On the representation of large integers as sums of four almost equal squares of primes

In this paper, we are able to establish two localized results on the conjecture that each large integer congruent to 4 modulo 24 can be written as the sum of four squares of primes. The proof is based on the new estimates for exponential sums over primes in short intervals and a technique to get the asymptotic formula on the enlarged major arcs in the circle method. This work is supported by the National Natural Science Foundation of China (Grant Nos. 10701048 and 10771127).     

On the mean square of the error term for the asymmetric two-dimensional divisor problems(II)

Let Δ(a, b; x) denote the error term of the asymmetric two-dimensional divisor problem. In this paper we shall study the relation between the discrete mean value ?_{n ￡ T} D²(a,b;n){\sum_{n\leq T} \Delta^2(a,b;n)} and the continuous mean value ò₁^TD²(a,b;x)dx{\int_1^T\Delta^2(a,b;x)dx} .     

Short Interval Results for a Class of Integers

For any subset , we introduce the definition of -numbers, which contains the well-known k-free numbers, k-full numbers, k-full and l-free numbers (k<l–1) as special cases. In this paper we study the distribution of -numbers in short intervals. We establish the connection of this problem with the gap problem of k-free numbers and multi-dimensional divisor problems. As applications, we study the short interval distribution of k-full and l-free numbers for k=2, 3, 4, 5, 6, 7.Received June 4, 2002; in revised form January 22, 2003 Published online June 30, 2003     

氯化聚氯乙烯热稳定性研究 Ⅰ.氯含量对热稳定性影响

本文用红外光谱分析了聚氯乙烯(PVC)和氯化聚氯乙烯(CPVC)的分子结构,用电导法评价了它们的热稳定性. 试料 PVC系天津化工厂生产,XS-7型;CPVC系前者的氯化产品,由安徽化工研究所提供,含氯量64％,日本产CPVC,牌号H827,含氯量68.5％.     

A composite of polyaniline with both conducting and ferromagnetic functions

A composite of polyaniline (PANI) with both conducting and ferromagnetic functions was synthesized by a chemical method proposed by the authors. For the electrical properties, its room-temperature conductivity was measured to be about 10⁻¹ S/cm when doped with 1.0M HCl, and it is independent of the preparation conditions, such as reaction temperature and concentration of FeSO₄ solution. Temperature dependence of the conductivity of the composites at temperature between 77 and 450 K is controlled by thermal activation and dedoping processes, which result in the decrease of conductivity with increase of temperature as T > 320 K. For their magnetic properties, unusual ferromagnetic properties with high saturated magnetization (M₂) and lower coercive force (H_c = 0) were observed. An effect of the preparation conditions on the ferromagnetic properties of composites was observed. The higher the reaction temperature and the concentration of FeSO₄ solution, the higher the saturated magnetization was observed. No hysteresis feature (i.e. H_c = 0) for any PANI composites synthesized in this paper was observed, and this is independent of the preparation conditions. This may be attributed to the nanometer size of the magnetic particles existing in composites. Thus, it suggests that the doping of PANI leads to electrical properties of composites, whereas the nanocrystalline magnetic particles (Fe₃O₄) are responsible for the observed ferromagnetic properties of PANI composites. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2129–2136, 1997     

Advances in properties and biodegradability of co-continuous,immicisible, biodegradable,polymer blends

A series of blends consisting of polylactic acid (PLA) and aliphatic succinate polyester (Bionolle#3000) have been prepared. The results of the mechanical property investigation have shown that using more than 20 wt % Bionolle#3000 can significantly increase the toughness of the PLA, increase the elongation at break (more than 200%) and increase the impact strength (more than 70 J/m). These properties were not significantly affected by the aging behavior of PLA for more than two months. DMA results show that Bio#3000 reduces the elastic modulus of the blends between −15°C and 60°C. Soil degradation rates of the PLA/Bio#3000 blends also increase with increasing Bio#3000 content. However, for the blends with less than 30 wt % of Bio#3000, the degradation rates do not significantly increase. Enzymatic degradation rates of the blends are higher than for those of the two polymers, and these rates increase with increasing PLA content. Composting biodegradation rates increase with increasing Bio#3000 content.     

原子连接次序的一些经验规则

在有关物质分子结构的教学中 ,经常有学生问起一些类似这样的问题 :(1)次磷酸Ｈ3ＰＯ3与ＰＦ3是等电子体 ,Ｈ3ＰＯ3为什么具有 ＰＯＨＯ ＯＨＨ的四面体结构而不与ＰＦ3相似呈 Ｐ··ＨＯ ＯＨＯＨ的三角锥结构(2种结构式中的Ｐ都为 + 3氧化态 ,都是ｓｐ3杂化 ) ;(2 )Ｎ2 Ｏ为什么具有线性的··Ｎ—Ｎ—Ｏ·　·　···　··　···结构 (方框表示π4 3键 ) ,但具有同样线性和键级的结构··Ｎ—Ｏ—Ｎ·　··　··　··　···却不存在 (2种结构式中中心原子的Ｎ、Ｏ均为ｓｐ杂化 ) ;(3)ＣＯ与ＨＣＮ也相当于等电子体 ,ＣＯ的结构…     

表面粗糙度特征对齿轮接触区润滑特性的影响

大部分工程实际粗糙表面符合非高斯分布,并对齿轮接触副润滑特性有重要影响.将渐开线齿轮啮合过程中齿面接触等效为三维无限长线接触,建立了一个可分析直齿轮和斜齿轮的混合弹流润滑计算模型;采用基于快速傅里叶变换的数值仿真方法生成给定参数的非高斯粗糙表面;运用该模型对直齿轮和斜齿轮啮合过程进行分析,求得不同表面粗糙度特征齿轮在各个啮合点的油膜厚度、接触区载荷以及接触区比例的情况.结果表明:对于标准差相等的非高斯粗糙表面,偏度值对齿轮润滑状况的影响与工况紧密相关,在润滑良好的条件下,偏度值越小润滑状况越优;润滑恶劣的条件下,偏度值越大润滑状况越优;而在各种工况下,峰度值对齿轮润滑状况的影响都表现出峰度值越大润滑状况越优的特点.     

Adatom ascending at step edges and faceting on fcc metal (110) surfaces

Using first-principles total-energy calculations, we show that an adatom can easily climb up at monatomic-layer-high steps on several representative fcc metal (110) surfaces via a place exchange mechanism. Inclusion of such novel adatom ascending processes in kinetic Monte Carlo simulations of Al(110) homoepitaxy as a prototypical model system can lead to the existence of an intriguing faceting instability, whose dynamical evolution and kinetic nature are explored in comparison with experimental observations.     

On Sums of Two Coprime k-th Powers

For fixed k3, let It is known that the asymptotic formula holds for some constant c_k. Let E_k(x)=R_k(x)–c_kx^2/k. We cannot improve the exponent 1/k at present if we do not have further knowledge about the distribution of the zeros of the Riemann Zeta function (s). In this paper, we shall prove that if the Riemann Hypothesis (RH) is true, then E_k(x)=O(x^4/15+), which improves the earlier exponent 5/18 due to Nowak. A mean square estimate of E_k(x) for k6 is also obtained, which implies that E_k(x)=(x^1/k–1/k2) for k6 under RH.