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Extension of Floquet's theory to nonlinear quasiperiodic differential equations

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Science China Mathematics 2005年第12期48卷 1670-1682页

作者： WU Hao LI Weigu School of Mathematical Sciences Peking UniversityBeijing 100871China School of Mathematical SciencesPeking UniversityBeijing 100871China

In this paper, we consider the following autonomous system of differential equations: x = Ax + f(x,θ), θ = ω, where θ∈Rm, ω = (ω1,…,ωm) ∈ Rm, x ∈ Rn, A ∈ Rn×n is a constant matrix and is hyperbolic, f is a C∞ function in both variables and 2π-periodic in each component of the vector e which satisfies f = O(||x||2) as x → 0. We study the normal form.of this system and prove that under some proper conditions this system can be transform.d to an autonomous system: x = Ax + g(x), θ = ω. Additionally, the proof of this paper naturally implies the extension of Chen's theory in the quasi-periodic case.

关键词： quasiperiodic system,normal form.

A New Model Inspired by the Pompeii Worm to Reverse Overheating in Nanosatellites

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Space(Science & Technology) 2023年第1期3卷 133-140页

作者： Ayşe MeriçYazıcı Erik Persson Department of Philosophy Lund UniversityLundSweden

Nanosatellites are exposed to extreme temperatures on the spacecraft surface,which can reach up to±100℃.In this paper,we suggest a novel solution to this challenge by the use of *** imitation of the behavior of living creatures in nature is an attempt to understand and synthesize a natural object or phenomenon in an abstract or concrete *** inspiration from living things in nature can come through the materials,processes,or designs we see around us,and there is no engineering effort *** nature,the best example of temperature reversal is the Pompeii *** Pompeii worm realizes the conversion of the excess heat it is exposed to into cooling inside a multilayered *** this work,inspired by the strategy of the Pompeii worm in reversing overheating,we present a new model for the overheating problem in nanosatellites.

关键词： form. heating extreme

On Browkin's conjecture about the elements of order five in K_2(Q)

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Science China Mathematics 2007年第1期50卷 116-120页

作者： Ke-jian XU Department of Mathematics, Qingdao University, Qingdao 266071, China Department of Mathematics Qingdao University Qingdao China

Based on the work of Lenstra, a succinct proof of Browkin’s conjecture about the elements of order five in K2(Q) is given.

关键词： K2 group cyclotomic polynomial lattice binary quartic form.

Iron fractions in the apoplast of intact root tips of Zea mays L. seedlings affected by nitrogen form

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Chinese Science Bulletin 2002年第9期47卷 727-731页

作者： H.E.Goldbach Institute of Agrichemistry Bonn University

The effects of ammonium (NH4+-N) and nitrate (NO3- - N) were examined on Fe fractions and FeCN (ferricyanide) reductase activity in intact root tips (0-3 cm) of young maize (Zea mays L. cv. Lenz) in solution culture by using short-term experiment under controlled Fe deficiency conditions (containing high HCO3- concentration in pre-culture solution). The results showed that Fe(Ⅱ) concentrations in root tip apoplast of maize were only 20-40 nmol/g FW which accounted for 7%-13% of total Fe. Most of Fe in root tips existed as Fe(Ⅲ) compounds. Imposition of the roots to NH4+ - N or NO3- - N for 60 min led to an increase of Fe(Ⅱ) in root tip apoplast. NH4+ - N led to an increased concentration of Fe(Ⅱ) and exchangeable Fe (Fe(Ⅱ) and Fe (Ⅲ)) in root tips, while NO3- - N increased FeCN reductase activity. The relationship between pH and Fe fractions, FeCN reductase activity was also discussed.

关键词： root apoplast iron fraction nitrogen form.

CONTINUED-FRACTION SOLUTION OF MATRIX EQUATION AX-XB=C

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Science China Mathematics 1989年第9期32卷 1025-1035页

作者：高维新 Peking University

The matrix equation AX-XB=C is quite well known and basic. It plays an important role in algebra and applied mathematics. This paper is an extension of the author’s previous work. Using the continued fraction associated with A and B, one obtains a standard constructive form.la of the solution X in an algebraic form. In contrast to other known results, it can simplify the numerical computation of X. When B=-A is asymptotically stable and C is a positive definite Hermitian matrix, the Hermitian form.with the coefficient matrix X for a Liapunov function can be immediately decomposed as the sum of some nonnegative definite Hermitian form. by this form.la.

关键词： matrix equation continued fraction Liapunov function Hermitian form.

THE UNIFIED form.FOR YIELD CRITERION OF METALLIC MATERIALS

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Chinese Science Bulletin 1991年第9期36卷 769-772页

作者：谭继锦 Department of Basic Courses Anhui Institute of Technology Hefei 230069 PRC

Ⅰ. INTRODUCTIONThe yield criteria are important foundations in the theory of plasticity and the strength of metallic materials. As the shear stress is the major cause for yielding, the yield criteria based on shear s... 详细信息

关键词： shear stress yield criterion unified form.

GAUSSIAN OPERATORS AND SKOROHOD INTEGRALS OF RANDOM FIELDS

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Chinese Science Bulletin 1991年第11期36卷 881-884页

作者：严绍宗张荫南 Institute of Mathematics Fudan University Shanghai 200433 PRC

During the last fifteen years, there have been many attempts to study the noncasual stochastic integrals and the related calculus, which have been made a very significant progress in stochastic analysis. Up to now, most of them are devoted to anticipating stochastic integrals with respect to Wiener process, and there is no unified theory of stochastic integrals. By Gaussian operators, we consider the Skorohod integrals with respect to random fields. These results would be used to study stochastic differential equations with ’noise fields’.

关键词： random field stochastic integral operator Gaussian measure Dirichlet form.

Independent ore deposits of dispersed elements

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Chinese Science Bulletin 1999年第S2期44卷 208-210页

作者： GAO Zhenmin, LI Chaoyang and YAO Linbo Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550002, China Institute of Geochemistry Chinese Academy of Sciences Guiyang 550002 China

EIGHT elements Ge, Ga, In, Tl, Re, Cd, Se and Te are usually referred to as dispersed elements. In the long past, there has been no report on independent ore deposits of dispersed elements at home andabroad. In recent years there have been continually discovered independent ore deposits of Ge, Tl, Cd,Se and Te in the southwestern part of China, which is a great breakthrough in the field of ore *** discovery of dispersed element independent deposits indicates that the dispersed elements are of dispersion in nature, but, on the other hand, they can also be concentrated to form.independent ore depositsunder favorable geological conditions, even to form.superlarge ore deposits under certain geological conditions. Having being restrained by traditional ideas, people have not paid sufficient attention to thestudy of independent ore deposits of dispersed elements as they have little knowledge about the geochemical behavior of dispersed elements in the processes of their mobilization, transport and enrichment.

关键词： dispersed element super-enrichment independent ore deposit existing form.

q-PSEUDOCONVEX DOMAIN IN γ-COMPLETE MANIFOLD

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Chinese Science Bulletin 1990年第5期35卷 366-370页

作者：陈志华陆志勤 Department of Applied Mathematics Shanghai Jiao Tong University Shanghai 200030 PRC

In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and *** 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)<0},

关键词： r-complete manifold q-pseudoconvex domain Levi form.