1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

This article presents a new magnetic equivalent circuit (MEC) for a real-time emulation of a 16/10 segmented-rotor switched reluctance motor (SSRM) based on the hardware-in-the-loop (HIL) configuration. The proposed real-time MEC contains the reluctances of slot leakage, air gap, and iron core of the SSRM. To speed up the emulation, a ten-by-ten matrix system is developed for the MEC. A new algorithm is proposed to solve the matrix system to reduce the computation time. To carry out the experiment, the HIL is employed in this article. It can provide a precise and real-time condition for the application of the new method. In the test bench, the field-programmable gate array provides an operating platform to realize the real-time emulation of the MEC model. As verified, the proposed real-time MEC model benefits the real-time emulation and the performance evaluation of the SSRM. The proposed method can be applied to other switched reluctance motors as an efficient way to verify their real-time characteristics with high accuracy and low emulation cost.

Real-Time HIL Emulation for a Segmented-Rotor Switched Reluctance Motor Using a New Magnetic Equivalent Circuit

Many studies have been conducted on digital image segmentation, seeking to overcome the limitations of different methods for specific applications. Thus, existing techniques are improved and new methods created. This paper proposes a new Active Contour Method (ACM) applied to the segmentation of objects in digital images. The proposed method is called Adaptive Balloon ACM and its main contribution is the new internal Adaptive Balloon energy that minimizes the energy of each point on the curve using the topology of its neighboring points, and thus moves the curve toward the object of interest. The method can be initialized inside or outside the object of interest, and can even segment objects that have complex shapes. There are no limitations as to its startup location. This work evaluates the proposed method in several applications and compares it with other ACMs in the literature. This new method obtained superior results, especially when the objects to be segmented were tubular and had bifurcations. Thus the proposed method can be considered effective in segmenting complex shapes in digital images and gave promising results in various applications.

Novel Adaptive Balloon Active Contour Method based on internal force for image segmentation - A systematic evaluation on synthetic and real images

In this paper, we propose a new Internet of Things (IoT) based predictive modelling by using fuzzy cluster based augmentation and classification for predicting the lung cancer disease through continuous monitoring and also to improve the healthcare by providing medical instructions. Here, the fuzzy clustering method is used and which is based on transition region extraction for effective image segmentation. Moreover, Fuzzy C-Means Clustering algorithm is used to categorize the transitional region features from the feature of lung cancer image. In this work, Otsu thresholding method is used for extracting the transition region from lung cancer image. Moreover, the right edge image and the morphological thinning operation are used for enhancing the performance of segmentation. In addition, the morphological cleaning and the image region filling operations are performed over an edge lung cancer image for getting the object regions. In addition, we also propose a new incremental classification algorithm which combines the existing Association Rule Mining (ARM), the standard Decision Tree (DT) with temporal features and the CNN. The experiments have been conducted by using the standard images that are collected from database and the current health data which are collected from patient through IoT devices. The results proved that the performance of the proposed prediction model which is able to achieve the better accuracy when it is compared with other existing prediction model.

An IoT Based Predictive Modelling for Predicting Lung Cancer Using Fuzzy Cluster Based Segmentation and Classification

A novel generalized gradient vector flow snake model using minimal surface and component-normalized method for medical image segmentation

Active contour model based on local and global Gaussian fitting energy for medical image segmentation

Magnetic levitation actuators (MLAs) are increasingly employed in the modern high-precision manufacturing industry. Since the current-wrench transformation matrix is calculated inaccurately in the controller, the existing MLA finds it hard to undertake high-precision multi-degrees-of-freedom (DOF) movement in the large stroke. A high-fidelity real-time model is required to design better controllers for MLAs. This paper proposes a universal FPGA-based real-time wrench model (RTWM); meanwhile an MLA capable of translation and rotation in the horizontal plane is employed as the modeling object. To obtain the high accuracy with excellent generality, the force and torque distribution is solved through the magnetic node, coordinate transformation, and Gaussian quadrature. The corresponding calculation components are developed on the field-programmable gate array (FPGA) by exploiting the fully pipelined arithmetic and parallel architecture processing. Utilizing the high level synthesis tool, the final register transfer level structure is optimized adequately to reduce the time and hardware overhead. In the experiment, the RTWM of the proposed MLA and an existing MLA from the literature are obtained together to highlight the generality, and the computational accuracy is compared with the finite element method (FEM) software Comsol Multiphysics and a boundary element method software package Radia, respectively. The results show that the relative deviation is less than $\text{2}\%$ choosing the FEM results as benchmark.

FPGA-Based Real-Time Wrench Model of Direct Current Driven Magnetic Levitation Actuator

Applications of switched reluctance machine (SRM) are increasing in the industry due to their many desirable features. This study proposes a hybrid analytical model (HAM) of the SRM for the hardware-in-the-loop (HIL) simulation. To obtain satisfactory accuracy, the phase flux linkage is solved by the magnetic equivalent circuit (MEC) method when the stator and rotor poles overlap, and by the space harmonic method (SHM) when the poles do not overlap. The backward Euler and Newton-Raphson methods are used to calculate the exciting current, while the Gaussian quadrature is used to compute the electromagnetic torque in the HIL simulation. The digital hardware implementation of computation components are developed on the field-programmable gate array by exploiting the parallel hardware architecture and fully pipelined arithmetic processing. To highlight the performance of the HAM, the captured real-time results are compared with the off-line transient solution obtained through the co-simulation of Ansys Maxwell
 ®
, Ansys Simplorer
 ®
, and Simulink
 ®
, which model the SRM, drive circuit, and control system, respectively.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-epa.2016.0831

Hybrid analytical model of switched reluctance machine for real-time hardware-in-the-loop simulation

A multi-step directional generalized gradient vector flow snake for target tumor segmentation in US-guided high-intensity focused ultrasound ablation

This paper investigates a kind of cylindrical linear single-axis actuator that is used in the magnetic levitation stage to provide fine movement. The magnetic flux density distribution due to the permanent magnet is determined using the surface charge method, and the magnitude of force generated by the actuator is calculated using the Lorentz force equation. Both of them can be solved by numerical integration. The results are verified by measurements. The magnetic force components are fitted as an analytical style that can be used in the real-time controlling of this actuator for the magnetic levitation stage.

Xianze Xu

Papers

Active contour model based on local and global Gaussian fitting energy for medical image segmentation

FPGA-Based Real-Time Wrench Model of Direct Current Driven Magnetic Levitation Actuator

Hybrid analytical model of switched reluctance machine for real-time hardware-in-the-loop simulation

A multi-step directional generalized gradient vector flow snake for target tumor segmentation in US-guided high-intensity focused ultrasound ablation

Numerical Calculation of the Magnetic Field and Force in Cylindrical Single-Axis Actuator