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Search Results: 1 - 10 of 23073 matches for " Xiquan Liang "
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Difference and Difference Quotient. Part III
Xiquan Liang, Ling Tang
Formalized Mathematics , 2010, DOI: 10.2478/v10037-010-0008-8
Abstract: In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions.
Inverse Trigonometric Functions Arctan and Arccot
Xiquan Liang, Bing Xie
Formalized Mathematics , 2008, DOI: 10.2478/v10037-008-0021-3
Abstract: This article describes definitions of inverse trigonometric functions arctan, arccot and their main properties, as well as several differentiation formulas of arctan and arccot. MML identifier: SIN COS9, version: 7.8.10 4.100.1011
Some Basic Properties of Some Special Matrices. Part III
Xiquan Liang, Tao Wang
Formalized Mathematics , 2012, DOI: 10.2478/v10037-012-0010-4
Abstract: This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.
Some Properties of p-Groups and Commutative p-Groups
Xiquan Liang, Dailu Li
Formalized Mathematics , 2011, DOI: 10.2478/v10037-011-0002-9
Abstract: This article describes some properties of p-groups and some properties of commutative p-groups.
The Quaternion Numbers
Xiquan Liang, Fuguo Ge
Formalized Mathematics , 2006, DOI: 10.2478/v10037-006-0020-1
Abstract: In this article, we define the set H of quaternion numbers as the set of all ordered sequences q = where x,y,w and z are real numbers. The addition, difference and multiplication of the quaternion numbers are also defined. We define the real and imaginary parts of q and denote this by x = (q), y = 1(q), w = 2(q), z = 3(q). We define the addition, difference, multiplication again and denote this operation by real and three imaginary parts. We define the conjugate of q denoted by q*' and the absolute value of q denoted by |q|. We also give some properties of quaternion numbers.
Integrability Formulas. Part II
Bo Li, Na Ma, Xiquan Liang
Formalized Mathematics , 2010, DOI: 10.2478/v10037-010-0016-8
Abstract: In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.
Several Integrability Formulas of Special Functions
Cuiying Peng, Fuguo Ge, Xiquan Liang
Formalized Mathematics , 2007, DOI: 10.2478/v10037-007-0023-6
Abstract: In this article, we give several integrability formulas of special and composite functions including trigonometric function, inverse trigonometric function, hyperbolic function and logarithmic function.
Several Classes of BCK-algebras and their Properties
Tao Sun, Dahai Hu, Xiquan Liang
Formalized Mathematics , 2007, DOI: 10.2478/v10037-007-0027-2
Abstract: In this article the general theory of Commutative BCK-algebras and BCI-algebras and several classes of BCK-algebras are given according to [2].
BCI-algebras with Condition (S) and their Properties
Tao Sun, Junjie Zhao, Xiquan Liang
Formalized Mathematics , 2008, DOI: 10.2478/v10037-008-0010-6
Abstract: 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
Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces
Xiquan Liang, Piqing Zhao, Ou Bai
Formalized Mathematics , 2010, DOI: 10.2478/v10037-010-0001-2
Abstract: In this article, we first extend several basic theorems of the operation of vector in 3-dimensional Euclidean spaces. Then three unit vectors: e1, e2, e3 and the definition of vector function in the same spaces are introduced. By dint of unit vector the main operation properties as well as the differentiation formulas of vector function are shown [12].
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