Xiquan Liang

Inverse Trigonometric Functions Arctan and Arccot

Inverse Trigonometric Functions Arctan and Arccot 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

Linear Congruence Relation and Complete Residue Systems

Linear Congruence Relation and Complete Residue Systems 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.

On Rough Subgroup of a Group

On Rough Subgroup of a Group This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group.

Basic Properties of Periodic Functions

Basic Properties of Periodic Functions In this article we present definitions, basic properties and some examples of periodic functions according to [5].

Gauss Lemma and Law of Quadratic Reciprocity

Gauss Lemma and Law of Quadratic Reciprocity 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

Partial Differentiation of Real Ternary Functions

Partial Differentiation of Real Ternary Functions In this article, we shall extend the result of [19] to discuss partial differentiation of real ternary functions (refer to [8] and [16] for partial differentiation).

Some Operations on Quaternion Numbers

Some Operations on Quaternion Numbers In this article, we give some equality and basic theorems about quaternion numbers, and some special operations.

Several Integrability Formulas of Special Functions. Part II

Several Integrability Formulas of Special Functions. Part II In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3]. MML identifier: INTEGR11, version: 7.11.01 4.117.1046

Several Higher Differentiation Formulas of Special Functions

Several Higher Differentiation Formulas of Special Functions 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

Basic Properties of Circulant Matrices and Anti-Circular Matrices

Basic Properties of Circulant Matrices and Anti-Circular Matrices This article introduces definitions of circulant matrices, line-and column-circulant matrices as well as anti-circular matrices and describes their main properties. MML identifier: MATRIX16, version: 7.9.03 4.108.1028