In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.
In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.
New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion functio...New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.展开更多
OBE(Outcome Based Education,成果导向教育)理念是工程教育认证的核心思想,已得到工程教育界的广泛认可与推广。其中,毕业要求指标体系与课程体系的对应关系是该理念落实的关键环节。但目前的构建思路是基于课程层面的,忽视课程体系的...OBE(Outcome Based Education,成果导向教育)理念是工程教育认证的核心思想,已得到工程教育界的广泛认可与推广。其中,毕业要求指标体系与课程体系的对应关系是该理念落实的关键环节。但目前的构建思路是基于课程层面的,忽视课程体系的功能模块结构(或课程群)特点,与指标体系对应课程选择存在较大的随机性、主观性问题。该文以广州大学环境工程专业为例,从尊重课程体系的功能模块化结构特点出发,探讨毕业要求指标体系与课程群的对应关系,具有逻辑结构清晰与操作简便、高效的优点。展开更多
文摘In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.
基金Supported by the National Natural Science Foundation of China（11071107, 11371184）
文摘In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
基金supported by the Natural Science Foundation of China(11071069 and 11171307)the Natural Science Foundation of the Department of Education of Zhejiang Province(Y201328799)
文摘The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.
基金Supported by National 973 Project of China(2006CB708304)National Natural Science Foundation of China(10771195)
文摘New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.
文摘OBE(Outcome Based Education,成果导向教育)理念是工程教育认证的核心思想,已得到工程教育界的广泛认可与推广。其中,毕业要求指标体系与课程体系的对应关系是该理念落实的关键环节。但目前的构建思路是基于课程层面的,忽视课程体系的功能模块结构(或课程群)特点,与指标体系对应课程选择存在较大的随机性、主观性问题。该文以广州大学环境工程专业为例,从尊重课程体系的功能模块化结构特点出发,探讨毕业要求指标体系与课程群的对应关系,具有逻辑结构清晰与操作简便、高效的优点。
