Some theta function identities related to the Rogers-Ramanujan continued fraction

In his first and second letters to Hardy, Ramanujan made several assertions about the Rogers-Ramanujan continued fraction . In order to prove some of these claims, G. N. Watson established two important theorems about that he found in Ramanujan's notebooks. In his lost notebook, after stating a version of the quintuple product identity, Ramanujan offers three theta function identities, two of which contain as special cases the celebrated two theorems of Ramanujan proved by Watson. Using addition formulas, the quintuple product identity, and a new general product formula for theta functions, we prove these three identities of Ramanujan from his lost notebooks.

     

The Uniformly 3-Homogeneous Subsets of PGL(2, q)

We use the character-table of PGL(2, q) to determine the subsets of that group acting uniformly 3-homogeneously on the projective line.     

粘弹塑性统一本构模型的参数评估

针对粘弹塑性统一本构模型参效众多的特点和传统评估参效方法的缺点，应用非线性最小二秉法与敏感系数分析方法相结合，提出了一个比较系统的对粘弹塑性统一本构模型的参数进行评估的方法。对铜合金在室温下不同加载速率的试验曲线进行参数适配，表明本方法的合理性与正确性。为粘弹塑性统一本构模型的工程应用奠定了基础。     

不同类型旅游移民的地方认同建构研究——以丽江古城为例

旅游移民在国内已经出现,却很少得到学者的关注.以丽江古城为例,通过修正后的量表对丽江古城的旅游移民进行实测.然后通过SPSS 20.0软件,综合运用独立样本T检验、单因素分析法对不同类型旅游移民的地方认同水平及影响因素做了分析.再将人口统计学特征、"城市融入""外出目的"依次投入模型进行阶层回归分析.研究发现:(1)不同类型旅游移民的地方认同的影响机制不同,生活方式型旅游移民对丽江的地方认同显著高于经济利益导向型旅游移民;(2)地方认同不存在"性别"差异,"居住时间"和"从事行业"显著影响生活方式型旅游移民的地方认同;(3)总体而言,"城市融入"对于旅游移民地方认同的解释力度要高于"外出目的",其中"是否与当地居民来往"仅对经济利益导向型旅游移民产生影响.研究丰富了旅游移民的人地关系研究,对于旅游地的可持续发展也具有一定的现实意义.     

Powers of Euler's Product and Related Identities

Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q) ^r satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q) ^r satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q) ^r (q ^t; q ^t) ^s , for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures.     

Higher order symmetric spaces and the roots of the identity in a Lie group

Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on .

     

LINEAR ISOMETRIC NON-ANTICIPATIVE TRANSFORMATIONS OF WIENER PROCESS

ThispaperisanoutcomeofnumerousdiscusionsandexchangeofideaswithlatePredragPerunicic,whosedeepandprofoundmathematicalknowledgeandhumanvaluesgaveusaninspirationandmotivationtofinalizeourjointideas.1.Wereferto[3,4]forthenotionofspectralmultiplicitytheoryintheseparableHilbertspace.LetHbeacyclicHilbertspacewiththeresolutionoftheidentity{p(t)}ofthemaximalspectraltypelIP(dt)ll'~dt-ordinaryLebesguemeasure.Anon-anticipativelineartransformationsisdefinedbyVolterrakernelg(t,u),uSt,ajsf'g(t)u)p(du),t>0…     

一种移动Agent的安全认证方案的设计与实现

针对移动Agent的安全问题，简要介绍了几种常用的安全认证技术，并在公钥密码体制认证方案的基础上，提出并实现了一种可用于移动Agent和Agent平台之间安全认证的方案。证书采用X.509证书格式，使用RSA和IDEA混合加密的算法，密钥管理采用PGP算法中公私钥环的方式，使该认证方案具有很高的安全性。文中详细说明了方案的实现流程，并深入分析了其安全性。结果表明，采用该方案能有效改善移动Agent的安全性。