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An Improved Estimation of the Fixed Point'sNeighborhood in Controlling Discrete Chaotic Systems

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 193-197页

作者： Enguo GU Jiong RUAN and Zhenxun HUANG(institution of mathematics Fudan University, Shanghai 200433, China) institution of mathematics Fudan University Shanghai 200433 China

This paper proposes a better method for determining the fixed point’sneighborhood in which the system remain stable when subjected to a linear law. Thevalidity of this method is shown by a theorem on effective local control of nonlinear,chaotic dynamical system, with numerical confirmation. The ways of implementing theobtained theorem in practice are proposed.

关键词： discrete chaotic system neighborhood of fixed point feedback gain matrix

On Reed-Solomon Codes

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Chinese Annals of mathematics,Series B 2011年第1期32卷 89-98页

作者： Qunying LIAO institution of mathematics and Software Science Sichuan Normal University Chengdu 610066 China

The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.

关键词：所罗门开放性问题特征和估计编码理论维数公式复杂性多项式 n码

Local well-posedness of lower regularity solutions for the incompressible viscoelastic fluid system

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Science China mathematics 2010年第6期53卷 1521-1530页

作者： ZHAO WenJing1,& DU DaPeng2 1School of mathematics Science,Fudan University,Shanghai 200433,China 2institution of mathematics,Fudan University,Shanghai 200433,China School of mathematics Science Fudan University Shanghai China institution of mathematics Fudan University Shanghai China

In the present paper,the local well-posedness of the incompressible viscoelastic fluid system in the whole space is proved under the following assumption on the initial data:the deformation tensor is Hlder continuou... 详细信息

关键词： Oldroyd-B model characteristic direction Stokes kernel

Recent landscape and trends for industry-sponsored pediatric clinical trials in China from 2013 to 2022

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儿科学研究(英文) 2024年第1期8卷 12-20页

作者： Liu Chang Liu Yi Ou Ling Qi Yuenan Zhang Jianmin Drug Clinical Trial institution Children’s Hospital Capital Institute of Pediatrics Beijing China

Importance: Pediatric medication is a challenging issue globally. Promoting trials of medications for children and implementing measures to encourage innovation for addressing unmet medical and health needs are important.Objective: To explore the recent landscape of pediatric clinical trials of new investigational drugs conducted by pharmaceutical enterprises in China from 2013 to 2022 to provide insight into pediatric drug development in the pharmaceutical industry and regulatory policy formulation.Methods: We performed a cross-sectional observational investigation of pediatric clinical trials registered from January 1, 2013, to December 31, 2022, on the Registration and Information Disclosure Platform for Drug Clinical Trials, the official registration platform established in 2013 for trials of new investigational drugs initiated by biopharmaceutical enterprises. Trials that included pediatric participants (under 18 years old) were retrieved, and their relevant characteristics were extracted and analyzed.Results: In total, 895 pediatric clinical trials were collected, accounting for 5.1% of the total registered clinical trials initiated prior to January 1, 2023. The overall average annual growth rate for the number of pediatric clinical trials was 12% (P < 0.001). Phase III trials accounted for the highest proportion (49.1%, 439). Of the 895 trials included, 736 (82.2%) were domestic trials, and 159 (17.8%) were international multicenter trials. In terms of tested drugs, investigations of biological products accounted for the largest proportion of trials (67.4%, 603). Among pediatric clinical trials, studies of vaccines accounted for the largest proportion of trials (41.0%, 367), followed by trials for rare diseases (17.2%, 154). Furthermore, geographical distribution analysis revealed that the largest and smallest numbers of trials were conducted in North China (35.7%, 320) and Northeast China (0.8%, 7), respectively.Interpretation: The growth trends for industry-sponsored clinical trials involving children il

关键词： Geographic distribution Pediatric clinical trials Pediatric medication Rare disease

Global Stability to Steady Supersonic Rayleigh Flows in One-Dimensional Duct

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Chinese Annals of mathematics,Series B 2024年第2期45卷 279-296页

作者： Fenglun WEI Jianli LIU Department of mathematics Shanghai University Newtouch Center for mathematics of Shanghai University

Heat exchange plays an important role in hydrodynamical systems,which is an interesting topic in theory and application.In this paper,the authors consider the global stability of steady supersonic Rayleigh flows for the one-dimensional compressible Euler equations with heat exchange,under the small perturbations of initial and boundary conditions in a finite rectilinear duct.

关键词： Compressible Euler equations Heat exchange Supersonic Rayleigh fow Steady solution Classical solution

The Complete Classification of Graphs Whose Second Largest Eigenvalue of the Eccentricity Matrix is Less than 1

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1741-1766页

作者： Jian Feng WANG Xing Yu LEI Shu Chao LI Zoran STANI? School of mathematics and Statistics Shandong University of Technology Faculty of mathematics and Statistics Central China Normal University Faculty of mathematics University of Belgrade

The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column, and replacing the remaining entries by zero. This matrix can be interpreted as an opposite to the adjacency matrix, which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1. In the paper, we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1.

关键词： Eccentricity matrix eigenvalue diameter principal submatrix forbidden subgraph 05C50

Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

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Science China mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng Department of mathematics and Statistics Fuyang Normal University School of mathematics Sichuan University

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of A from the category CZ/t（A） of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra. Moreover, we describe the semiderived Ringel-Hall algebra by the generators and defining relations. In particular, if t is an odd integer, we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of $\mathbb{Z}/t$-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1674-1684页

作者： Hui LIU Yu Chen WANG School of mathematics and Statistics Wuhan University School of mathematics Tianjin Normal University

Let M = S~n/Γ and h be a nontrivial element of finite order p in π1（M）, where the integers n, p ≥ 2, Γ is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that there are infinitely many noncontractible closed geodesics of class [h] on the compact space form with Cr-generic Finsler metrics,where 4 ≤ r ≤ ∞. The conclusion also holds for Cr-generic Riemannian metrics for 2 ≤ r ≤ ∞. The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

关键词： Compact space forms non-contractible closed geodesics generic Finsler metrics resonance identity 53C22 58E05 58E10

Finite Groups with Some Bounded Codegrees

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1778-1784页

作者： Dong Fang YANG Yu ZENG Heng LV School of mathematics and Statistics Southwest University Department of mathematics Changshu Institute of Technology

For a character χ of a finite group G, the number cod（χ） := |G : ker（χ）|/χ（1） is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the... 详细信息

关键词： Finite group codegree degree simple group 20C15 20D10