructing an auxiliary function and combining the concave method, the finite time blowup of the solution under the condition of positive initial energy is obtained,  and the accurate upper bound estimation of blowup time is given for the first time. Furthermore, the results are extended to the case of non-positive initial energy. In order to more intuitively explain the theoretical results, some numerical examples are given to show the long-time decay behavior and the blowup properties of solutions under different initial energy levels, the effects of parameter $ p$ on the evolution of solutions and the correctness of the theoretical results.

With the continuous increasing of railway operation speed and traffic volume, the phenomenon of rail scratches caused by the interaction between wheels and rails has become more and more prominent. The acceleration of the axle box can effectively describe the short-wave irregularity of the track, and the scratches appear at fixed intervals. There will be periodic fluctuations. In view of the periodic characteristics of continuous rail scratches, we proposes an adaptive time-frequency analysis method for periodic track diseases. First, the adaptive short-time Fourier transform is performed on the acceleration data of the axle box, and the energy spectrum of time-frequency of the signal is obtained. After extracting the time energy signal using the $L^P$ norm criterion, then using the moving Gaussian weighted average filter and the least squares smoothing filter to smooth and detrend the time-energy signal. Finally, using a fixed window to smooth the signal perform post-intersection analysis and threshold judgment determine the continuous abrasion section. The algorithm is tested in the field, and the results show that the method of self-adaptive time-frequency analysis can effectively identify the continuous scratched section of the rail.

The evaluation of fighter's combat capability aims to give reliable conclusions on the overall combat performance of fighter, which is of great significance. However, with the transformation of the operational mode, the simpler traditional operational capability evaluation framework is not suitable for more complex operational scenarios. Therefore, this paper comprehensively considers various situations that may occur in the real combat scenario. In view of the limitations of the traditional combat capability evaluation methods, and comprehensively considers the two factors of index system and test data, this paper uses the normal cloud model to aggregate the index completion score and combination weight, and gives a comprehensive solution to the problem of fighter combat capability evaluation. At the same time, this paper focuses on the rationality and effectiveness of weight distribution in the process of comprehensive evaluation, uses the combined weight method based on relative entropy as the final index weight calculation method, and comprehensively considers the advantages and disadvantages of subjective weight and objective weight by balancing the prior knowledge of domain experts and the internal patterns of data, so as to make the comprehensive evaluation results more authentic and reliable.

Based on the modified FR type spectral conjugate gradient method, the conjugate parameters and spectral coefficients are improved, and hence a sufficiently descending spectral conjugate gradient method is proposed. The spectral conjugate gradient method's global convergence is established under the standard Wolfe line search criteria. Finally, numerical experiments are carried out to compare the proposed method with two FR spectral conjugate gradient methods proposed in other literatures. The numerical results indicate that the proposed method enjoys certain advantages in numerical calculation.