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.     

Mössbauer study on surface magnetic properties in magnetic fluids

The presence of m=0 lines of the Mössbauer spectra of small Fe₃O₄ particles coated with an organic surfactant in an applied field of 7 T at 5 K shows a non-collinear magnetic structure in the surface layer of these particles. From the temperature dependence of the hyperfine field, the anisotropy constantK was calculated.Projects supported by the Science Fund of the Chinese Academy of SciencesNow working at the Shanghai Institute of Education     

液晶的激光拉曼光谱研究——Ⅰ.十九种液晶的固相激光拉曼光谱

本文报道联苯、联苯酯、单酯、双酯、Schiff碱和氧化偶氮苯型十九种液晶化合物的固相激光拉曼光谱,讨论了2300～400 cm~(-1)范围内基团的特征谱带归属以及光谱与结构之间的关系.     

A new C21-steroidal glycoside from Cynanchum stauntonii

A new C21-steroidal glycoside with two known compounds were isolated from the root of Cynanchum Stauntonii.Based on thespectral analysis,including MS,1H NMR,13C NMR,DEPT,1H-1H COSY,13C-1H COSY,HMQC and HMBC,their chemicalstructures were determinated as glaucogenin-C 3-O-a-L-cymaropyranosyl-(1→4)-b-D-digitoxopyranosyl-(1→4)-β-D-canaropyranoside(1),stigmasterol(2)and ursolic acid(3).     

耐尔蓝分光光度法间接测定铵

以耐尔蓝为显色剂，采用分光光度法进行铵的测定。选择了ＮａＯＨ碱解蒸馏分离氨的条件，探讨了表面活性剂ＯＰ，ＳＤＳ增敏增溶作用，分别测定了雨水，土壤，绿叶中铵含量，结果满意。     

流动注射分析中样品分散与反应管长度的关系

根据串联釜模型给出样品分散度与通过管长的关系式，应用此式可以满意地解释分散度随管长的变化。     

A new method for determination of uric acid by the lactic acid-acetone-BrO(3)(-)-Mn(2+)-H(2)SO(4) oscillating reaction using the analyte pulse perturbation technique

A new analytical method for the determination of uric acid (UA) by the perturbation of UA on the Belousov-Zhabotinsky oscillating reaction is proposed. The method is based on the linear relationship between the changes in the oscillating period and the concentration of UA. The calibration curve is linear over the range of 2.0 × 10⁻⁵ to 5.0 × 10⁻⁴ M, with a detecting limit of 3.28 × 10⁻⁶ M. The method features good precision (R.S.D.: 3.59%) and excellent throughput (10 samples h⁻¹). The possible mechanism of the perturbation of UA on the oscillating reaction is discussed.     

含氰基侧基聚芳醚砜的合成与表征

汉２，６－二卤苯甲腈、４，４′－二氯二苯砜、４，４′－二羟基二苯砜、间苯二酚、对苯二酚、酚酞及双酚Ａ为主要原料，合成了含不同结构单元和不同氰基含量的含氰基侧基的聚芳醚砜，并采用ＩＲ、＾１３ＣＮＭＲ等分析手段对其结构进行了表征，同时研究了结构单元和氰基含量对聚芳醚砜性能的影响。     

A Kinetic Evidence for the Nitroxyl Radicals Recycling Mechanism in the Photostabilizing Process of HALS

The photoinduced bulk polymerization of a reactive-hindered amine fight stabilizers(r-HALS), 4-acryloyl-2, 2, 6, 6-tetramethylpiperidinyl (ATMP), was performed at 80℃ by using a DPC technique. An unique periodic exponential attenuation-type oscillating curve was found when the polymerization was carried out in air, but this phenomenon was not found in nitrogen.It is supposed that this unique kinetic performance may be attributed to nitroxyl radicals that are produced in situ from the oxidation of ATMP. ATMP polymer with narrow polydispersity (d =1.03) can be obtained by photoinduced solution polymerization of ATMP. The signal detected in ESR may be assigned to the nitroxyl radicals in the matrix of ATMP polymer. Since this kind of recycling of nitroxyl radicals is well documented for the photostabilizing mechanism of HALS, the present results may serve as a kinetic evidence for this mechanism.