Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 32

Liczba wyników na stronie
first rewind previous Strona / 2 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 2 next fast forward last
1
Content available remote

Difference and Difference Quotient. Part III

100%
Liang X., Tang L.
Formalized Mathematics
|
2010
|
tom 18
|
nr 1
57-64
EN
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.
2
Content available remote

Basic Properties of Circulant Matrices and Anti-Circular Matrices

100%
Yue X., Liang X.
Formalized Mathematics
|
2008
|
tom 16
|
nr 4
355-360
EN
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
3
Content available remote

Some Basic Properties of Some Special Matrices. Part III

100%
Liang X., Wang T.
Formalized Mathematics
|
2012
|
tom 20
|
nr 1
73-77
EN
This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.
4
Content available remote

On Rough Subgroup of a Group

100%
Liang X., Li D.
Formalized Mathematics
|
2009
|
tom 17
|
nr 3
213-217
EN
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.
5
Content available remote

Basic Properties of Primitive Root and Order Function

100%
Ma N., Liang X.
Formalized Mathematics
|
2012
|
tom 20
|
nr 4
265-269
EN
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].
6
Content available remote

The Quaternion Numbers

100%
Liang X., Ge F.
Formalized Mathematics
|
2006
|
tom 14
|
nr 4
161-169
EN
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 = 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.
7
Content available remote

Some Properties ofp-Groups and Commutativep-Groups

100%
Liang X., Li D.
Formalized Mathematics
|
2011
|
tom 19
|
nr 1
11-15
EN
This article describes some properties of p-groups and some properties of commutative p-groups.
8
Content available remote

Inverse Trigonometric Functions Arctan and Arccot

100%
Liang X., Xie B.
Formalized Mathematics
|
2008
|
tom 16
|
nr 2
147-158
EN
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
9
Content available remote

Linear Congruence Relation and Complete Residue Systems

81%
Liang X., Yan L., Zhao J.
Formalized Mathematics
|
2007
|
tom 15
|
nr 4
181-187
EN
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.
10
Content available remote

Several Integrability Formulas of Special Functions

81%
Peng C., Ge F., Liang X.
Formalized Mathematics
|
2007
|
tom 15
|
nr 4
189-198
EN
In this article, we give several integrability formulas of special and composite functions including trigonometric function, inverse trigonometric function, hyperbolic function and logarithmic function.
11
Content available remote

Some Operations on Quaternion Numbers

81%
Li B., Liang X., Wang P., Zhuang Y.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
61-65
EN
In this article, we give some equality and basic theorems about quaternion numbers, and some special operations.
12
Content available remote

Second-Order Partial Differentiation of Real Binary Functions

81%
Xie B., Liang X., Shen X.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
79-87
EN
In this article we define second-order partial differentiation of real binary functions and discuss the relation of second-order partial derivatives and partial derivatives defined in [17].
13
Content available remote

General Theory of Quasi-Commutative BCI-algebras

81%
Sun T., Pan W., Wu C., Liang X.
Formalized Mathematics
|
2008
|
tom 16
|
nr 3
253-258
EN
It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.
14
Content available remote

Nilpotent Groups

81%
Li D., Liang X., Men Y.
Formalized Mathematics
|
2010
|
tom 18
|
nr 1
53-56
EN
This article describes the concept of the nilpotent group and some properties of the nilpotent groups.
15
Content available remote

Several Integrability Formulas of Special Functions. Part II

81%
Li B., Zhuang Y., Men Y., Liang X.
Formalized Mathematics
|
2009
|
tom 17
|
nr 1
23-35
EN
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
16
Content available remote

Partial Differentiation of Real Ternary Functions

81%
Inoué T., Xie B., Liang X.
Formalized Mathematics
|
2010
|
tom 18
|
nr 1
39-46
EN
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).
17
Content available remote

Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces

81%
Liang X., Zhao P., Bai O.
Formalized Mathematics
|
2010
|
tom 18
|
nr 1
1-10
EN
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].
18
Content available remote

Several Classes of BCK-algebras and their Properties

81%
Sun T., Hu D., Liang X.
Formalized Mathematics
|
2007
|
tom 15
|
nr 4
237-242
EN
In this article the general theory of Commutative BCK-algebras and BCI-algebras and several classes of BCK-algebras are given according to [2].
19
Content available remote

Several Differentiation Formulas of Special Functions. Part III

81%
Li B., Zhang Y., Liang X.
Formalized Mathematics
|
2006
|
tom 14
|
nr 1
37-45
EN
In this article, we give several differentiation formulas of special and composite functions including trigonometric function, inverse trigonometric function, polynomial function and logarithmic function.
20
Content available remote

Some Properties of Some Special Matrices. Part II

81%
Yue X., Hu D., Liang X.
Formalized Mathematics
|
2006
|
tom 14
|
nr 1
7-12
EN
This article provides definitions of idempotent, nilpotent, involutory, self-reversible, similar, and congruent matrices, the trace of a matrix and their main properties.
first rewind previous Strona / 2 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.