On the maximum modulus of complete trigonometric sums

LetQ _k (p) be a set consisting of all polynomials of degreek with integral coefficientsf(x)=a _k x ^k +...+a ₁ x, wherep×a _k . For givenk andp any polynomialf _k,p (x)εQ _k (p) satisfying ‖S(p, f _k,p )‖=sup ‖S(p, f)‖fεQ(p) is called a maximum modular polynomial inQ _k (p), where $$S(p,f) = \sum\limits_{x = 0}^{p - 1} {e^{2\pi if(x)/p} } $$ Moreover, we definec(k, p)=‖S(p, f _k.p (x))‖. The main results are the following theorems.

1. For k=p?1 and p≥3 we have $$c(k,p) = \sqrt {p^2 - 4(p - 1)\sin ^2 \frac{\pi }{p}} $$ Besides, we may take \(f_{k,p} (x) = \prod\limits_{r = 0}^{p - 2} {(x - r)} \)
2. For k=p?s, 2≤s≤(p+1)/2 and p≥5, we have $$c(k,p) \leqslant p - 4(s - 1)\sin ^2 \frac{\pi }{p}$$ .

In Theorems 3 and 4, an interesting connextion between the present question and the famous problem of Prouhet and Tarry is given, some conditions under which the sign of equality in Theorem 2 holds are given and a method used to construct a maximum modular polynomial inQ _k (p) is also given.     

微量元素对人体健康的影响

阐述了微量元素的生理作用以及对人体健康的影响和微量元素平衡的重要性，对临床医学及日常生活有一定的参考价值。     

All-atom molecular dynamic simulations and relative NMR spectra study of weak C-H...O contacts in amide-water systems

Amide-water mixtures are studied by all-atom molecular dynamics (MD) simulations and the relative temperature-dependent NMR experiment. The weak C-H...O contacts are found in the amide-water systems theoretically and experimentally. The statistical results of the average numbers of hydrogen bonds indicate that the methyl groups in amide molecules represent different capabilities in forming the weak C-H...O contacts. The statistics also imply that the C-H...O contacts are more obvious in the amide-rich region than those in the water-rich region. The temperature-dependent NMR spectra are also adopted to investigate the weak C-H...O contacts in the amide-water systems. The relative chemical shifts of the methyl groups are in good agreement with the MD simulations.     

制备高比表面积碳化硅的几种影响因素

采用溶胶凝胶法，以蔗糖和正硅酸乙酯(TEOS)为原料，草酸为TEOS水解的催化剂，制备均相碳化硅前驱体，在氩气氛和高温条件下(1 350～1 600 ℃)将碳化硅先驱体进行碳热还原，制备出高比表面积的SiC。考察了水/TEOS物质的量的比、碳/硅物质的量的比及镍盐等因素对碳化硅比表面积的影响。结果表明，当n_water/n_TEOS=7.5，n_C/n_Si=4时，适宜的镍催化剂(n_Ni/n_TEOS=0.005)，凝胶形成的时间最短，镍盐的加入可使碳热还原温度降低200 ℃。     

容量法测定氧化钒中的各种价态钒

用NaOH溶液处理样品，分离V（V）然后以Fe(Ⅱ）滴定测定之。定量加入过量的V（V）到上述残渣中并用H2SO4溶解，用Fe(Ⅱ）滴定，计算出V（Ⅱ），V（Ⅲ）的含量。V（Ⅳ）的测定是通过从总钒量中扣除V（Ⅱ）、V（Ⅲ）、V（Ⅴ）的含量得到。V（Ⅱ）、V（Ⅲ）和V（Ⅴ）的回收率均大于96％，其8次测定结果的相对标准偏差分别为：9．8％、0．4％、1．2％；本法快速、简便，在实际应用中效果良好。     

有机锗化合物中碳氢的快速测定

报道了用Co3O4 作覆盖氧化剂分析有机锗化合物中碳氢元素的方法。通过对 9个样品的十几次分析 ,碳、氢的相对误差分别小于± 1.30 % ,4 .4 0 %。方法简便 ,结果稳定可靠 ,可用于含锗有机化合物的碳氢分析。     

固体磷酸催化剂的活性相

研究了固体磷酸催化剂活性与其自由磷酸聚合态及磷酸硅晶型的关系，指出高活性磷酸催化剂应具备的条件，即自由磷酸中应为正磷酸和焦磷酸的混合物，结合态磷应具有“Ｃ”晶型。     

Crystal Structure of Dimethylamine 3,5-Dinitrobenzoic Acid Organic Adduct

1 INTRODUCTION Nonlinear optics (NLO) is at the forefront of cur- rent researches because of its importance in provi- ding the key functions of frequency shifting, optical modulation, optical switching, optical logic and op- tical memory for the emerging …     

JD树脂刻蚀及涂层的XPS研究

ＪＤ光学树脂表面刻蚀过程的ＸＰＳ研究表明，引进树脂遥ＣＯＨ，Ｃ＝Ｏ，Ｃ－ＳＯ３Ｈ，ＣＯＯＨ等基因随刻蚀温度的提高或时间的延长而增加，对其相对含量进行了计算，固化后的耐磨涂层具有ＳｉＯ２结构，ＪＤ板材的最佳刻蚀条件为２０℃，２０ｍｉｎ。     

C12-s-C12·2Br与低碳醇混合水溶液胶团化行为的温度效应和焓/熵补偿

季铵盐Gemini表面活性剂C12-s-C12·2Br(s=2,3,4,6)与丙醇、丁醇、戊醇、己醇混合水溶液的In(cmc)随温度升高而逐渐增大.计算所得热力学数据表明,C12-s-C12·2Br与醇混合胶团化过程服从熵驱动机理,也出现了焓/熵补偿现象.随着温度上升,熵驱动力增大,在指定温度时,醇分子烷烃链上碳原子数n增大使△Gm0值减小,胶团结构更加稳定;而增加s使值增大,胶团稳定性下降.