作者机构：
[Xiao, Qizhen; Liu, Hongliang; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Fourth-order elliptic equation;Logarithmic nonlinearity;Ground state solution
摘要：
In this paper, we study the existence of ground state solutions of nonlinear elliptic equation with logarithmic nonlinearity by the Linking theorem and logarithmic Sobolev inequality. Our results are quite different from those in the case of polynomial nonlinearity. (C) 2017 Elsevier Ltd. All rights reserved.
摘要：
Recommendation algorithms based on bipartite networks have become increasingly popular, thanks to their accuracy and flexibility. Currently, many of these methods ignore users’ negative ratings. In this work, we propose a method to exploit negative ratings for the network-based inference algorithm. We find that negative ratings play a positive role regardless of sparsity of data sets. Furthermore, we improve the efficiency of our method and compare it with the state-of-the-art algorithms. Experimental results show that the present method outperforms the existing algorithms.
摘要：
Carbon honeycomb, a new kind of 3D carbon allotrope experimentally synthesized recently, has received much attention for its fascinating applications in electronic device and energy storage. In the present work, we perform equilibrium molecular dynamics (EMD) to study the thermal transport properties of carbon honeycombs with different chirality. It is found that the thermal conductivity along the honeycomb axis ([Formula: see text]) is three times larger than that normal to the axis ([Formula: see text]), which shows strong anisotropy reflecting their geometric anisotropy. Lattice dynamics calculations reveal that this anisotropy stems from the orientation-dependent phonon group velocities. Moreover, when ambient temperature ([Formula: see text]) increases from 200 K to 800 K, the [Formula: see text] dependence of [Formula: see text] is observed due to the enhanced Umklapp scattering. The detailed phonon spectra analyses indicate phonon group velocities are insensitive to the variation of ambient temperature, and the temperature dependence of the relaxation times of low-frequency phonons (<20 THz) follows [Formula: see text] behavior. Our results have a certain guiding significance to develop carbon honeycomb for effective thermal channeling devices.
摘要：
In this paper, we study the multiplicity and concentration of solutions for the following critical fractional Schrödinger–Poisson system: \begin{eqnarray*} \left\{ \begin{array}{ll} \epsilon^{2s}(-\triangle)^{s} {u}+ V(x)u+\phi u =f(u)+|u|^{2^*_{s}-2}u &\mbox{in}\,\,\R^3, \\[2.5mm] \epsilon^{2t}(-\triangle)^{t}{\phi}=u^2 &\mbox{in}\,\, \R^3, \end{array} \right. \end{eqnarray*} where <i>ϵ<i/>> 0 is a small parameter, (− △ )<sup><i>α<i/><sup/> denotes the fractional Laplacian of order <i>α<i/> = <i>s,t<i/> ∈ (0,1), where 2<sub><i>α<i/><sub/><sup>∗<sup/>6/3−2α is the fractional critical exponent in Dimension 3; <i>V<i/> ∈ <i>C<i/><sup>1<sup/>(ℝ<sup>3<sup/>,ℝ<sup>+<sup/>) and <i>f<i/> is subcritical. We first prove that for <i>ϵ<i/>> 0 sufficiently small, the system has a positive ground state solution. With minimax theorems and Ljusternik–Schnirelmann theory, we investigate the relation between the number of positive solutions and the topology of the set where <i>V<i/> attains its minimum for small <i>ϵ<i/>. Moreover, each positive solution <i>u<i/><sub><i>ϵ<i/><sub/> converges to the least energy solution of the associated limit problem and concentrates around a global minimum point of <i>V<i/>.
作者机构：
[Yang, Liu] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.;[Ouyang, Zigen; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Multiplicity;Kirchhoff type equation;Critical growth
摘要：
In this paper, we study the following Kirchhoff type equation with critical growth {-(a + b integral(Omega) vertical bar del u vertical bar(2)dx) del u = lambda u + mu vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0 on partial derivative Omega, where a > 0, b >= 0 and Omega is a smooth bounded domain in R-3. When the real parameter mu is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter lambda belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator -Delta. (C) 2016 Elsevier Ltd. All rights reserved.
作者机构：
[Zhang, Chunhong] Hunan Vocat Coll Sci & Technol, Dept Publ Courses, Changsha 410004, Hunan, Peoples R China.;[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Multiplicity;Degenerate Kirchhoff type equation;Critical growth;Variational method
摘要：
In this paper, we study the following Kirchhoff type problem with critical growth {-M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u = lambda vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0, on partial derivative Omega, where Omega is a smooth bounded domain in R-3, M is an element of C(R+, R) and lambda > 0. We prove the existence of multiple nontrivial solutions for the above problem, when parameter lambda belongs to some left neighborhood of the eigenvalue of the nonlinear operator -M(integral(Omega) vertical bar del u vertical bar(2) dx)Delta. (C) 2017 Elsevier Ltd. All rights reserved.
摘要：
Graphene nanoribbons (GNRs) recently have drawn much interest because of their novel electronic properties such as well-controlled electronic structures, high Seebeck coefficient, and intriguing electronic transport. For the thermoelectric energy conversion, GNRs are thought to be rather poor candidates because of too high phonon thermal conductance, though they own good electronic conduction. Thus, the reduction of the phonon thermal conductance of GNRs is particularly important for their thermoelectric applications. Several methods such as strain, structural defects, etc., have been proposed to reduce the phonon thermal conductance of GNRs. In these methods, however, a central difficulty is that reducing the phonon thermal conductance always brings the adverse effects to the electron transport, which limits the further improvement of the thermoelectric efficiency of GNRs.
期刊：
Nonlinear Analysis: Real World Applications,2017年36:116-138 ISSN：1468-1218
通讯作者：
Guo, Shangjiang
作者机构：
[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Guo, Shangjiang] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Zhang, Ziheng] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China.
通讯机构：
[Guo, Shangjiang] H;Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
关键词：
Generalized Nehari manifold;Ground state;Homoclinic orbit;Second-order Hamiltonian system
摘要：
We deal with the following second-order Hamiltonian systems u - L(t)u + del W (t, u) = 0, where L is an element of C(R,R-N2) is a symmetric and positive define matrix for all t is an element of R, W is an element of C-1 (R x R-N, R) and del W(t, u) is the gradient of W with respect to u. Under the superquadratic condition, we obtain the existence of ground state homoclinic orbits by means of the generalized Nehari manifold developed by Szulkin and Weth. Under the subquadratic condition, we employ variational techniques and the concentration-compactness principle to establish new criteria guaranteeing the multiplicity of classical homoclinic orbits. Recent results in literature are generalized and significantly improved. (C)2017 Elsevier Ltd. All rights reserved.
作者机构：
[Li, Zhenbo] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Tang, Jiashi] Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Li, Zhenbo] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Generalized binary function projective synchronization;Special matrix structure;Adaptive control
摘要：
Based on function projective synchronization theorem, a novel type of synchronization scheme called generalized binary function projective synchronization is proposed. Combining adaptive control theory with special matrix structure, an extended adaptive controller which is more general than some existing controllers is designed. Under the controller, the proposed synchronization between two different uncertain chaotic systems is achieved and the unknown parameters are also estimated. Numerical simulation result is presented to show the validity and feasibility of the scheme and controller. (C) 2017 Elsevier GmbH. All rights reserved.
作者机构：
[Xu, Zhenghua; Min, Z.] School of Math and Physics, University of South China, Hengyang, 421001, China;[Wen, Shiwei] School of Computer Science and Technology Software School, University of South China, Hengyang, 421001, China;[Song, Yingming] School of Nuclear Science and Technology, University of South China, Hengyang, 421001, China
通讯机构：
[Xu, Z.] S;School of Math and Physics, University of South China, Hengyang, China
关键词：
Dose Distribution of Radioactive Source;Mathematical Structural Method;Sparse Grid Data
摘要：
In the case of loss of the source of the radioactive source, the distribution of radiation field needs to be mastered, which is an important basis for radioactive sources search strategy and the evacuation of the radiation area. In this paper, the inversion of the particle field is put forward by a function constructed for solid radioactive sources. we made use of mathematical construction techniques to construct dose function tactfully. An inversion model is established which is based on the dose of nodes in the grid. The dose of the grid lines is restored by the cubic spline interpolation. According to an idea of dose dominance of adjacent point, the function of interior point of grid is structured, which is consistent with the characteristics of the radiation field. During the simulation experiment, the dose of node is obtained by MCNP code based on the Monte Carlo method. It is verified that the dose function is close to the real dose field.
作者机构：
[饶益花] School of Mathematics and Physics, University of South China, Hengyang;421001, China;[陈文光; 胡波] School of Electrical Engineering, University of South China, Hengyang;[饶军; 余珮炫; 曹建勇] China Southwestern Institute of Physics, Chengdu;610041, China
通讯机构：
[Chen, W.] S;School of Electrical Engineering, University of South China, Hengyang, China
摘要：
Fast wave in the ion-cyclotron resonance frequency (ICRF) range is a promising candidate for non-inductive current drive (CD), which is essential for long pulse and high performance operation of tokamaks. A numerical study on the ICRF fast wave current drive (FWCD) and mode-conversion current drive (MCCD) in the Experimental Advanced Superconducting Tokamak (EAST) is carried out by means of the coupled full wave and Ehst-Karney parameterization methods. The results show that FWCD efficiency is notable in two frequency regimes, i.e., f ≥ 85 MHz and f = 50–65 MHz, where ion cyclotron absorption is effectively avoided, and the maximum on-axis driven current per unit power can reach 120 kA/MW. The sensitivity of the CD efficiency to the minority ion concentration is confirmed, owing to fast wave mode conversion, and the peak MCCD efficiency is reached for 22% minority-ion concentration. The effects of the wave-launch position and the toroidal wavenumber on the efficiency of current drive are also investigated.
期刊：
PHYSICS OF PLASMAS,2016年23(1):012301 ISSN：1070-664X
通讯作者：
Cao, Jinjia
作者机构：
[Xiang, Dong; Huang, Qianhong; Gong, Xueyu; Cao, Jinjia] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.;[Wang, Aike] Southwestern Inst Phys, POB 432, Chengdu 610041, Peoples R China.;[Yu, Jun] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Cao, Jinjia] U;Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.
关键词：
plasma collision processes;plasma flow;plasma kinetic theory;plasma transport processes
摘要：
The enhanced transport of passing energetic ions (PEIs) in presence of the resonant interactions with a rotating magnetic island is investigated within the drift kinetic framework. When the island rotation plays a role in the resonant interaction, we find that the velocities of PEIs satisfy a constraint relation of resonant flux surface in phase space. The resonant flux surfaces overlap with the magnetic flux surfaces in real space. A new transport channel responsible for the PEIs moving across the magnetic flux surfaces, i.e., continuously overlapping, is found. Two kinds of radial motions can be induced by the surface overlapping: one arises from the coupling between the resonance and the collision with the background plasma and the other from not completely overlapping of the two surfaces. The two radial motions and the symmetry-breaking induced radial motion constitute the total radial motion. When the pitch-angle scattering rate is very weak, the surface-shear induced transport is dominant. Only a small increase in the collision rate can significantly influence the total transport.
