He was not good at algebra in middle school.

他中学时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从学校毕业四年, 重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

他同学们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最利用外积性质构造了个3 维loop代数 ,由此可设计出许多新等谱问题，作为应用，本文得到了个类似多分量Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚至三角学。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任有界域拓扑边界上连续函数代数K_1-群与其边界上上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法中导数代换对基本方程进行了简化处理,将基本微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复数代数引入矢量水听器信号处理领域，用超复数来整体表示了矢量水听器输出4个信号分量，并建立了矢量水听器阵列超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数半格定义与作为偏序集半格定义是等价。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术发展要求,以及代数拓扑学复形等概念引入到几何造型中,因此产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群性质得出了李群两个李子群交依然是李子群结论,进而得出这李子群李代数形式。

He was not good at algebra in middle school.

他中学时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从学校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

他同学们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外积性质构造了一个3 维loop代数 ,由此可设计出许新等谱问题，作为应用，本文得到了一个类分量Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚学。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任意有界域拓扑边界上连续函数代数K_1-群与其边界上上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法中一阶导数代换对基本方程进行了简化处理,将基本微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复数代数引入矢量水听器信号处理领域，用超复数来整体表示了矢量水听器输出4个信号分量，并建立了矢量水听器阵列超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数半格定义与作为偏序集半格定义是等价。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术发展要求,以及代数拓扑学复形等概念引入到几何造型中,因此产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群性质得出了李群两个李子群交依然是李子群结论,进而得出这一李子群李代数形式。

He was not good at algebra in middle school.

他中学时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从学校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

他同学们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外积性质构造了一个3 维loop代数 ,由此可设计出许新等谱问题，作为应用，本文得到了一个类分量Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚学。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任意有界域拓扑边界上连续函数代数K_1-群与其边界上上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法中一阶导数代换对基本方程进行了简化处理,将基本微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复数代数引入矢量水听器信号处理领域，用超复数来整体表示了矢量水听器输出4个信号分量，并建立了矢量水听器阵列超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数半格定义与作为偏序集半格定义是等价。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术发展要求,以及代数拓扑学复形等概念引入到几何造型中,因此产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群性质得出了李群两个李子群交依然是李子群结论,进而得出这一李子群李代数形式。

He was not good at algebra in middle school.

他中学时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从学校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

他的同学们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外的性质构造了一个3 维的loop代数 ,由此可设计出许多新的等谱问题，作为应用，本文得到了一个类似的多量的Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚至三角学。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性析法中的一阶导数代换对基本程进行了简化处理,将基本的微程转化为非线性代数程组,并结合双参数摄动研究了悬臂梁的大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复数代数引入矢量水听器信号处理领域，用超复数来整体表示了矢量水听器输出的4个信号量，并建立了矢量水听器阵列的超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术的发展要求,以及代数拓扑学复形等概念引入到几何造型中,因此产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。

He was not good at algebra in middle school.

他中学时不擅长代。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从学校毕业四年后, 决意重温代。

In algebra, the sign X usually denotes an unknown quantity.

在代里, 符号X常用来表示未知。

His classmates were labouring with elementary algebra.

他的同学们正在绞尽脑汁地演算初等代题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外积的性质构造了一个3 维的loop代 ,可设计出许多新的等谱问题，作为应用，本文得到了一个类似的多分量的Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代和几何，甚至三角学。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系矩阵和极大项，证明了这类李代是半单李代有二维交换子代。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任意有界域的拓扑边界上连续函代的K_1-群与其边界上的上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法中的一阶导代换对基本方程进行了简化处理,将基本的微分积分方程转化为非线性代方程组,并结合双参摄动研究了悬臂梁的大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复代引入矢量水听器信号处理领域，用超复来整体表示了矢量水听器输出的4个信号分量，并建立了矢量水听器阵列的超复模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代的半格的定义与作为偏序集的半格的定义是等价的。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术的发展要求,以及代拓扑学复形等概念引入到几何造型中,因产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代形式。

He was not good at algebra in middle school.

时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

的同们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外积的性质构造了一个3 维的loop代数 ,由此可设计出许多新的等谱问题，作为应用，本文得到了一个类似的多分量的Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚至三角。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法的一阶导数代换对本方程进行了简化处,本的微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁的大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要超复数代数引入矢量水听器信号处领域，用超复数来整体表示了矢量水听器输出的4个信号分量，并建立了矢量水听器阵列的超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术的发展要求,以及代数拓扑复形等概念引入到几何造型,因此产生了非流形几何造型论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。

He was not good at algebra in middle school.

他中时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

他的同们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后用外积的性质构造了一3 维的loop代数 ,由此可设计出许多新的等谱问题，作为应用，本文得到了一的多分量的Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚至三。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

用系数矩阵和极大项，证明了这李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

用拟线性分析方法中的一阶导数代换对基本方程进行了简化处理,将基本的微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁的大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复数代数引入矢量水听器信号处理领域，用超复数来整体表示了矢量水听器输出的4信号分量，并建立了矢量水听器阵列的超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术的发展要求,以及代数拓扑复形等概念引入到几何造型中,因此产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群的性质得出了李群的两李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。

He was not good at algebra in middle school.

他中学时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从学校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用未知数。

His classmates were labouring with elementary algebra.

他的学们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外积的性质构造了一个3 维的loop代数 ,由此可设计出许多新的等谱问题，作为应用，本文得到了一个类似的多分量的Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚至三角学。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C中，任意有界域的拓扑边界上连续函数代数的K_1-与其边界上的上构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法中的一阶导数代换对基本方程进行了简化处理,将基本的微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁的大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要将超复数代数引入矢量水听器信号处理领域，用超复数整体了矢量水听器输出的4个信号分量，并建立了矢量水听器阵列的超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术的发展要求,以及代数拓扑学复形等概念引入到几何造型中,因此产生了非流形几何造型理论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子的性质得出了李的两个李子的交依然是李子的结论,进而得出这一李子的李代数形式。

He was not good at algebra in middle school.

时不擅长代数。

Four years after he graduated from school, Tom decided to dust off his algebra book.

汤姆从校毕业四年后, 决意重温代数。

In algebra, the sign X usually denotes an unknown quantity.

在代数里, 符号X常用来表示未知数。

His classmates were labouring with elementary algebra.

的同们正在绞尽脑汁地演算初等代数题。

As its application, a multi-component system similar to the BPT hierarchy is obtained.

最后利用外积的性质构造了一个3 维的loop代数 ,由此可设计出许多新的等谱问题，作为应用，本文得到了一个类似的多分量的Boite-Pempinelli-Tu(BPT)族。

If you want to be a draftsman, a machinist, a molder, or a patternmaker, you'll need algebra and geometry and even trigonometry.

如果你想成为手艺人、缝纫、造型或制模，你需要代数和几何，甚至三角。

Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

在复平面C，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.

利用拟线性分析方法的一阶导数代换对本方程进行了简化处,本的微分积分方程转化为非线性代数方程组,并结合双参数摄动研究了悬臂梁的大挠度问题。

A hypercomplex model of acoustic vector sensor array is introduced.The hypercomplex number is used to model holistically the four output signal components of an acoustic vector sensor.

摘要超复数代数引入矢量水听器信号处领域，用超复数来整体表示了矢量水听器输出的4个信号分量，并建立了矢量水听器阵列的超复数模型。

In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.

业产品几何造型技术的发展要求,以及代数拓扑复形等概念引入到几何造型,因此产生了非流形几何造型论。

In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.

文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。