ON THE DIOPHANTINE EQUATION X4-Dy2=1(II)

For the Diophantine equation x^4 — Dy^2 = 1 (1) where D>0 and is not a perfect square, we prove the following theorems in this paper. Theorem 1. If D\[{\not \equiv }\]7 (mod 8)，D=p1p2...ps，s≥2，where pi（i = 1，…，s) are distincyt primes，p1≡1(mod 4) such that either 2p1=a^2+b^2，а≡\[ \pm \]3(mod 8)，b三\[ \pm \]3(mod 8) or there is a j(2≤j≤s), for which Legendre symbal \[\left( {\frac{{{p_j}}}{{{p_1}}}} \right) = - 1\],and pi≡7(mod8) (i=2,..., s) or pi≡3(mod 8) (i=2,..., s), then (1) has no solutions in positive integer x,y. Theorem 2. If D=p1...ps,s≥2, where pi（i = 1，…，s) are distinct primes, and pi≡3(mod 4)（i = 1，…，s), then (1) has no solutions in positive integer x, y. Theorem 3. The equation (1) with D=2p1...ps has no solutions in positive integer x, y, if (1) p1≡(mod 4), pi≡7(mod 8) (i = 2, ???, s), snch that either 2p1 = a^2+b^2 a≡\[ \pm \]3(mod 8)，b≡\[ \pm \]3(mod 8)or there is a j (2≤j≤s)，for which \[\left( {\frac{{{p_j}}}{{{p_1}}}} \right) = - 1\]; or (2) p1≡5(mod8),pi≡3(mod8) (i = 2,..., s)； or ⑶p1≡5(mod8)，pi≡7(mod 8) (i=2，…，s). Corollary of theorem 3. If D = 2pq, p≡5(mod 8), q≡3(mod 4), where p, q are distinct primes, then (1) has no solutions in positive integer x, y. Theorem 4. If D=2p1...ps, pi≡3(mod 4)(0 = 1,...,s), then (1) has no solutions In positive integer x, y.     

一个研究型物理实验项目——周期物成像规律实验

介绍清华大学物理系如何将“Talbot效应实验”排成研究型实验,以利激发学生的求知欲,拓宽知识面,进而促进其综合能力提高的有益经验。     

硝基甲烷中爆轰波绕射的实验研究和数值模拟

叙述了对硝基甲烷中拐角分别为６０、９０、１２０三种情形的爆轰波绕射现象进行的实验研究。实验上观测到爆轰波绕过９０、１２０拐角时有未反应的死区，而且拐角增大时死区变大，绕射爆轰波可以近似地按爆心在拐角顶点附近变化的散心爆轰波看待。从数值模拟和理论分析得出，爆轰波绕射时硝基甲烷的化学反应不同于正常爆轰，拐角顶点附近各处反应速率不同，出现部分反应区和未反应区。     

A decision support methodology to enhance the competitiveness of the Turkish automotive industry

Three levels of competitiveness affect the success of business enterprises in a globally competitive environment: the competitiveness of the company, the competitiveness of the industry in which the company operates and the competitiveness of the country where the business is located. This study analyses the competitiveness of the automotive industry in association with the national competitiveness perspective using a methodology based on Bayesian Causal Networks. First, we structure the competitiveness problem of the automotive industry through a synthesis of expert knowledge in the light of the World Economic Forum’s competitiveness indicators. Second, we model the relationships among the variables identified in the problem structuring stage and analyse these relationships using a Bayesian Causal Network. Third, we develop policy suggestions under various scenarios to enhance the national competitive advantages of the automotive industry. We present an analysis of the Turkish automotive industry as a case study. It is possible to generalise the policy suggestions developed for the case of Turkish automotive industry to the automotive industries in other developing countries where country and industry competitiveness levels are similar to those of Turkey.     

玩具材料在四种人体模拟液中特定元素迁移方法探讨

选择塑料、纺织品和油漆涂层三类常见玩具材料,采用模拟胃液、酸性汗液、碱性汗液和唾液浸泡提取样品,使用ICP-AES法测试提取液中17种欧盟玩具新指令限制元素(铝、锑、砷、钡、硼、镉、铬、钴、铜、铅、锰、汞、镍、硒、锶、锡、锌)迁移量,试验了前处理过程中不同振荡频率对金属元素迁移量的影响。试验结果表明：胃液对金属元素溶出能力最大,汗液溶出能力最弱,样品提取过程中,恒温水浴振荡器振荡频率在80-160U/min范围内时,特定元素溶出量基本不受振荡频率的影响。     

Chemoenzymatic Synthesis of Spinosyn A

Following the biosynthesis of polyketide backbones by polyketide synthases (PKSs), post‐PKS modifications result in a significantly elevated level of structural complexity that renders the chemical synthesis of these natural products challenging. We report herein a total synthesis of the widely used polyketide insecticide spinosyn A by exploiting the prowess of both chemical and enzymatic methods. As more polyketide biosynthetic pathways are characterized, this chemoenzymatic approach is expected to become readily adaptable to streamlining the synthesis of other complex polyketides with more elaborate post‐PKS modifications.     

Extended Darboux function in a Weyl hypersurface

In this paper, by means of the prolonged differentiation, we introduce a pair of operators D andD ^* which enable us to extend the Darboux functions associated with a surface to the case of hypersurface in a Weyl space and discuss a few properties of these functions.     

Special networks in the hypersurfaces of generalised recurrent and birecurrent Weyl spaces

In this paper, we study some properties of the Chebyshev nets and geodesic nets in the hypersurfaces of the generalised recurrent and birecurrent Weyl spaces. Received 4. Dezember 1998.     

Determination of mercury in table salt samples by on-line medium exchange anodic stripping voltammetry

A new method for the determination of traces of total mercury by using a gold film electrode in salt samples was developed. Table salts are known to contain mercury at ultra-trace level as well as a high quantity of chloride ions that cause severe disturbance during the stripping step when gold is used as the electrode material in voltammetric measurements. The interference of high chloride content in the determination of mercury was eliminated by reducing its concentration down to 3 x 10(-3) mol L(-1) level which is optimum for the determination by using on-line medium exchange procedure immediately after the deposition step. The deposition potential applied to the electrode was maintained at 0.2 V (vs. Ag/AgCl double junction electrode) while the cell content was sucked by a pump and replaced with fresh electrolyte simultaneously. The analyte loss resulted from the air contact of the electrode was prevented by this means. The mercury ions present in the salt samples were collected at +0.2 V for 60 s, the electrolyte was replaced by 0.1 mol L(-1) HClO4 and the potential was scanned, attaining a detection limit of 0.17 microg L(-1), with R.S.D. of 1.2% (S/N=3). The recovery of the method was 94.6%. The performance and accuracy of the method was compared with that of atomic fluorescence spectrometry (AFS). Consequently, this developed method can offer a wide range of application in saline samples.