One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis

Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.

Double Reduction and Exact Solutions of Zakharov–Kuznetsov Modified Equal width Equation with Power Law Nonlinearity via Conservation Laws

The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.

A Direct Method of Moving Planes to Fractional Power Sub Laplace Equations on the Heisenberg Group

We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved.

Simple groups with orders 2~a3~b5~cp^d, 2~a3~b7~cp^d and 2~a3~b5~c7~d

This work deals with the power exponent 1rand 2r respectively of the maximal and second-maximal prime factors of the order of simple K4-group, and the classification for simple 4{5,7}K--group G (i.e. G can not be divided by 5 nor by 7 or ()Gp= 4 ), simple 5 -4K-group G (i.e. G can not divided by 5 and ()Gp=4) and simple 7-4K-group G (i.e. G can not divided by 7 and ()Gp= 4). It is derived that 1r =1, 2 and 4, and 2r is not greater than 4. All the simple 4K-groups with order 235,237abcdabcdpp and 2357abcd are obtained.

Evolution of Generalized Sizing for Evaluation of Converter Fed Machines

Based on the concept of the converter fed machines (CFMs), an optimal machine design can be considered as the best match of the machine topology, the power electronic converter and the performance specifications. To evaluate power production potentials of machines with various topologies with different waveforms of back emf and current, the generalized sizing equations and the power density equation are needed to evaluate the main dimensions and the power of such machines. In this paper. a general approach is presented to develop and to discuss these equations. Sample applications of the generalized sizing and power density equations are utilized to evaluate the induction machine and the double-salient permanent magnet (DSPM) machine.

Deep Active Learning for Solvability Prediction in Power Systems

Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism and handle limited types of power flow models.In this letter,we propose a deep active learning framework for solvability prediction in power systems.Compared with passive learning where the training is performed after all instances are labeled,active learning selects most informative instances to be labeled and therefore significantly reduces the size of the labeled dataset for training.In the active learning framework,the acquisition functions,which correspond to different sampling strategies,are defined in terms of the on-the-fly posterior probability from the classifier.First,the IEEE 39-bus system is employed to validate the proposed framework,where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the high-dimensional numerical experiments.Then,the Northeast Power Coordinating Council(NPCC)140-bus system is used to validate the performance on large-scale power systems.