Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field I: Schr\"odinger equation

This is the first of a series of papers in which we investigate the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In this first starting paper, we prove the local-in-time dispersive estimates and Strichartz estimates for Schr\"odinger equation with one Aharonov-Bohm solenoid in a uniform magnetic field. The key ingredient is the construction of Schr\"odinger propagator, we provide two methods to construct the propagator. The first one is combined the strategies of \cite{FFFP1} and \cite{GYZZ22, FZZ22}, and the second one is based on the Schulman-Sunada formula in sprit of \cite{stov, stov1} in which the heat kernel has been studied. In future papers, we will continue investigating this quantum model for wave with one or multiple Aharonov-Bohm solenoids in a uniform magnetic field.Comment: 22 page

Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field II: wave equation

This is the second of a series of papers in which we investigate the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In our first starting paper \cite{WZZ}, we have studied the Strichartz estimates for Schr\"odinger equation with one Aharonov-Bohm solenoid in a uniform magnetic field. The wave equation in this setting becomes more delicate since a difficulty is raised from the square root of the eigenvalue of the Schr\"odinger operator $H_{\alpha, B_0}$ so that we cannot directly construct the half-wave propagator. An independent interesting result concerning the Gaussian upper bounds of the heat kernel is proved by using two different methods. The first one is based on establishing Davies-Gaffney inequality in this setting and the second one is straightforward to construct the heat kernel (which efficiently captures the magnetic effects) based on the Schulman-Sunada formula. As byproducts, we prove optimal bounds for the heat kernel and show the Bernstein inequality and the square function inequality for Schr\"odinger operator with one Aharonov-Bohm solenoid in a uniform magnetic field.Comment: 35 pages, comments are welcome

Roles of ncRNAs in Ovarian Dysfunction of Polycystic Ovary Syndrome

Polycystic ovary syndrome (PCOS) is a common endocrine disease in women of childbearing age. Many heterogeneous clinical manifestations of PCOS, including hyperandrogenism, obesity, insulin resistance, hirsutism, acne, chronic anovulation and infertility, seriously affected the quality of life of women worldwide and made it difficult to clearly demonstrate the specific pathophysiology. In recent years, large-scale studies have shown that non-coding RNAs (ncRNAs) play an important role in the regulation of ovarian functions, which did not have the ability to encode proteins and could regulate hormone synthesis and germ cell development, differentiation, and apoptosis by silencing transposable elements and regulating coding genes. A number of researches by whole transcriptome sequencing of polycystic ovaries (PCO) from PCOS patients or PCOS model animals found that the abnormal expressions of many ncRNAs were involved in the regulation of ovarian dysfunctions of PCOS, including the development of oocytes, the microenvironment of follicular fluid, and the proliferation, differentiation, and apoptosis of granulosa cells. The present review focused on the roles of ncRNAs in the PCO of PCOS, in order to provide a theoretical basis for further understanding of the molecular mechanisms of PCO formation in PCOS

Nonlinear magnetotransport shaped by Fermi surface topology and convexity in WTe2

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe2, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe2, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter

The finite element modeling and stability prediction of high-speed spindle system dynamics with spindle-holder-tool joints

The stability of high-speed spindle system affects the surface finish and tool life directly, which is an important factor to evaluate its performance. Meanwhile, the spindle dynamics and cutting stability are affected by the structure and dynamics of spindle-holder-tool joints significantly. The joints are simplified as the distribution-spring, and the FEM modeling process of spindle system is proposed based on the thought of parallel rotor system. Taking a vertical machining center as example, the effectiveness of the modeling method is verified. Starting from the stability evaluation criteria and different ways of getting FRF, the influence factors of unconditional and conditional stability regions are analyzed. Based on the proposed model, the influence laws of cutting stability on cutting force amplitude and speed are characterized by the three-dimensional lobes, limit cutting depths and lobe intersections, which provide the theoretical basis for optimizing the processing and improving the cutting stability

An explicit formula based estimation method for distribution network reliability

An improved explicit estimation algorithm is proposed for reliability estimation of distribution network. Firstly, hierarchical clustering is used to identify and cluster typical feeders based on topology structure. Secondly, the explicit formula of reliability indices under each typical feeder topology is derived by regression analysis, to establish the model for network reliability estimation. Numerical simulations show the suitability of the proposed method in obtaining accurate reliability index for diversified network topology

Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: a DOBC approach

In this paper, a new predictor-based consensus disturbance rejection method is proposed for high-order multi agent systems with Lipschitz nonlinearity and input delay. First, a distributed disturbance observer for consensus control is developed for each agent to estimate the disturbance under the delay constraint. Based on the conventional predictor feedback approach, a non-ideal predictor based control scheme is constructed for each agent by utilizing the estimate of the disturbance and the prediction of the relative state information. Then, rigorous analysis is carried out to ensure that the extra terms associated with disturbances and nonlinear functions are properly considered. Sufficient conditions for the consensus of the multi-agent systems with disturbance rejection are derived based on the analysis in the framework of Lyapunov-Krasovskii functionals. A simulation example is included to demonstrate the performance of the proposed control scheme. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.National Natural Science Foundation of China [61673034]SCI(E)ARTICLE1,SI298-31535