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PBVP of Integrodifferential Equations with Carathéodory Functions

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Acta Mathematica Sinica,English Series 1998年第4期14卷 463-472页

作者： Zhuang Wan chen yubo, department of mathematics, shandong normal university, jinan 250014, china department of mathematics Shandong Normal University 250014 Jinan China

We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.

关键词： Integrodifferential equations Periodic boundary value problems Carathéodory conditions Lower and upper solutions Sobolev spaces Topological degree

Study on sea water intrusion into palaeochannels on south coastal plain of the Laizhou Bay by the Bohai Sea

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Acta Oceanologica Sinica 2003年第1期22卷 69-74页

作者： Han Mei Geography department, shandong normal university, jinan 250014, china shandong normal Univ Dept Geog Jinan 250014 Peoples R China

The palaeochannel evolution in the study region is divided into four stages by such methods as 14C dating. Sea water intrusion through palaeochannels has been studied as a focal point. Palaeochannels are the main passageways through which the sea water intrudes at a higher speed, through many means and in a changeable dynamic state.

关键词： Palaeochannel sea water intrusion south coastal plain of Laizhou Bay

A note on a result of Abercrombie

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Chinese Science Bulletin 1997年第14期42卷 1151-1154页

作者： ZHAI Wenguangdepartment of mathematics, shandong normal university, jinan 250014, china department of mathematics Shandong Normal University Jinan 250014 China

SUPPOSE θ∈[1,+ ∞) is any real number. The sequence B_θ={[nθ]|n∈N}is calledBeatty’s sequence determined by θ. Beatty sequences have been the subject of intensive inves-tigation in recent years on account of the... 详细信息

关键词： Bealty’s sequence divisor problem rational approximation.

The Existence of Periodic Orbits for Nonlinear Impulsive Differential Systems

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 50-53页

作者： Xilin FU Jiangang QI and Yansheng LIU (department of mathematics, shandong normal university, jinan 250014, china) department of mathematics Shandong Normal University Jinan 250014 China

In this paper, we gave the necessary and sufficient condition for the existence of the periodic solutions of nonlinear impulsive differential systems by using a special function and study the stable properties of suc... 详细信息

关键词： impulsive differential equation periodic orbit stable

Reciprocal sums of a class of additive functions in short intervals

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Chinese Science Bulletin 1997年第2期42卷 102-105页

作者： ZHAI Wenguangdepartment of mathematics, shandong normal university, jinan 250014, china department of mathematics Shandong Normal University Jinan China

USING the method of probabilistic number-theory, De Koninck, and De Koninck and Galambos studied the reciprocal sum of the additive function f（n） satisfying f（n）≥t0>0 （n≥2） and f（p）≡1 and obtained an asymptotic formula, where t0 is an absolute positive constant. Let B（x） denote the number of n≤x not satisfying the inequality loglogn-R（x）≤f（n）≤loglogn+R（x）, （1） where R（x） is a function tending to infinity. Then in refs. [1, 2], it is proved that if R（x）=o（loglogx） and B（x）=o（x/loglogx）,

关键词： additive functions Riemann zeta-function asymptotic formula.

On the Average Number of Unitary Factors of Finite Abelian Groups (Ⅱ)

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Acta Mathematica Sinica,English Series 2000年第4期16卷 549-554页

作者： Wenguang Zhai department of mathematics, shandong normal university. jinan 250014. P. B. china department of mathematics Shandong Normal University Jinan 250014 P. R. China

Let t（G） be the number of unitary factors of finite abelian group G. In this paper we prove T（x）=∑(G≤（）t（G） =main terms+O(x(（1+2k）/（3+4k）for any exponent pair （k, 1/2+2K）. which improves on the exponen... 详细信息

关键词： Unitary factor Finite Abelian group Exponential sum Divisor problem

A Hybrid of Theorems of Goldbach and Piatetski-Shapiro

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Chinese Annals of mathematics,Series B 2006年第3期27卷 341-352页

作者： Xianmeng MENG Mingqiang WANG School of Computer Science and Technology, shandong university, jinan 250100, china department of Statistics and mathematics, shandong Finance Institute, jinan 250014, china. School of Computer Science and Technology, shandong university, jinan 250100, china department of mathematics, Qufu normal university, Qufu 273165, shandong, china. School of Computer Science and Technology Shandong University Jinan 250100 China department of Statistics and mathematics Shandong Finance Institute Jinan 250014 China department of mathematics Qufu Normal University Qufu 273165 Shandong China

It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p1 ＋ p2, p1 ∈ Pγ is solvable, with 13/15 〈γ≤ 1, where Pγ = {p ｜p = [m^1/γ], for integer m and prime p} is t... 详细信息

关键词： Circle method Sieve method Goldbach problem

Existence and uniqueness for BSDE with stopping time

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Chinese Science Bulletin 1998年第2期43卷 96-99页

作者： chen Zengjing department of mathematics, shandong university, jinan 250100, china department of mathematics Shandong University Jinan China

The existence and uniqueness of the solutions for a class of backward stochastic differential equations (BSDEs for short) in a random interval are discussed.

关键词： BSDE stopping time adapted solution.

Extraction of Surface Roughness from the Central δ-peak of Light Scattering Using a Multi-wavelength Ar~+ Laser

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Chinese Journal of Lasers 2000年第3期9卷 22-27页

作者： LIU Deli QI Dongping chenG Chuanfu (department of Physics, shandong normal university, jinan 250014, china) 山东师范大学山东济南

In this paper, a new light scattering method for measuring t he roughness of random surfaces is proposed. The method is based on the relation between the specularly reflected intensity I s, i.e., the central δ-peak intensity and wave vector component k z. The linear fit of the logarithm graph of the normalized central δ-peak intensity I sr versus k-2 z, whose variation is induced by changing illuminating wavelength, gives the square of the surface roughness w. The roughnesses of 6 silicon backside samples were measured.

关键词： random surface roughness light scattering multi-wavelength