The Galerkin Approximation to Forward-Backward Stochastic Partial Differential Equations

In this paper, the authors utilized the Galerkin approximation scheme approach to solve a class of fully coupled forward-backward stochastic partial differential equations in an infinite dimensional functional setup

A Four Step Scheme Approach to the Forward-Backward Stochastic Navier-Stokes Equations

In this paper, the authors presented a novel fluid dynamics system, the forward-backward stochastic Navier-Stokes equations in two dimensions for incompressible fluid flows. The well-posedness of the system is obtained through a two-step process. First, certain projections of the system to the finite dimensions are employed, and the existence and uniqueness of solutions in finite dimensions are proved via the four step scheme. Then the Galerkin approximation is used to show the existence and uniqueness of a solution to the system in an infinite dimensional functional setup

A novel surface inset permanent magnet synchronous motor for electric vehicles

© 2020 by the authors. Aiming to successfully meet the requirements of a large output torque and a wide range of flux weakening speed expansion in permanent magnet synchronous motors (PMSM) for electric vehicles, a novel surface insert permanent magnet synchronous motor (SIPMSM) is developed. The method of notching auxiliary slots between the magnetic poles in the rotor and unequal thickness magnetic poles is proposed to improve the performance of the motor. By analyzing the magnetic circuit characteristics of the novel SIPMSM, the notching auxiliary slots between the adjacent magnetic poles can affect the q-axis inductance, and the shape of magnetic pole effects the d-axis inductance of the motor. The combined action of the two factors not only weakens the cogging torque, but also improves the flux weakening capability of the motor. In this paper, the response surface methodology (RSM) is used to establish a mathematical model of the relationship between the structural parameters of the motor and the optimization objectives, and the optimal design of the motor is completed by solving the mathematical model. Experimental validation has been conducted to show the correctness and effectiveness of the proposed SIPMSM

Lumbopelvic Fixation Versus Novel Adjustable Plate for Sacral Fractures: A Retrospective Comparative Study

Purpose: The purpose of this study is to compare the therapeutic effects of the lumbopelvic technique and a novel adjustable plate for sacral fractures. Materials and Methods: Patients with unilateral sacral fractures fixed via the lumbopelvic technique or using a novel adjustable plate from June 2011 to June 2017 were recruited into this study and were divided into two groups: group A (lumbopelvic fixation) and group B (novel adjustable plate). Surgical time, intraoperative blood loss, frequency of intraoperative fluoroscopy, reduction quality, and related complications were reviewed. Fracture healing was assessed by the radiographs conducted at follow-up. Functional outcome was evaluated according to the Majeed score at the final follow-up. Results: The mean blood loss and frequency of intraoperative fluoroscopy in group B were reduced compared with group A (both P  0.05) in this study. The complication rate was 22.22% (4/18) in group A and 4.16% (1/24) in group B (P = 0.191). Conclusion: For patients with unilateral sacral fractures, satisfactory radiographic appearance and functional outcome could be obtained by both the lumbopelvic technique and a novel adjustable plate. However, the novel adjustable plate represents a less invasive technique with lower radiograph exposure