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A matrix version of the Wielandt inequality and its application to statistics

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Chinese Science Bulletin 1999年第2期44卷 118-121页

作者： WANG Songgui Wai-Cheung Ipdepartment of applied mathematics, Beijing polytechnic university, Beijing 100022, china Institute of applied mathematics, Chinese Academy of Sciences, Beijing 100080, china department of applied mathematics, hong kong polytechnic university, hong kong, china department of applied mathematics Beijing Polytechntc University Beijing China Institute of applied mathematics Chinese Academy of Sciences Beijing China department of applied mathematics Hong Kong Polytechnic University Hong Kong China

Suppose that A is an n×n positive definite Hemitain matrix. Let X and Y ben×p and n×q matrices（p+q≤n）, such that X*Y=O. The following inequality is provedX*AY（YAY）-Y*AX≤（（λ1-λn）/（λ1+λn）2）X*AX,where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covariance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation.

关键词： Wielandt inequality Cauchy-Schwarz inequality Wishart matrix.

REFINEMENTS OF THE FAN-TODD'S INEQUALITIES

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Chinese Annals of mathematics,Series B 2002年第1期23卷 75-84页

作者： K. K. Chong department of applied mathematics, the hong kong polytechnic university hong kong, china. E-mail:makkchon@inet.po1yu.edu.hk department of applied mathematics The Hong Kong Polytechnic University Hong Kong China

Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties dealt with in this paper are: Cauchy’s inequality, Bessel’s inequality, Fan-Todd’s inequality and Fan-Todd’s determinantal inequality. In each case, a strictly increasing function is put for-ward, which lies between the smaller and the larger quantities of each inequality. As a result. an improved condition for equality of the Fan-Todd’s determinantal inequality is deduced.

关键词： Cauchy's inequality Bessel's inequality Fan-Todd's inequality Fan-Todd's determinantal inequality Refinements of inequalities

Formation Control for Nonlinear Multi-Agent Systems with Time-Delay Coupling and Noise Disturbance in Directed Graphs

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Formation Control for Nonlinear Multi-Agent Systems with Tim...

PRaG 3.0 therapy for human epidermal growth factor receptor 2-positive metastatic pancreatic ductal adenocarcinoma:A case report

2011 Chinese Control and Decision Conference（CCDC）

作者： Xiaoqing Lu,Shihua Chen are with the College of mathematics and Statistics,Wuhan university,Wuhan 430072,china.Francis Austin is with the department of applied mathematics,The hong kong polytechnic university,hong kong,PR china

In this paper,by using the stability theory of stochastic delay differential equations,we investigate a formation control problem of nonlinear multi-agent systems with time-delay coupling and noise disturbance under the assumption that the interconnection topology is a directed *** conditions are obtained for the attainment of both time-invariant and time-varying formations as well as for timevarying formations for trajectory tracking by using a special multiple leaders’ framework that attains the formations at exponentially converging speeds with a probability of *** numerical simulations are also given to illustrate the effectiveness of the theoretical results.

关键词： Multi-agent system Time delay Formation control Directed topology Nonlinear system Noise disturbance

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World Journal of Gastroenterology 2024年第9期30卷 1237-1249页

作者： Yue-hong kong Mei-Ling Xu Jun-Jun Zhang Guang-Qiang Chen Zhi-Hui hong hong Zhang Xiao-Xiao Dai Yi-Fu Ma Xiang-Rong Zhao Chen-Yang Zhang Rong-Zheng Chen Peng-Fei Xing Li-Yuan Zhang Center for Cancer Diagnosis and Treatment The Second Affiliated Hospital of Soochow UniversitySuzhou 215000Jiangsu ProvinceChina department of Radiotherapy&Oncology The Second Affiliated Hospital of Soochow UniversitySuzhou 215000Jiangsu ProvinceChina Institution of Radiotherapy&Oncology Soochow UniversitySuzhou 215000Jiangsu ProvinceChina department of Radiology The Second Affiliated Hospital of Soochow UniversitySuzhou 215000Jiangsu ProvinceChina department of Nuclear Medicine The Second Affiliated Hospital of Soochow UniversitySuzhou 215000Jiangsu ProvinceChina department of Clinical Laboratory The Second Affiliated Hospital of Soochow UniversitySuzhou 215000Jiangsu ProvinceChina department of Pathology The Second Affiliated Hospital of Soochow UniversitySuzhou 215000Jiangsu ProvinceChina

BACKGROUND Pancreatic ductal adenocarcinoma(PDAC)is a highly fatal disease with limited effective treatment especially after first-line *** human epidermal growth factor receptor 2(HER-2)immunohistochemistry(IHC)positive is associated with more aggressive clinical behavior and shorter overall survival in *** SUMMARY We present a case of multiple metastatic PDAC with IHC mismatch repair proficient but HER-2 IHC weakly positive at diagnosis that didn’t have tumor regression after first-line nab-paclitaxel plus gemcitabine and PD-1 inhibitor treatment.A novel combination therapy PRaG 3.0 of RC48(HER2-antibody-drug conjugate),radio-therapy,PD-1 inhibitor,granulocyte-macrophage colony-stimulating factor and interleukin-2 was then applied as second-line therapy and the patient had confirmed good partial response with progress-free-survival of 6.5 months and overall survival of 14.2 *** had not developed any grade 2 or above treatment-related adverse events at any *** of peripheral CD8^(+) Temra and CD4^(+) Temra were increased during first two activation cycles of PRaG 3.0 treatment containing radiotherapy but deceased to the baseline during the maintenance cycles containing no *** PRaG 3.0 might be a novel strategy for HER2-positive metastatic PDAC patients who failed from previous first-line approach and even PD-1 immunotherapy but needs more data in prospective trials.

关键词： Pancreatic ductal adenocarcinoma PRaG 3.0 therapy Human epidermal growth factor receptor 2 Novel combination therapy Case report

Reflections on the Mechanism of Calcium Phosphate Nucleation on Titanium in Simulated Body Fluids

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Journal of Materials Science & Technology 2005年第5期21卷 613-617页

作者： F.T.Chengdepartment of applied Physics, the hong kong polytechnic university, hong kong, china department of applied Physics Hong Kong Polytechnic University Hong Kong Hong Kong

The results and main findings of studies reported in the literature in relation to the deposition of calcium phosphate on Ti in simulated body fluids are summarized. The effects of the surface hydroxyl groups and the sign of surface charge on the nucleation of calcium phosphate are reviewed. One major controversy among the conclusions of different studies is the order of adsorption of the calcium ions and the phosphate ions in the initial stage of immersion. A simple model based on the amphoteric nature of the hydroxyl groups on Ti is proposed in an attempt to delineate the nucleation process for calcium phosphate on Ti in simulated body fluids. HPO4^2- ions interact with the hydroxyl groups via ion exchange and/or electrostatic attraction, and Ca^2＋ ions, via electrostatic attraction only. There is no preferential order of adsorption. Seemingly inconsistent results in different studies possibly arise from different prior treatments of the samples, which affect the adsorption properties.

关键词： Titanium Calcium phosphate Simulated body fluid Hydroxyl group Point of zero charge Surface charge

On comparison of jump point detection for an exchange rate series

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Science china mathematics 2004年第1期47卷 52-64页

作者： IP Wai-Cheung, WONG Heung, XIE Zhongjie & LUAN Yihuidepartment of applied mathematics, hong kong polytechnic university, hong kong, china department of Probability and Statistics, Peking university, Beijing 100871, china department of applied mathematics Hong Kong Polytechnic University Hong Kong China department of Probability and Statistics Peking University Beijing China

The main purpose of this paper is to investigate the detection of jump points of a discontinuous function in the presence of a noise by the wavelet approach. A computing algorithm of our method is proposed and then applied to the daily exchange rate of US Dollar against Deutsche Mark. All the points detected by our method reflect very strong economic and political impacts. Other statistical methods to detect jump points have also been applied to the same exchange rate data. Our proposed method has produced more convincing empirical results than others.

关键词： exchange rate, jump points, threshold, wavelets.

FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID

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Journal of Hydrodynamics 2003年第4期15卷 10-16页

作者： Lu Dong-qiang department of Mechanical Engineering, The university of hong kong, hong kong, china Shanghai Institute of applied mathematics and Mechanics, Shanghai university, Shanghai 200072, china Dept. of Mech. Eng. Univ. of Hong Kong Hong Kong Hong Kong Inst. of Appl. Math. and Mech. Shanghai Univ. Shanghai 200072 China

The free-surface waves and the flow field due to a body moving on the surfaceof an incompressible viscous fluid of infinite depth were studied analytically. The floating bodywas modeled as a normal point pressure on the free surface. Based on the Oseen approximation forgoverning equations and the linearity assumption for boundary conditions, the exact solutions inintegral form for the free-surface elevation, the velocities and the pressure were given. Byemploying Lighthill's two-stage scheme, the asymptotic representations in far field for largeReynolds numbers were derived explicitly. The effect of viscosity on the wave profiles was expressedby an exponential decay factor, which removes the singular behavior predicted by the potentialtheory.

关键词： free-surface waves velocity distribution floating body viscosity asymptotic representation light-hill's two-stage scheme

Partitioning series-parallel multigraphs into υ*-excluding edge covers

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Science china mathematics 2006年第8期49卷 1082-1093页

作者： LIU Guizhen, DENG Xiaotie & XU Changqing School of mathematics and System Science, Shandong university, Jinan 250100, china department of Computer Science, City university of hong kong, Kowloon, hong kong, china department of applied mathematics, Hebei university of Technology, Tianjin 300130, china School of mathematics and System Science Shandong University Jinan 250100 China department of Computer Science City University of Hong Kong Kowloon Hong Kong Hong Kong department of applied mathematics Hebei University of Technology Tianjin 300130 China

We prove that, for any given vertexν* in a series-parallel graph G, its edge set can be partitioned into k= min{k′(G) + 1,δ(G)} subsets such that each subset covers all the vertices of G possibly except forν*, whereδ(G) is the minimum degree of G and k′(G) is the edge-connectivity of G. In addition, we show that the results in this paper are best possible and a polynomial time algorithm can be obtained for actually finding such a partition by our proof.

关键词： series-parallel graph, edge-connectivity, edge cover coloring, min-max theorem.

The structure of L*-inverse semigroups

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Science china mathematics 2006年第8期49卷 1065-1081页

作者： REN Xueming & SHUM Karping department of mathematics, Xi’an university of Architecture and Technology, Xi’an 710055, china Faculty of Science, The Chinese university of hong kong, hong kong, china department of mathematics Xi'an University of Architecture and Technology Xi'an 710055 China Faculty of Science The Chinese University of Hong Kong Hong Kong Hong Kong

The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.

关键词： L*-inverse semigroups type A semigroups left regular bands left wreath products.