1995年中国数学奥林匹克

１９９５年中国数学奥林匹克葛军，浦敏亚（南京师范大学数学系２１００９７）１９９５年中国数学奥林匹克（第十届中学生数学冬令营）于一月份在合肥中国科学技术大学举行，下面是试题与我们所拟的解答．第一天（月１０日８：００－１２：３０）１设２ｎ个实数ａ１，ａ２...     

问题征解

问题征解本栏目特邀主持人陈计葛军有关不等式与组合几何的稿件邮送陈计老师（３１５２１１，宁波大学应用数学系），其它稿件邮送葛军老师（２１００２４，南京师范大学数学系）．问题１６８．河南吴伟朝提供给定正整数ｎ≥３和集合Ｚｎ＝｛０，１，２，３，…，ｎ－１｝...     

Fokker-Planck方程与Vlasov方程在模耦合理论研究中的比较

模耦合理论比较成功地解释了微波不稳定性的发生,其理论基础是Vlasov方程.Fokker-Planck方程包含了束团的辐射阻尼效应和量子激发效应,是比较完备地描述粒子运动状态的束团分布方程.比较了Fokker-Planck方程和Vlasov方程在来源、意义和解法方面的关联和不同,同时介绍了一种多项式展开束团耦合模式来求解Fokker-Planck方程的方法,并在静态分布中包含了势阱畸变的效应.     

问题征解

问题征解陈计，葛军（本栏目特约主持人）有关不等式与组合几何极值方面的稿件邮送陈计老师（３ｕ５２１１，宁波大学教学系），其它方面的稿件邮送葛军老师（２１００２４，南京师范大学数学系）．题号右上角的星号（＊）表示问题提出时尚无解答。１问题１４４＊．湖南匡...     

戊二醛交联前后明胶微球热转变研究

在空气和氮气气氛中,对未交联的明胶微球(GMs)和戊二醛交联明胶微球(CGMs)进行了受热转变研究,并利用250℃热处理的明胶球制备出具有多孔内核的明胶基结构.经过热重分析(TGA)、差示扫描量热法(DSC)、扫描电子显微镜(SEM)和付里叶变换红外光谱(FTIR)等分析测试表明:戊二醛交联明胶微球300℃后热失重略大于未交联明胶微球,两者的熔化温度Tm都为228℃;在空气中250℃热处理7 h的未交联明胶微球经过稀硫酸处理后可以得到多孔内核结构,多孔内核含碳、氧元素,外壳以碳元素为主;105℃和190℃热处理的明胶球化学成分基本相同,250℃热处理使明胶分子中的酰胺键减少、并发生三级结构的转变.     

明胶基多孔碳球电极材料的制备及电化学性能研究

Gelatin-based porous carbon beads have been fabricated from gelatin micro-spheres by means of solidification, carbonization and chemical activation with KOH. The physical properties of gelatin-based porous carbon beads were studied by a t-plot method based on N₂ adsorption isotherms. The gelatin-based porous carbon beads activated at 800 ℃ exhibited the largest specific surface area and resulted in the highest capacitance. Carbon/carbon super-capacitors cells assembled with the electrode materials in 1.0 mol·L^-1 NEt₄BF₄ / acetonitrile electrolyte have also been studied. The electrochemical properties of gelatin-based porous carbon beads electrode were studied by using constant-current discharge tests. The results indicate that the gelatin-based porous carbon beads electrode is with good cycling stability and specific capacitance of 119.8 F·g^-1.     

问题征解

有关不等式与组合几何的稿件邮送陈计（３１５２１１,宁波大学数学系;或ｃｈｅｎｄｉ○ａｎｂｕ．ｅｄｕ．ｃｎ）,平面几何与数学游戏的稿件邮送叶中豪（２０００３１,上海教育出版社数学编辑室）,其它稿件邮送葛军（２１００９７,南京师范大学数学系）．题号右上角...     

Superconductivity and Fermi Surface Anisotropy in Transition Metal Dichalcogenide NbTe_2

Transition metal dichalcogenides, featuring layered structures, have aroused enormous interest as a platform for novel physical phenomena and a wide range of potential applications. Among them, special interest has been placed upon WTe_2 and MoTe_2, which exhibit non-trivial topology both in single layer and bulk as well as pressure induced or enhanced superconductivity. We study another distorted IT material NbTe_2 through systematic electrical transport measurements. Intrinsic superconductivity with onset transition temperature(T_c~(onset)) up to 0.72 K is detected where the upper critical field(H_c) shows unconventional quasi-linear behavior,indicating spin-orbit coupling induced p-wave paring. Furthermore, a general model is proposed to fit the angledependent magnetoresistance, which reveals the Fermi surface anisotropy of NbTe_2. Finally, non-saturating linear magnetoresistance up to 50 T is observed and attributed to the quantum limit transport.     

Gd掺杂ErNi2B2C体系的超导和磁特性研究

本文研究了Gd掺杂对Er1-xGdxNi2B2C体系超导和磁转变行为的影响.随着稀土元素Gd逐步替代Er,体系的超导电性被强烈抑制,反铁磁转变温度逐渐升高.本文就Gd掺杂对体系超导和磁性的影响机制进行了讨论,并基于DG因子模型,对实验结果进行了分析.     

问题征解

有关不等式与组合几何的稿件邮送陈计（３１５２１１,宁波大学数学系;或ｃｈｅｎｄｉ＠ｎｂｕ．ｅｄｕ．ｃｎ）,平面几何与数学游戏的稿件邮送叶中豪（２０００３１,上海教育出版社数学编辑室）,其它稿件邮送葛军（２１００９７,南京师范大学数学系）．问　题２００．上海田廷彦提供有ｎ（≥４）个人,每个人有一条消息．为让每人均知道所有消息,他们开始互通电话．每次打电话时,双方都把自己知道的所有消息告诉对方．这样,他们至少打２ｎ－４次电话．（责任编辑　叶中豪）解　答１７９．［１９９８,１］天津郭军伟与上海田廷彦…