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关键词： Quantum theory  

摘要： We study the quantum dynamics of the two impurities in a trapped quasi-one-dimensional Bose-Einstein condensate (BEC). We explore the effect of impurity-BEC and impurity-impurity interaction strengths on the dynamics of impurities inside the Bose-Einstein condensate. By studying the auto-correlation function of impurities and the BEC, we analyze and quantify the trapping of impurities inside the BEC. We find out that for the small value of inter-species coupling strength the BEC starts to oscillate inside the trap. For mild coupling strengths, attractive and repulsive impurities are captured after a few cycles of oscillation inside the BEC. In the strong interaction strength regime, the to-and-fro motion of impurities suppressed quite fast. Our conclusion indicates that quench dynamics can be a tool for studying impurity BEC interactions or impurity-impurity interactions. Our analysis shows that the generation of phonon, shock-waves, soliton-train, and self-trapping is strongly dependent on the impurity-BEC coupling coefficient.

关键词： charge trapping   core–   shell quantum dots   organic photodetectors   photomultiplication   response speed  

摘要： A novel photomultiplication (PM)-type organic photodiode (OPD) that responds much faster (109 kHz bandwidth) than conventional PM-type OPDs is demonstrated. This fast response is achieved by introducing quantum dots (QDs) as a PM-inducing interlayer at the interface between the electrode and the photoactive layer. When the device is illuminated, the photogenerated electrons within the photoactive layer are rapidly transferred and trapped in the trap states of the QD interlayer. The electron trapping subsequently leads to charging of the QD and a consequent shift of the QD energy levels, thereby inducing hole injection from the electrode. This PM mechanism is distinct from that of conventional PM-type OPDs, whose PM usually requires a long time to induce hole (or electron) injection because of the slow transport and accumulation of electrons (or holes) within the photoactive layer. Because of its PM mechanism, the proposed QD-interlayer PM-type OPD achieves high bandwidth and high specific detectivity. In addition, it is demonstrated that the response speed of the proposed device is closely related to the charge trapping/detrapping dynamics of the QDs. This work not only offers a new concept in the design of fast-responding PM-type OPDs but also provides comprehensive understanding of the underlying device physics.

关键词： 1-Laplacian problem   Radial solution   Mountain pass theorem   Symmetric criticality principle of   Palais  

摘要： We obtain the existence of a radial solution to the following 1-Laplacian problem {-Delta(1)u + u vertical bar u vertical bar = Q(x)f(u), in R-N, (0.1) u is an element of BV (R-N). The work is carried out in the space of functions of bounded variation BV (R-N). The proof of the main result relies on a version of mountain pass theorem without Palais-Smale condition to Lipschitz continuous functionals, and symmetric criticality principle of Palais for non-smooth functionals . (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Robin eigenvalue   p-Laplacian   Eigenvalue comparison   Barta's inequality  

摘要： We consider the first Robin eigenvalue lambda(p)(M, alpha) for the p-Laplacian on a compact Riemannian manifold M with nonempty smooth boundary, with alpha is an element of R being the Robin parameter. Firstly, we prove eigenvalue comparison theorems of Cheng type for lambda(p)( M, a). Secondly, when alpha > 0 we establish sharp lower bound of lambda p(M, alpha) in terms of dimension, inradius, Ricci curvature lower bound and boundary mean curvature lower bound, via comparison with an associated one-dimensional eigenvalue problem. The lower bound becomes an upper bound when alpha < 0. Our results cover corresponding comparison theorems for the first Dirichlet eigenvalue of the p-Laplacian when letting alpha -> +infinity.

关键词： Spatiotemporal data   Traffic data prediction   Missing data imputation   Temporal matrix factorization   Deep learning   Intelligent transportation system  

摘要： Accurate prediction of traffic status in real time is critical for advanced traffic management and travel navigation guidance. There are many attempts to predict short-term traffic flows using various deep learning algorithms. Most existing prediction models are only tested on spatiotemporal data assuming no missing data entries. However, this ideal situation rarely exists in real world due to sensor or network transmission failure. Missing data is a nonnegligible problem. Previous studies either remove time series with missing entries or impute missing data before building prediction models. The former may cause insufficient data for model training, while the latter adds extra computational burden and the imputation accuracy has direct impacts on the prediction performance. In this study, we propose an online framework that can make spatiotemporal predictions based on raw incomplete data and impute possible missing values at the same time. We design a novel spatial and temporal regularized matrix factorization model, namely LSTM-GL-ReMF, as the key component of the framework. The Long Short-term Memory (LSTM) model is chosen as the temporal regularizer to capture temporal dependency in time series data and the Graph Laplacian (GL) serves as the spatial regularizer to utilize spatial correlations among network sensors to enhance prediction and imputation performance. The proposed framework integrating with the LSTM-GL-ReMF model are tested and compared with other state-of-the-art matrix factorization models and deep learning models on three uni-variate and multi-variate spatiotemporal traffic datasets. The experimental results show our approach has a robust and accurate performance in terms of prediction and imputation accuracy under various data missing scenarios.

关键词： Strong maximum principle   Spectral Dirichlet Laplacian   Fractional Sobolev spaces   Poincare inequality  

摘要： In this paper, we obtain a version of the strong maximum principle for the spectral Dirichlet Laplacian. Specifically, let d is an element of {1, 2, 3, ... }, s is an element of (1/2, 1), and Omega subset of R-d be open, bounded, connected with Lipschitz boundary. Suppose u is an element of L-1(Omega) satisfies u >= 0 a.e. in Omega and (-Delta)(s)u is a Radon measure on Omega. Then u has a quasi-continuous representative (u) over tilde. Let a is an element of L-1(Omega) be such that a >= 0 a.e. in Omega. Then if (-Delta)(s) u + au >= 0 a.e. in Omega and (u) over tilde = 0 on a subset of positive H-s-capacity of Omega, then u = 0 a.e. in Omega.

关键词： 电磁辐射  

ISBN: (纸本)9787562863595

摘要： 本书主要介绍了太赫兹光谱在自旋电子学中的应用, 包括三个部分, 首部分包括1-3章, 介绍了太赫兹概述和光谱技术; 第二部分为本书的重点, 包括第4-6章, 主要介绍了太赫兹波与磁有序介质的相互作用; 第三部分包括第7、8章, 介绍了太赫兹强场与电子自旋的非线性相互作用, 进而实现自旋波的太赫兹非线性调控。

关键词： ferumoxytol   triple-negative breast cancer   MRI   [Fe]MRI  

摘要： Simple Summary With the incorporation of immune-modulating therapies into the standard management of triple-negative breast cancer, there is increased interest in the non-invasive imaging of the tumor immune microenvironment. Ferumoxytol is FDA-approved as an iron replacement therapy for iron-deficiency anemia and is also a superparamagnetic iron oxide nanoparticle (SPION) resulting in negative enhancement on T-2-weighted MR imaging. It has previously been established that ferumoxytol is taken up by macrophages. In the current study, we used ferumoxytol-contrasted MRI to quantitatively image the iron concentration, and, by extension, the tumor-associated macrophage infiltration within the tumor microenvironment of a highly inflammatory model of triple-negative breast cancer. Tumor-associated macrophages (TAMs) in breast cancer regulate inflammation, immunosuppression, angiogenesis, and metastasis. However, TAM imaging remains a clinical challenge. Ferumoxytol has long been an FDA-approved superparamagnetic iron oxide nanoparticle (SPION) preparation used as an intravenous (IV) treatment for iron-deficiency anemia. Given its high transverse relaxivity, ferumoxytol produces a negative image contrast upon cellular uptake in T-2-weighted magnetic resonance imaging (MRI) studies. Here we evaluated ferumoxytol as a contrast agent to image/quantify TAMs in an aggressive mouse model of breast cancer: We developed [Fe]MRI to measure the 5-dimensional function c(x,y,z,t), where c is the concentration of nanoparticle iron and {x,y,z,t} is the 4-dimensional set of tumor space-time coordinates. Ferumoxytol SPIONs are readily phagocytosed (similar to 10(4)/cell) by the F4/80(+)CD11b(+) TAMs within breast tumors. Quantitative [Fe]MRIs served to determine both the spatial and the temporal distribution of the SPION iron, and hence to measure [Fe] = c(x,y,z,t), a surrogate for TAM density. In single-dose pharmacokinetic studies, after an IV dose of 5 mg/Kg iron, [Fe]MRI measurements

关键词： Key Words and Phrases   Sturm-Liouville boundary-value problem   vari-ational method   impulsive effects   p-Laplacian operator  

摘要： In this paper, we consider a class of nonlinear fractional impulsive differential equation involving Sturm-Liouville boundary-value conditions and p-Laplacian operator. By making use of critical point theorem and variational methods, some new criteria are given to guarantee that the considered problem has infinitely many solutions. Our results extend some recent results and the conditions of assumptions are easily verified. Finally, an example is given as an application of our fundamental results.

摘要： We study the relaxation dynamics of quantum turbulence in a two-component Bose-Einstein condensate containing half-quantum vortices. We find a temporal scaling regime for the number of vortices and the correlation lengths that at early times is strongly dependent on the relative strength of the inter-species interaction. At later times we find that the scaling becomes universal, independent of the inter-species interaction, and approaches that numerically observed in a scalar Bose-Einstein condensate. Copyright (C) 2021 The author(s) Published by the EPLA under the terms of the Creative Commons Attribution 4.0 International License (CC BY).