EXISTENCE AND NON-EXISTENCE FOR SCHR¨ODINGER EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

Henghui Zou 대한수학회 2010 대한수학회지 Vol.47 No.3

We study existence of positive solutions of the classical nonlinear Schr¨odinger equation [수식]In fact, we consider the following more general quasi-linear Schr¨odinger equation [수식]where m ∈ (1, n) is a positive number and [수식]is the corresponding critical Sobolev embedding number in Rn. Under appropriate conditions on the functions V (x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

EXISTENCE AND NON-EXISTENCE FOR SCHRÖDINGER EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

Zou, Henghui Korean Mathematical Society 2010 대한수학회지 Vol.47 No.3

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

An Improved Thermal Conductivity Model for Unsaturated Clay

Xinye Song,Henghui Fan,Jiawei Liu,Xiujuan Yang 대한토목학회 2020 KSCE JOURNAL OF CIVIL ENGINEERING Vol.24 No.8

The thermal properties of soils vary because of the different textures of soils; thus, it is valuable to conduct research on the development of thermal conductivity models for soils with different textures. Clay samples with different dry densities and increasing incremental water contents were prepared, their thermal conductivities were measured by the transient plane source (TPS) method. The experimental results show that the thermal conductivity of clay increases with increasing water content and dry density. The water content has a stronger influence than the dry density on the thermal conductivity. This paper presents an improved model to predict the thermal conductivity of unsaturated clay. The model considers the different contributions of minerals in the soil and the distribution of water and air in pores. The accuracy of the model is verified by soil thermal conductivity data that was previously measured and collected from ten regions. Compared with the three similar models proposed in the literature, the new model proposed in this paper has a higher degree of correlation to describe the thermal conductivity of clay.

Localization in Unknown Environments for the Fifth-GenerationWireless Systems

Watcharapan Suwansantisuk,Henghui Lu 대한전자공학회 2017 대한전자공학회 학술대회 Vol.2017 No.1

Localization based on the received signal strengths is a prominent technique of positioning for the fifth-generation wireless communication systems, due to its low cost, low complexity, and the ability to function in heterogeneous infrastructures. Existing methods to localization, however, do not fully consider constraints on the position and path-loss parameters, resulting in positional inaccuracy and a large distance error. In this paper, we account for every necessary constraint and estimate jointly the target position and path-loss parameters. We formulate an optimization and transform the objective function to simplify a localization method. We compare the proposed method to a competitive baseline using the distance error as a metric. The results show that the proposed method outperforms the baseline in most test cases. The proposed method to localization is accurate, simple, and suitable for unknown environments.

Surface Coating of Polytetrafluoroethylene with Extracellular Matrix and Anti-CD34 Antibodies Facilitates Endothelialization and Inhibits Platelet Adhesion Under Sheer Stress

Lei Chen,Haipeng He,Mian Wang,Xiaoxi Li,Henghui Yin 한국조직공학과 재생의학회 2017 조직공학과 재생의학 Vol.14 No.4

Expanded polytetrafluoroethylene (ePTFE) polymers do not support endothelialization because of nonconductive characteristics towards cellular attachment. Inner surface modification of the grafts can improve endothelialization and increase the long-term patency rate of the ePTFE vascular grafts. Here we reported a method of inner-surface modification of ePTFE vascular graft with extracellular matrix (ECM) and CD34 monoclonal antibodies (CD34 mAb) to stimulate the adhesion and proliferation of circulating endothelial progenitor cells on ePTFE graft to enhance graft endothelialization. The inner surface of ECM-coated ePTFE grafts were linked with CD34 mAb in the presence of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide/N-hydroxysuccinimide (EDC/NHS) solution and the physicochemical properties, surface morphology, biocompatibility, and hemocompatibility of the grafts were studied. The hydrophilicity of CD34 mAb-coated graft inner surface was significantly improved. Fourier transform infrared spectroscopy analysis confirmed ECM and CD34 mAb cross-linking in the ePTFE vascular grafts with our method. Scanning electron microscopy analysis showed protein layer covering uniformly on the inner surface of the modified grafts. The cell-counting kit-8 (CCK-8) assay confirmed that the modified graft has no obvious cytotoxicity. The modified graft showed a low hemolytic rate (0.9%) in the direct contact hemolysis test, suggesting the modification improved hemocompatibility of biopolymers. The modification also decreased adhesion of platelets, while significantly increased the adhesion of endothelial cells on the grafts. We conclude that our method enables ePTFE polymers modification with ECM and CD34 mAb, facilitates endothelialization, and inhibits platelet adhesion on the grafts, thus may increase the long-term patency rate of the prosthetic bypass grafts.

Recent Development in the Rate Performance of Li₄Ti₅O₁₂

Lin, Chunfu,Xin, Yuelong,Cheng, Fuquan,Lai, Man On,Zhou, Henghui,Lu, Li The Korean Vacuum Society 2014 Applied Science and Convergence Technology Vol.23 No.2

Lithium-ion batteries (LIBs) have become popular electrochemical devices. Due to the unique advantages of LIBs in terms of high operating voltage, high energy density, low self-discharge, and absence of memory effects, their application range, which was primarily restricted to portable electronic devices, is now being extended to high-power applications, such as electric vehicles (EVs) and hybrid electrical vehicles (HEVs). Among various anode materials, $Li_4Ti_5O_{12}$ (LTO) is believed to be a promising anode material for high-power LIBs due to its advantages of high working potential and outstanding cyclic stability. However, the rate performance of LTO is limited by its intrinsically low electronic conductivity and poor $Li^+$ ion diffusion coefficient. This review highlights the recent progress in improving the rate performance of LTO through doping, compositing, and nanostructuring strategies.

Recent Development in the Rate Performance of Li4Ti5O12

Chunfu Lin,Li Lu,Yuelong Xin,Fuquan Cheng,Man On Lai,Henghui Zhou 한국진공학회 2014 Applied Science and Convergence Technology Vol.23 No.2

Lithium-ion batteries (LIBs) have become popular electrochemical devices. Due to the unique advantages of LIBs in terms of high operating voltage, high energy density, low self-discharge, and absence of memory effects, their application range, which was primarily restricted to portable electronic devices, is now being extended to high-power applications, such as electric vehicles (EVs) and hybrid electrical vehicles (HEVs). Among various anode materials, Li4Ti5O12 (LTO) is believed to be a promising anode material for high-power LIBs due to its advantages of high working potential and outstanding cyclic stability. However, the rate performance of LTO is limited by its intrinsically low electronic conductivity and poor Li+ ion diffusion coefficient. This review highlights the recent progress in improving the rate performance of LTO through doping, compositing, and nanostructuring strategies.

Recent Development in the Rate Performance of Li4Ti<SUB>5</SUB>O<SUB>12</SUB>

Chunfu Lin,Yuelong Xin,Fuquan Cheng,Man On Lai,Henghui Zhou,Li Lu 한국진공학회(ASCT) 2014 Applied Science and Convergence Technology Vol.23 No.2

Lithium-ion batteries (LIBs) have become popular electrochemical devices. Due to the unique advantages of LIBs in terms of high operating voltage, high energy density, low self-discharge, and absence of memory effects, their application range, which was primarily restricted to portable electronic devices, is now being extended to high-power applications, such as electric vehicles (EVs) and hybrid electrical vehicles (HEVs). Among various anode materials, Li4Ti5O12 (LTO) is believed to be a promising anode material for high-power LIBs due to its advantages of high working potential and outstanding cyclic stability. However, the rate performance of LTO is limited by its intrinsically low electronic conductivity and poor Li<SUP>+</SUP> ion diffusion coefficient. This review highlights the recent progress in improving the rate performance of LTO through doping, compositing, and nanostructuring strategies.