Theory of amplification of sound (acoustic phonons) by absorption of laser radiation in quantum wires with parabolic potential

Based on the quantum transport equation for the electron-phonon system, the absorption coefficient of sound (acoustic phonons) by absorption of a laser radiation in quantum wires with parabolic potential is calculated for the case of monophoton absorption and the case of multiphoton absorption. Analytical expressions and conditions for the absorption coefficient of sound are obtained. Differences between the two cases of monophoton absorption and of multiphoton absorption are discussed; numerical computations and plots are carried out for a GaAs/GaAsAl quantum wire. The results are compared with bulk semiconductors and quantum wells.Comment: 7 pages, 1 figur

Energy conservation for inhomogeneous incompressible and compressible Euler equations

Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient conditions for a weak solution to conserve the energy. By exploiting a suitable test function, the spatial regularity for the density is only required to be of order $2/3$ in the incompressible case, and of order $1/3$ in the compressible case. When the density is constant, we recover the existing results for classical incompressible Euler equation.Comment: The new version deals with general pressure law for compressible equations. By using a new test function, we allow the density to be zero instead of excluding completely vacuum. Required regularities for the density in the compressible case are also reduce

Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data

In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: $$u_t-\operatorname{div}(A(x,t,\nabla u))=\operatorname{div}(F),$$ in a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$, under minimal regularity assumptions on the boundary of domain and on nonlinearity $A$. Then results yields existence of a solution to the Riccati type parabolic equations: $$u_t-\operatorname{div}(A(x,t,\nabla u))=|\nabla u|^q+\operatorname{div}(F)+\mu,$$ where $q>1$ and $\mu$ is a bounded Radon measure.Comment: to appear Calculus of Variations and Partial Differential Equation

A survey of embedding models of entities and relationships for knowledge graph completion

Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.Comment: 13 pages, 2 figures and 6 table

Gradient estimates for singular quasilinear elliptic equations with measure data

In this paper, we prove $L^q$-estimates for gradients of solutions to singular quasilinear elliptic equations with measure data $$-\operatorname{div}(A(x,\nabla u))=\mu,$$ in a bounded domain $\Omega\subset\mathbb{R}^{N}$, where $A(x,\nabla u)\nabla u \asymp |\nabla u|^p$, $p\in (1,2-\frac{1}{n}]$ and $\mu$ is a Radon measure in $\Omega$Comment: 20 pages. arXiv admin note: text overlap with arXiv:1511.0621

Non-commutative Chern Characters of the C*-Algebras of spheres and quantum spheres

We propose in this paper the construction of non-commutative Chern characters of the C*-algebras of spheres and quantum spheres. The final computation gives us a clear relation with the ordinary Z/(2)-graded Chern characters of tori or their normalizers.Comment: 12 pages, AmSTeX fil

A neural joint model for Vietnamese word segmentation, POS tagging and dependency parsing

We propose the first multi-task learning model for joint Vietnamese word segmentation, part-of-speech (POS) tagging and dependency parsing. In particular, our model extends the BIST graph-based dependency parser (Kiperwasser and Goldberg, 2016) with BiLSTM-CRF-based neural layers (Huang et al., 2015) for word segmentation and POS tagging. On Vietnamese benchmark datasets, experimental results show that our joint model obtains state-of-the-art or competitive performances.Comment: In Proceedings of the 17th Annual Workshop of the Australasian Language Technology Association (ALTA 2019

Rationality of almost simple algebraic groups

We prove the stable rationality of almost simple algebraic groups, the connected components of the Dynkin diagram of anisotropic kernel of which contain at most two vertices. The (stable) rationality of many isotropic almost simple groups with small anisotropic kernel and some related results over $p$-adic and arbitrary fields are discussed.Comment: originally the manuscript has been circulated since March 1995, LaTe

A Fast and Accurate Vietnamese Word Segmenter

We propose a novel approach to Vietnamese word segmentation. Our approach is based on the Single Classification Ripple Down Rules methodology (Compton and Jansen, 1990), where rules are stored in an exception structure and new rules are only added to correct segmentation errors given by existing rules. Experimental results on the benchmark Vietnamese treebank show that our approach outperforms previous state-of-the-art approaches JVnSegmenter, vnTokenizer, DongDu and UETsegmenter in terms of both accuracy and performance speed. Our code is open-source and available at: https://github.com/datquocnguyen/RDRsegmenter.Comment: In Proceedings of the 11th International Conference on Language Resources and Evaluation (LREC 2018), to appea

Brezis-Gallouet-Wainger type inequality with critical fractional Sobolev space and BMO

In this paper, we prove the Brezis-Gallouet-Wainger type inequality involving the BMO norm, the fractional Sobolev norm, and the logarithmic norm of $\mathcal{\dot{C}}^\eta$, for $\eta\in(0,1)$.Comment: 12 pages, Accepted Paper: Comptes Rendus Mathematiqu