4,638 research outputs found
Correction to: The Landau Equation with the Specular Reflection Boundary Condition (Archive for Rational Mechanics and Analysis, (2020), 236, 3, (1389-1454), 10.1007/s00205-020-01496-5)
No full textIn the paper [5, Section 6], we quoted a crucial lemma in [7, Proposition 4.1] for the proof of the main L2 decay estimates [5, Theorem 13]. Unfortunately, an omission was recently discovered in its proof. We now present an alternative proof for [5, Theorem 13] based on the methodology in [3,4] without using the method of [7, Proposition 4.1]. We consider the following linearized Landau equation. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.11Nsciescopu
The Vanishing surface tension limit for the Hele-Shaw problem
No full textIn this paper, we show the existence of solutions of the Hele-Shaw problem in two dimensions in the presence of surface tension and for a general class of initial data. The limit problem from nonzero to zero surface tension will also be investigated. In the case of injection and when volume conservation holds, for a sufficiently small surface tension, we prove the existence and uniqueness of perturbed solutions with nonzero surface tension near solutions with zero surface tension. We also show that solutions with nonzero surface tension exist up to a finite time before a possible singularity occurs in which solutions with zero surface tension are well defined. In addition, in the finite time interval, we prove that the solutions with nonzero surface tension approach the solutions with zero surface tension as the surface tension coefficient goes to zero. In the case of suction, for sufficiently small surface tension, we prove the existence of perturbed solutions near solutions with zero surface tension in any initially smooth domains. In this case, the local existence time depends on the surface tension coefficient.110sciescopu
DS_10.1177_0022034518811642 – Supplemental material for High-Frequency Ultrasound Imaging for Examination of Early Dental Caries
No full textSupplemental material, DS_10.1177_0022034518811642 for High-Frequency Ultrasound Imaging for Examination of Early Dental Caries by J. Kim, T.J. Shin, H.J. Kong, J.Y. Hwang and H.K. Hyun in Journal of Dental Research</p
The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach
No full textThe model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In this paper, we consider a diagram of the diffusion limit from the Vlasov-Poisson-Fokker-Planck (VPFP) system on a bounded interval with the specular reflection boundary condition to the Poisson-Nernst-Planck (PNP) system with the no-flux boundary condition. We provide a Deep Learning algorithm to simulate the VPFP system and the PNP system by computing the time-asymptotic behaviors of the solution and the physical quantities. We analyze the convergence of the neural network solution of the VPFP system to that of the PNP system via the Asymptotic-Preserving (AP) scheme. Also, we provide several theoretical evidence that the Deep Neural Network (DNN) solutions to the VPFP and the PNP systems converge to the a priori classical solutions of each system if the total loss function vanishes.11Ysciescopu
Data analytic approach for bankruptcy prediction
No full textBankruptcy prediction problem has been intensively studied over the past decades. From traditional statistical models to state of the art machine learning models, various predictive models are developed and applied to various datasets. However, models that use machine learning are not used in the field of business, for two main reasons. First, the prediction accuracy does not far exceed the statistical models and second, the results are not interpretable. In this study, we focused on solving the skewness which is a characteristic of financial data. By solving this problem, we obtained 17% average improvement in AUC over existing models. To address the second shortcoming, we analyze the importance of features identified by the XGBoost model. The interpretation of the model differs among categories of data. Our bankruptcy prediction model has high predictive accuracy with clear explanations and is therefore directly applicable to the industry. (C) 2019 Elsevier Ltd. All rights reserved.11Nsciescopu
Compactness properties and local existence of weak solutions to the landau equation
No full text© 2020 American Mathematical Society. We consider the Landau equation nearby the Maxwellian equilibrium. Based on the assumptions on the boundedness of mass, energy, and entropy in the sense of Silvestre [J. Diffential Equations 262 (2017), no. 3, 3034–3055], we enjoy the locally uniform ellipticity of the linearized Landau operator to derive local-in-time L∞x,v uniform bounds. Then we establish a compactness theorem for the sequence of solutions using the L∞x,v bounds and the standard velocity averaging lemma. Finally, we pass to the limit and prove the local existence of a weak solution to the Cauchy problem. The highlight of this work is in the low-regularity setting where we only assume that the initial condition f0 is bounded in L∞x,v, whose size determines the maximal time-interval of the existence of the weak solution11Nsciescopu
Operation Principles of ZnO/Al2O3-AlDMP/ZnO Stacked-Channel Ternary Thin-Film Transistor
No full textFor many decades, novel devices demonstrating step-wise current–voltage characteristic at room temperature have been pursued to realize multi-valued logic computing that has significant advantages such as extremely low power consumption and high-density information-processing capability. Recently, a novel ternary logic transistor has been constructed using an ultrathin ZnO/Al11Nsciescopu
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