Quan Jiang

Conformal mapping technique is important in theoretical analysis and numerical computation for the fields of stress and displacement. In general, a unlined tunnel with arbitrary shape has no analytical solution for conformal mapping. Therefore, the study of numerical method for conformal mapping has great significance. The basic functions of numerical conformal mapping are given based on Symm’s method in this paper. Furthermore, the inverse mapping functions were deduced according to the relationships between the boundary nodes in physical and mapped plane. Compared to the other numerical methods, the presented method has some advantages such that, it is simple in concept to be understood, and can give the mapping function without iteration process. The method can be used to the forward and inverse numerical conformal mappings for multiple underground unlined tunnels with arbitrary shapes in finite and infinite domains. With the help of method of fundamental solutions (MFS), the interpolation equations were proposed for multiple underground unlined tunnels with arbitrary shapes. Finally, several numerical examples for the groups of U-shaped and rectangle tunnels have been given to verify the effectiveness of this method. The numerical results can convergent to real cases, which show that the proposed method has the properties of good accuracy and strong adaptability.

In this paper, we construct a Bessel-class kernels for Support Vector Machine. This new class of kernels are proved that they are continuous and satisfy Mercer’s condition. The presented Bessel-class kernels can degenerate to Gaussian kernel in an infinite smooth case. Compared to the other kernels, these present Bessel kernels can be flexibly applied to classification and regression with fewer constants to be adjusted. Additionally, four simulation experiments including classifications and regressions, have been carried out to show the good performance of these Bessel-class kernels.

Semi-supervised object detection has become a hot topic in recent years, but there are still some challenges regarding false detection, duplicate detection, and inaccurate localization. This paper presents a semi-supervised object detection method with multi-scale regularization and bounding box re-prediction. Specifically, to improve the generalization of the two-stage object detector and to make consistent predictions related to the image and its down-sampled counterpart, a novel multi-scale regularization loss is proposed for the region proposal network and the region-of-interest head. Then, in addition to using the classification probabilities of the pseudo-labels to exploit the unlabeled data, this paper proposes a novel bounding box re-prediction strategy to re-predict the bounding boxes of the pseudo-labels in the unlabeled images and select the pseudo-labels with reliable bounding boxes (location coordinates) to improve the model’s localization accuracy based on its unsupervised localization loss. Experiments on the public MS COCO and Pascal VOC show that our proposed method achieves a competitive detection performance compared to other state-of-the-art methods. Furthermore, our method offers a multi-scale regularization strategy and a reliably located pseudo-label screening strategy, both of which facilitate the development of semi-supervised object detection techniques and boost the object detection performance in autonomous driving, industrial inspection, and agriculture automation.

Some inverse problems of Stokes flow, including noisy boundary conditions, unknown angular velocity, and dynamic viscous constant identification are studied in this paper. The interpolation equations for those inverse problems are constructed using the method of fundamental solutions (MFS). Based on the noise addition technique, the inverse problems are solved using MFS and a Kalman filter. It is seen from numerical experiments that these approaches and algorithms are valid and have strong robustness and high accuracy in solving inverse Stokes problems.

Conformal mapping technique is important in theoretical analysis and numerical computation for the fields of stress and displacement, since that these computations for tunnels with arbitrary shapes are always based on it. In general, a tunnel with arbitrary shape has no analytical solution for conformal mapping. Therefore, the study of numerical method for the conformal mapping has great significance. The basic functions of numerical conformal mapping are given based on Symm’s method. Furthermore, the inverse mapping functions were deduced firstly according to the relationships between the boundary nodes in physical and mapped plane. Compared to the other numerical methods, the presented method has some advantages such that, it is simple in concept to be understood, and can give the mapping function without iteration process. The method can be used to the numerical forward and inverse conformal mappings for multiple underground tunnels with arbitrary shapes in finite and infinite domains. With the help of method of fundamental solutions, the interpolation equations were proposed for multiple underground tunnels with arbitrary shapes. Finally, several numerical examples for the groups of U-shaped and rectangle tunnels have been given to verify the effectiveness of this method. The numerical results can convergent to real cases, which show that the proposed method has the properties of high accuracy and strong adaptability.

The properties of Rayleigh wave velocity are analyzed by considering the rotation and electric bias. The algebraic equation is derived for determining the piezoelectric Rayleigh wave velocity analytically and numerically for Lithium Niobate. The main results reveal that the rotation as well as electric bias has exerted an appreciable influence on the wave velocity. Particularly, the Coriolis force under the rotatory condition can decrease wave velocity considerably, and such attributes are significant for the acoustic electronics.

This paper extends the method of fundamental solutions (MFS) for solving the boundary value problems of analytic functions based on Cauchy-Riemann equations and properties of harmonic functions. The conformal mapping technique is applied to introduce the singularities of the approximate analytic functions and reconstruct the fundamental solutions. The presented method can naturally introduce the information of homogeneous boundary conditions and singularity properties, when the conformal mapping technique or the reconstructed fundamental solutions are used. The numerical examples show that the proposed method has the advantages of conciseness, reliability, efficiency, high accuracy and easy-using, respectively. The developed method can be used to solve the boundary value problems (BVPs) of analytic functions without considering single-valuedness, which simplify the numerical analysis.