http://hdl.handle.net/11320/21403 2026-11-03T18:25:34Z http://hdl.handle.net/11320/21409 Tytuł: Several Integrability Formulas of Special Functions Autorzy: Peng, Cuiying; Ge, Fuguo; Liang, Xiquan Abstrakt: In this article, we give several integrability formulas of special and composite functions including trigonometric function, inverse trigonometric function, hyperbolic function and logarithmic function. 2007-01-01T00:00:00Z http://hdl.handle.net/11320/21408 Tytuł: Linear Congruence Relation and Complete Residue Systems Autorzy: Liang, Xiquan; Yan, Li; Zhao, Junjie Abstrakt: In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundamental properties. 2007-01-01T00:00:00Z http://hdl.handle.net/11320/21407 Tytuł: Congruences and Quotient Algebras of BCI-algebras Autorzy: Ding, Yuzhong; Pang, Zhiyong Abstrakt: We have formalized the BCI-algebras closely following the book [7] pp. 16-19 and pp. 58-65. Firstly, the article focuses on the properties of the element and then the definition and properties of congruences and quotient algebras are given. Quotient algebras are the basic tools for exploring the structures of BCI-algebras. 2007-01-01T00:00:00Z http://hdl.handle.net/11320/21406 Tytuł: Arrow's Impossibility Theorem Autorzy: Wiedijk, Freek Abstrakt: A formalization of the fi rst proof from [6]. 2007-01-01T00:00:00Z