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3 Formalized Mathematics

3 2008

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BCI-algebras with Condition (S) and their Properties

100%

Sun T. , Zhao J. , Liang X.

tom 16

nr 1

65-71

In this article we will first investigate the elementary properties of BCI-algebras with condition (S), see [8]. And then we will discuss the three classes of algebras: commutative, positive-implicative and implicative BCK-algebras with condition (S).MML identifier: BCIALG 4, version: 7.8.09 4.97.1001

Gauss Lemma and Law of Quadratic Reciprocity

100%

Yan L. , Liang X. , Zhao J.

tom 16

nr 1

23-28

In this paper, we defined the quadratic residue and proved its fundamental properties on the base of some useful theorems. Then we defined the Legendre symbol and proved its useful theorems [14], [12]. Finally, Gauss Lemma and Law of Quadratic Reciprocity are proven.MML identifier: INT 5, version: 7.8.05 4.89.993

Several Higher Differentiation Formulas of Special Functions

100%

Zhao J. , Liang X. , Yan L.

tom 16

nr 2

141-145

In this paper, we proved some basic properties of higher differentiation, and higher differentiation formulas of special functions [4].MML identifier: HFDIFF 1, version: 7.8.10 4.100.1011