Sums of nine almost equal prime cubes

We prove that each sufficiently large odd integer N can be written as sum of the form N = p1^3 ＋p2^3 ＋... ＋p9^3 with [pj - （N/9）^1/31 ≤ N^（1/3）-θ, where pj, j = 1,2,...,9, are primes and θ = （1/51） -ε.     

Estimate for exponential sums and its applications

In this paper, we establish a new estimate on exponential sums by using the Bombieri-type theorem and the modified Huxley-Hooley contour. We also generalize the famous Goldbach-Vinogradov theorem, via different argument from that of Vinogradov. In particular, our major arcs are quite large and these enlarged major arcs are treated by the estimate we have established.     

Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

非线性光学研究水及电解质水溶液界面——空气/电解质水溶液界面特定阴阳离子效应

水及电解质溶液界面在物理、化学、环境及生物等各种过程中扮演着至关重要的角色。百年来科学家用各种实验及理论方法研究水及电解质溶液界面,试图理解其界面的结构及动力学。最近的实验和理论研究表明离子能够影响电解质水溶液界面结构,可极化性大的阴离子甚至会在界面富集。本文综述了我们研究组近年来利用二阶非线性光学方法--非共振的二次谐波与和频振动光谱研究水及电解质溶液界面的进展。首先我们研究了空气/纯水界面非共振二次谐波信号的来源,研究结果证明了空气/纯水界面非共振二次谐波信号完全可以归结为电偶极贡献,为此方法在电解质溶液界面的研究奠定了基础。同时,用偏振及对称性分析对空气/纯水界面和频振动光谱峰进行了归属,提供了纯水/空气界面结构新的物理图像。在此基础上,我们对几种电解质水溶液界面进行了深入研究,结果证明不仅可极化性大的离子会在水界面富集,并使界面层增厚,可极化性小的阴离子对界面层厚度也有影响,甚至阳离子也会在一定程度上影响界面水分子结构。     

用于红外变频的大尺寸AgGaS2晶体生长

在红外变频非线性光学应用中需要高光学质量大尺寸AgGaS2晶体元件.我们采用改进的Bridgman方法生长直径28mm、长度60～80mm的晶体棒.成功生长的关键是要采用C向籽晶.[001]籽晶生长的晶体中很少发现裂纹、聚片孪晶等宏观缺陷.在Ag2S共存下的热处理能有效地排除晶体中的异相沉淀,显著改善透明度.我们制备的Ⅰ型相位匹配8mm×10mm×16mm和5mm×5mm×15mm?AgGaS2晶体元件分别成功地应用于差频、和频激光实验.     

关于有限阿贝尔群单因子个数的均值(Ⅱ)

令ｔ（Ｇ）为有限阿贝尔群Ｇ的单因子个数．本文得到了∑｜Ｇ｜≤ｘｔ（Ｇ）带有更好余项的渐近公式．     

Sums Over States of the Atoms and Singly and Doubly Charged Ions of Rare-Earth Elements

The sums over states of the atoms and singly and doubly charged ions of rare-earth elements that are required for a theoretical study of thermochemical processes in high-temperature plasma spectral sources are calculated in the temperature range 2500–12,000 K.     

Modified constructions of binary sequences using multiplicative inverse

Two new families of finite binary sequences are constructed using multiplicative inverse. The sequences are shown to have strong pseudorandom properties by using some estimates of certain exponential sums over finite fields. The constructions can be implemented fast since multiplicative inverse over finite fields can be computed in polynomial time.     

用等离子体粒子能谱拟合温度的新方法

用最小二乘法拟合等离子体粒子能谱实验数据时，通常使拟合函数与实验能谱数据之间的误差平方和极小化。如果将能谱实验数据的对数拟合成直线以求得粒子温度，则最好对温度误差的平方和极小化。给出了这种拟合方法的计算公式，并对两种不同方法得到的结果进行了比较。