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Pointwise estimates for the maximal multilinear singular integral operators

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Science china mathematics 2005年第12期48卷 1696-1706页

作者： HU Guo’en, LI Dengfeng & LU Shanzhen Department of Applied mathematics, university of information Engineering, P. O. Box 1001 -747, Zhengzhou 450002, china college of Mathematical and information sciences, henan university, kaifeng 475001, china Department of mathematics, Beijing Normal university, Beijing 100875, china Department of Applied mathematics University of Information Engineering Zhengzhou 450002 China college of Mathematical and information sciences Henan University Kaifeng 475001 China Department of mathematics Beijing Normal University Beijing 100875 China

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) est... 详细信息

关键词： multilinear singular integral,maximal operator,BMO (Rn),BLO (Rn).

The Ternary Goldbach Problem with Primes in Arithmetic Progressions

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Acta Mathematica Sinica,English Series 2001年第4期17卷 679-696页

作者： Zhen Feng ZHANG Tian Ze WANG State Key Laboratory of information Security, Graduate School, Chinese Academy of sciences, Beijing 100039, P. R. china Depariment of mathematics, henan university, kaifeng 475001, P. R. china Department of mathematics, henan university, kaifeng 475001, P. R. china State Key Laboratory of information Security Graduate School Chinese Acacemy of Sciences Beijing 100039 P. R. China Department of mathematics Henan University Kaifeng 475001 P. R. China

In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik const... 详细信息

关键词： Ternary Goldbach problem Prime Arithmetic progression Circle method

A Note for one of Inequality

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Chinese Quarterly Journal of mathematics 2004年第4期19卷 399-400页

作者： ZHANG Zhi-ping, WANG Jian-ping(college of mathematics and information Science, henan university, kaifeng 475001, china college of mathematics and information Science Henan University Kaifeng 475001China

In this paper, we find the largest contant C such that sin2 x + xtanx > 2x2 + cx5tan x 0

关键词： Maclaurin expansions Bernoulli’s numbers

The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group

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Chinese Quarterly Journal of mathematics 2004年第4期19卷 426-435页

作者： ZHENG Zhu-jun, WANG Guo-an, LU Ke-ping,LUO Xue-bo(1. college of mathematics and information Science, henan university, kaifeng 475001, china 2.Institute of mathematics, henan university, kaifeng 475001, china 3. information Network Center, henan university, kaifeng 475001, china 4. Institute of Applied mathematics, Northwestern Ploytechnical university, Xi'an 710072, china) college of mathematics and information Science Henan University Kaifeng 475001china institute of mathematics Henan University Kaifeng 475001china information Network Center Henan University Kaifeng 475001china college of mathematics and information Science Henan University Kaifeng 475001china Institute of Applied mathematics Northwestern Ploytechnical University Xi'an 710072 china

Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation-ΔHnu = |u|p-1u,x∈Hnhas infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.

关键词： subelliptic operator Z2 index Heisenberg group generalized critical point

GLOBALIZATION AND RESPONSE OF LARGE STATED-OWNED ENTERPRISES IN AGRICULTURAL RELATED INDUS-TRIES: COMPANY CASE STUDIES FROM CENTRAL china

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Chinese Geographical Science 2001年第2期11卷 120-128页

作者： LI Xiao-jian (college of Environment and Planning, henan university, kaifeng 475001, P.R.china) college of Environment and Planning Henan University Kaifeng P. R. China

By using interview data from three large state-owned enterprises (SOEs) in agriculture related industries, this paper reveals that SOEs in inland area are much slow in response to globalization. Although they pursued some strategies to adjust themselves, they are far behind the position to utilize the opportunities generated by economic globalization. Most of them are still out of the networks of transnational corporations. The strategies they adopted are quite different from SOEs in the coastal area. They overlook the importance of information infrastructure, well-educated personnel, and collaboration with the competitive leaders in their industries. The lagging situation is related to isolated location, traditional culture, and slow progress in enterprise reform. International comparison shows that the case companies did follow the general patterns that globalization promotes extension of company′s networks of linkages but in a rather slow phase. The decision makers should encourage intra-regional linkages between SOEs, between SOEs and private, foreign owned companies, as well as inter-regional linkages among them. The latter appears particularly important given the enlarging gaps between coastal and inland areas.

关键词： state-owned enterprise enterprise reform regional development globalization

Hydrogen peroxide-induced changes in intracellular pH of guard cells precede stomatal closure

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Cell Research 2001年第1期11卷 37-43页

作者： ZHANG XIAO, FA CAI DONG, JUN FENG GAO, CHUN PENG SONG (Department of Biology, henan university, kaifeng 475001, china) (college of Life sciences, Northwest Sci-Tech university of Agriculture and Forestry, Yangling 712100, china) Department of Biology Henan University Kaifeng China college of Life sciences Northwest Sci-Tech University of Agriculture and Forestry Yangling China

Epidermal bioassay demonstrated that benzylamine, a membrane-permeable weak base, can mimick hydrogen peroxide (H2O2) to induce stomatal closure, and butyric acid, a membrane-permeable weak acid, can partly abolish the H2O2-induced stomatal closure. Confocal pH mapping with the probe 5-(and-6)- carboxy seminaphthorhodafluor- 1 - acetoxymethylester (SNARF-1-AM) revealed that H2O2 leads to rapid changes in cytoplasmic and vacuolar pH in guard cells of Viola faba L, i. e. alkalinization of cytoplasmic areas occur red in parallel with a decrease of the vacuolar pH, and that butyric acid pretreatment can abolish alkalinization of cytoplasmic areas and acidification of vacuolar areas of guard cells challenged with H2O2. These results imply that the alkalinization of cytoplasm via efflux of cytosol protons into the vacuole in guard cells challenged with H2O2 is important at an early stage in the signal cascade leading to stomatal closure.

关键词： H2O2 pH SNARF-1-AM confocal Vicia guard cell.

L_p-mixed intersection bodies

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Science china mathematics 2008年第12期51卷 2172-2188页

作者： ZHAO ChangJian Department of information and mathematics sciences, college of Science, china Jiliang university, Hangzhou 310018, china Department of information and mathematics sciences College of Science China Jiliang University Hangzhou China

In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.

关键词： L p -dual mixed volumes L p -intersection bodies L p -mixed intersection bodies 52A40

On the least primitive root in number fields

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Science china mathematics 2010年第9期53卷 2489-2500页

作者： WANG TianZe1,& GONG Ke21School of mathematics and information sciences,North china university of Water Resources and Electric Power,Zhengzhou 450011,china 2Department of mathematics,henan university,kaifeng 475004,china School of mathematics and information sciences North China University of Water Resources and Electric Power Zhengzhou China Department of mathematics Henan University Kaifeng China

Let K be an algebraic number field and OK its ring of *** any prime ideal p,the group(OK/p) of the reduced residue classes of integers is *** call any element of a generator of the group(OK/p) a primitive root modulo *** both by Shoup's bound for the rational improvement and Wang and Bauer's generalization of the conditional result of Wang Yuan in 1959,we give in this paper a new bound for the least primitive root modulo a prime ideal p under the Grand Riemann Hypothesis for algebraic number *** results can be viewed as either the improvement of the result of Wang and Bauer or the generalization of the result of Shoup.

关键词： primitive root algebraic number fields Hecke zeta function

Lp-dual Quermassintegral sums

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Science china mathematics 2007年第9期50卷 1347-1360页

作者： Chang-jian ZHAO Department of information and mathematics sciences,college of Science,china Jiliang university,Hangzhou 310018,china Department of information and mathematics sciences College of Science China Jiliang University Hangzhou China

In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral ***,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion *** applications,we prove some interrelated results.

关键词： mixed volumes mixed projection bodies dual Quermassintegral sum polar of mixed projection bodies 52A40 53A15