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A simple proof of the formal duality of the Kerdock and Preparata codes

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chinese science Bulletin 2000年第14期45卷 1279-1282页

作者： WAN ZhexianInstitute of systems science, chinese academy of sciences, beijing 100080, china Institute of systems science Chinese Academy of Sciences Beijing China

The nonlinearity of the Z2-Kerdock code Km+1, where m is an odd integer ≥3, is not at all obvious. By regarding Km+1 as the binary image of the Z4-Kerdock code .,K(m) under the Gray map[1], a simple proof can be achieved (cf. Theorems 8.7 and 8.9 of [2]). Similarly, the formal duality of the Z2-Kerdock code Km+1 and the Z2-Preparata code Pm+1 is even more not at all obvious. A simple proof is given in the present note, by regarding Km+1 as the binary image of .K (m) and using the duality of .K(m) and the Z4-Preparata code . (m) established in [1].

关键词： 4-code. Kerdock code Preparata code formal duality.

Boundedness of a class of super singular integral operators and the associated commutators

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science china mathematics 2004年第6期47卷 842-853页

作者： CHEN Qionglei & ZHANG Zhifei Department of mathematics, Zhejiang University, Hangzhou 310028, china academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of mathematics Zhejiang University Hangzhou China academy of mathematics and system sciences Chinese Academy of Sciences Beijing China

In this paper we give the (L p α, L p ) boundedness of the maximal operator of a class of super singular integrals defined by $$T_{\Omega ,\alpha }^* f(x) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int_{|x - y| > \varepsilon } {b(|y|)} \Omega (y)|y|^{ - n - \alpha } f(x - y)dy} \right|,$$ which improves and extends the known result. Moreover, by applying an off-Diagonal T1 Theorem, we also obtain the (L p , L q ) boundedness of the commutator defined by $$C_{\Omega ,\alpha } f(x) = p.v. \int_{\mathbb{R}^n } {(A(x)} - A(y))\Omega (x - y)|x - y|^{ - n - \alpha } f(y)dy.$$

关键词： singular integral operator maximal operator commutator T1 Theorem

Expert Consensus on the Prevention and Treatment of Chronic Hepatitis B in Children

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Infectious Diseases & Immunity 2024年第3期4卷 106-120页

作者： chinese Society of Infectious Diseases chinese Medical Association chinese Society of Hepatology chinese Medical Association Group of Infectious Diseases chinese Pediatric Society chinese Medical Association National Clinical Research Center for Infectious Diseases(beijing) Fu-Sheng Wang Shishu Zhu Min Zhang Jianshe Wang Shuangjie Li Junliang Fu Yuanyuan Li Yuming Guo Jing Li Hongmei Xu Wenxian Ouyang Yuemin Nan Sainan Shu Shuangsuo Dang Xiaoyuan Xu Taisheng Li Jinlin Hou 不详 The Fifth Medical Center of PLA General Hospital Beijing 100039China Fudan University Children’s Hospital Hunan Children’s Hospital Children’s Hospital of Chongqing Medical University Third Hospital Hebei Medical University Tongji Hospital Tongji Medical CollegeHuazhong University of Science and Technology The Second Affiliated Hospital of Xi’an Jiaotong University Peking University First Hospital Peking Union Medical College Hospital Chinese Academy of Medical Sciences&Peking Union Medical College Nanfang Hospital Southern Medical University

The aim of this consensus is to standardize the prevention, diagnosis, and treatment of chronic hepatitis B in children and to achieve the goal of “eliminating viral hepatitis as a major public health threat by 2030” issued by the World Health Organization. Formulated by organized experts of the chinese Society of Infectious Diseases and chinese Society of Hepatology, chinese Medical Association;Group of Infectious Diseases, chinese Pediatric Society, chinese Medical Association;and the National Clinical Research Center for Infectious Diseases (beijing), the consensus provides the latest evidence and recommendations for the prevention, diagnosis, and treatment of chronic hepatitis B in children.

关键词： Chronic hepatitis B Children Treatment Prevention Consensus

Variational Description for the Generating Function Method of First Kind

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 693-702页

作者： Ya-Juan Sun, Meng-Zhao Qinacademy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china academy of mathematics and system sciences Chinese Academy of Sciences Beijing China

We propose the variational description of generating function approach of first kind for Hamil-tonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.

关键词： Generating function method inultisyrnplectic variational description

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(r,k)-catching code

chinese science Bulletin 1998年第10期43卷 812-815页

作者： LI Anping Institute of Applied mathematics, chinese academy of sciences, beijing 100080, china Institute of Applied mathematics Chinese Academy of Sciences Beijing China

A collection of r_words on an alphabet of n letters is called (r,k)_catching code if for every r_word w there is one selected member v such that v coincides with w in at least k places. How large is the smallest size of the (r,k)_catching code and how to find the minimal (r,k)_\%catching code? Some methods are advanced to construct such codes.

关键词： catching code.

Existence of SURU estimators in SURE model with special covariance structures

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chinese science Bulletin 1997年第14期42卷 1149-1151页

作者： WU QiguangInstitute of systems science, chinese academy of sciences, beijing 100080, china Institute of systems science Chinese Academy of Sciences Beijing China

THROUGHOUT this note, the following notations are used: For a matrix A, A>0 means thatA is positive definite symmetric; R （A）, A′and A- stand for the column space, transposeand any g-inverse of A respectively; PA = A （A′A）- A′and PA = Ik - PA, where Ik is theidentity matrix of order k that is the number of rows in A. Rm×n is the totality of m×n realmatrices.

关键词： seemingly unrelated regression equations (SURE) model uniformly minimum risk unbiased (UMRU) estimator uniform covariance structure serial covariance structure.

The gravity wave instability induced by photochemistry in summer polar mesopause region

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chinese science Bulletin 2000年第3期45卷 267-272页

作者： Center for Space science and Applied Research, chinese academy of sciences, beijing 100080, china Laboratory of Numeric Study of Heliospheric Physics, chinese academy of sciences, beijing 100080, china Center for Space science and Applied Research Chinese Academy of Sciences Beijing China Laboratory of Numeric Study of Heliospheric Physics Chinese Academy of Sciences Beijing China

The effect of diabatic process due to the photochemical heating and cooling on the gravity wave propagation in middle atmosphere is studied. A linear gravity wave model which considers the diabatic process is established. The unstable region and the growth rate of the gravity wave caused by photochemistry are calculated. And the comparison between the model and the adiabatic gravity wave theory of pure dynamics is made. The results indicate that the photochemical heating process can induce the instability of gravity wave at mesopause. The intensity of the instability becomes stronger as the temperature decreases. The temperature feature and the altitude characteristics of the instability are consistent with the observation. Therefore, the instability of the gravity wave induced by photochemistry may be an important mechanism in polar mesopause region in summer.

关键词： photochemistry instability gravity wave growth rate.

On Semi-tensor Product of Matrices and Its Applications

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Acta Mathematicae Applicatae Sinica 2003年第2期19卷 219-228页

作者： Dai-zhan Cheng, Li-jun ZhangInstitute of systems science, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, P.R. china Institute of systems science Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing P. R. China

Abstract The left semi-tensor product of matrices was proposed in [2]. In this paper the right semi-tensor product is introduced first. Some basic properties are presented and compared with those of the left semi-tensor *** two new applications are investigated. Firstly, its applications to connection, an important concept in differential geometry, is considered. The structure matrix and the Christoffel matrix are introduced. The transfer formulas under coordinate transformation are expressed in matrix form. Certain new results are obtained. Secondly, the structure of finite dimensional Lie algebra, etc. are investigated under the matrix *** applications demonstrate the usefulness of the new matrix products.

关键词： Keywords Matrix semi-tensor product connection Christoffel symbol algebra

Exponential inequalities for associated random variables and strong laws of large numbers

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science china mathematics 2007年第5期50卷 705-714页

作者： Shan-chao YANG & Min CHEN Deptartment of mathematics, Guangxi Normal University, Guilin 541004, china academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Deptartment of mathematics Guangxi Normal University Guilin China academy of mathematics and systems science Chinese Academy of Sciences Beijing China

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.

关键词： associated random variable exponential inequality strong law of large numbers rate of convergence 60E15 60F15