Search Results

You are looking at 1 - 10 of 32 items for

  • Author: Xiquan Liang x
Clear All Modify Search
Open access

Xiquan Liang and Dailu Li

Some Properties of p-Groups and Commutative p-Groups

This article describes some properties of p-groups and some properties of commutative p-groups.

Open access

Xiquan Liang and Tao Wang

Some Basic Properties of Some Special Matrices. Part III

This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.

Open access

Na Ma and Xiquan Liang

Summary

In this paper we defined the reduced residue system and proved its fundamental properties. Then we proved the basic properties of the order function. Finally, we defined the primitive root and proved its fundamental properties. Our work is based on [12], [8], and [11].

Open access

Xiquan Liang and Bing Xie

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

Open access

Xiaopeng Yue and Xiquan Liang

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

Open access

Xiquan Liang and Ling Tang

Difference and Difference Quotient. Part III

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.

Open access

Xiquan Liang and Fuguo Ge

The Quaternion Numbers

In this article, we define the set H of quaternion numbers as the set of all ordered sequences q = <x,y,w,z> 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 = ℜ(q), y = ℑ1(q), w = ℑ2(q), z = ℑ3(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.

Open access

Xiquan Liang and Dailu Li

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.

Open access

Xiquan Liang, Ling Tang and Xichun Jiang

Difference and Difference Quotient. Part IV

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.

Open access

Bo Li, Yan Zhang and Xiquan Liang

Several Differentiation Formulas of Special Functions. Part III

In this article, we give several differentiation formulas of special and composite functions including trigonometric function, inverse trigonometric function, polynomial function and logarithmic function.