ESTIMATES FOR THE HIGHER ORDER RIESZ TRANSFORMS RELATED TO SCHRÖDINGER TYPE OPERATORS

Wang, Yanhui Korean Mathematical Society 2021 대한수학회보 Vol.58 No.1

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

ESTIMATES FOR THE RIESZ TRANSFORMS ASSOCIATED WITH SCHRÖDINGER TYPE OPERATORS ON THE HEISENBERG GROUP

Wang, Yanhui Korean Mathematical Society 2022 대한수학회보 Vol.59 No.5

We consider the Schrödinger type operator 𝓛 = (-𝚫_ℍⁿ)² + V² on the Heisenberg group ℍⁿ, where 𝚫_ℍⁿ is the sub-Laplacian and the non-negative potential V belongs to the reverse Hölder class RH_s for s ≥ Q/2 and Q ≥ 6. We shall establish the (L^p, L^q) estimates for the Riesz transforms T_𝛼,𝛽,j = V^2𝛼𝛁^j_ℍⁿ𝓛^-𝛽, j = 0, 1, 2, 3, where 𝛁_ℍⁿ is the gradient operator on ℍⁿ, 0 < α ≤ 1-j/4, j/4 < 𝛽 ≤ 1, and 𝛽 - 𝛼 ≥ j/4.

The Factors and Processes Relating with the Accumulation of Zn in Rice Grains

Guo Wang,Lijun Sun,Yanhui Chen,Mingkuang Wang 한국토양비료학회 2014 한국토양비료학회 학술발표회 초록집 Vol.2014 No.6

Matrix-Diffusion-Controlled Coarsening of the γ′ Phase in Waspaloy

Haiping Wang,Dong Liu,Yongzhao Shi,Jianguo Wang,Yanhui Yang,Longxiang Wang,Weidong Qin 대한금속·재료학회 2019 METALS AND MATERIALS International Vol.25 No.6

This paper discussed the coarsening behavior of the γ′ phase in Waspaloy during heat treatment at different aging timesunder the temperatures of 960 °C and 1000 °C. The morphology of γ′ phase is obtained by scanning electron microscopyand it is measured by the software Image Pro Plus 6.0 in a variety of aging conditions. The volume fraction of the γ′ phase isdecreasing with the increase of the temperature. The radius of the γ′ phase is subject to involve the coarsening process duringaging treatment, and the coarsening rate decreases with the extension of the aging time at certain temperature. Besides,the coarsening kinetics of γ′ phase in Waspaloy is adequately characterized by the Lifshitz–Slyozov–Wagner (LSW) theorymodel as the particle size distribution and coarsening behavior show excellent agreement with the LSW model. Accordingto the experimental results and LSW model, the coarsening rate coefficients were determined to be 27.23 nm3/s and58.67 nm3/s under the aging temperature of 960 °C and 1000 °C respectively. Meanwhile, on the basis of the experimentalstatistics analysis and the LSW model, the mathematical model of the coarsening behavior of the γ′ phase in Waspaloy wasdeveloped. Mathematical model developed in this paper can be used to evaluate the coarsening process of the γ′ phase duringthermal exposure. The interfacial energy between the γ′ phase and the γ matrix was determined to be 56.04 mJ/m2 and44.27 mJ/m2 at the temperature of 960 °C and 1000 °C respectively.

Network Information Target Search Model and Strategy Based on Web Vertical Crawler System

Bin Wang,Jian Zhang,Na Wang,Xiaohua Sun,Yanhui Wang 보안공학연구지원센터 2016 International Journal of Future Generation Communi Vol.9 No.4

With the explosive growth of the web information, acquiring the target information quickly, precisely and effectively in a large number of network information is restricted by many factors. In response to it, this paper analyzed the key technician part in the network information search engine-web crawler technology and proposed a network information target search model based on the web vertical crawler system with discussion on the implementation of the corresponding search strategy. Firstly, it builds the structure of the web crawler system and analyzes different function models. Next, it discusses some crucial problems including the options of deleting duplicated URL, the strategies to choose duplicated URL deletion method and the control model of error probability estimate model to acquire the closest network information to the target information. Finally, it verifies and discusses the operability and effectiveness of the model and the implementation strategy through case study.

FINITE ELEMENT MODELING FOR CONCRETE RANDOM PARTICLE MODEL

YanHui Yin,HaiWen Wang 한국멀티미디어학회 2006 한국멀티미디어학회 국제학술대회 Vol.2006 No.-

How to select the reasonable aggregate based on the engineering need and the actual condition of the locality and perform effectually computational simulation base on the type of the aggregate is important. This paper generalize the affection of all kinds of parameters of the aggregate to the concrete function base on the importance of concrete aggregate and lots of engineering background. The geometrical representation and finite element mesh of concrete random particle model are all generated automatically in this paper.

An Improved H.264 Encoded Algorithm Based on Weber-Fechner Law

Yanhui Xia,Baisheng Nie,Zhengyou Wang,Liying Li,Jianhua Ming,Zheng Wan,Shuying Huang 보안공학연구지원센터 2015 International Journal of Multimedia and Ubiquitous Vol.10 No.9

With the study of human visual system (HVS), people find that the human eye shows different degree of sensitivity to different light signals. A higher background brightness region of the human eye for the distortion, the degree of sensitivity will be greatly reduced. The human eye’s sensitivity will be greatly reduced to the distortion of a higher brightness background region. This finding is discribed in Weber-Fechner law. Therefore, the encoder can be improved by employing this characteristic of human visual system. In this paper, the authors use this characteristic to improve the H.264 video coding algorithm. In order to improve the compression efficiency of encoder, give the brightness of different regions with different levels of quantification by adjusting the quantization step size (QP), without affecting the subjective quality of video. Experimental results show that the output bit rate decrease up to 10% -20% by using this improved algorithm in H.264 reference encoder, and the subjective quality of decoded image by using this improved algorithm is as good as the standard H.264 encoders.

Web-Based Collaborative Learning System and Its Key Techniques

Yanhui Xia,Zhengyou Wang,Yi Li,Jinfeng Hu 보안공학연구지원센터 2015 International Journal of Multimedia and Ubiquitous Vol.10 No.12

On the basis of concept, characteristics and related work of collaborative learning, this paper proposes an intelligent web collaborative learning system prototype based on multi-agent technology. At first, the paper introduces a collaborative learning framework which supporting group learning and illustrates the whole learning process. Secondly, the paper presents some key issues to implementation of the virtual learning environment, such as intelligent grouping, automatic question answering, knowledge management, and opinion mining. Preliminary learning practice shows that it is a practical and efficient way.

Viscosity evaluation of Fe–Ni–Co ternary alloy from the measured binary systems

Yanhui Liu,Xuewei Lv,Chenguang Bai,Pingsheng Lai,JinSheng Wang 한국공업화학회 2015 Journal of Industrial and Engineering Chemistry Vol.30 No.-

The iso-viscosity curves of liquid Fe–Ni–Co ternary alloys at 1600 8C were investigated with consideringthe excess viscosity of ternary alloy by the means of three models (Kohler, Toop and Chou) from themeasured sub-binary data in this work. Excess viscosities were used instead of excess thermodynamicproperties in geometrical models, and the excess viscosities of the sub-binary systems were fit by usingthe 3rd degree (n = 3) Redlich–Kister polynomial. The increase of Ni content results in the decrease of theviscosity of the ternary alloy, while Fe has opposite effect. When the molar content of Ni within the alloydoes not exceed 50%, the increase of Co lowers the viscosity. Once its content is above 50%, Co canpromote the increase of the viscosity of the ternary alloy. Similarity coefficients of the Fe–Ni, Fe–Co andNi–Co three binary systems mentioned in the Chou model have been calculated and their values are 0.82,0.20 and 0.47, respectively, showing that the Fe–Ni–Co ternary system is not exactly the ‘‘Kohler model’’or ‘‘Toop model’’, so both Kohler model and Toop model cannot obtain the accurate predicted values. Thepredicted iso-viscosity curves calculated by the Chou model should be recommended. Some activationenergies of the ternary alloy were calculated by the three models and compared with three sub-binarysystems, and the evaluated activation energies calculated by the Chou model should be recommended. Except the sample AE3 and AE6, other activation energy values predicted by three different models aresimilar by a narrow margin. The activation energies for AE3 and AE6 are the lowest and highest,respectively, because of the mix effect of the ternary alloy.

A New Image Quality Assessment Algorithm based on SSIM and Multiple Regressions

Zhengyou Wang,Liying Li,Shuang Wu,Yanhui Xia,Zheng Wan,Cong Cai 보안공학연구지원센터 2015 International Journal of Signal Processing, Image Vol.8 No.11

Image quality assessment (IQA) is crucial in image processing algorithms. In the state-of-the-art IQA index, the structural similarity (SSIM) index has been proved to be better objective quality assessment metric. However, the accuracy of SSIM is relatively lacking when used to access blurred images. And the component weights of structural similarity (SSIM) index are fixed in some past environments. So an improved assessment algorithm incorporating multiple linear regressions and SSIM index was proposed in this paper. We use regression analysis to adjust the component weight of SSIM index. So the improved algorithm is more accuracy on different distortion types’ quality assessment. Experimental results show that the improved SSIM algorithm is better than traditional methods in nonlinear regression correlation coefficient, Spearman correlation coefficient and out ratio.