查询词典 polynomial ring

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The main products are: K-DAS combination of letters, letters sturt, Greggains circle, TC type oil seal, SC-type oil seal, KC-type oil seal, VC-type oil seal, TB-type oil seal, SB-type oil seal, KB-type oil seal, VB-type oil seal, TA-type oil seal, SA-type oil seal, KA-type oil seal, VA-type oil seal, IDI-type ring, UN-type ring, UHS-type ring, OSI-type ring, UPH type ring, YX-type ring, YA-type ring, QY-type ring, KY-type seals, O-type ring, Rectangle ring, star-shaped ring, L type collar ring, DKB-type dust ring, DKI type dust ring, DKBI type dust ring, AF-type dust ring, DH-type dust ring, DHS-type dust ring, V-type rubber cloth portfolio folder closure, U-type cloth rubber ring, J-type seal , combination washer, support ring, wearable-oriented loop, nylon cutting sets, ring, plum-type coupling cushion, Ling-type coupling cushion, rubber buffer body, rubber stent seals and many other materials.

主要产品有：K-DAS组合封、斯特封、格莱圈、TC型油封、SC型油封、KC型油封、VC型油封、TB型油封、SB型油封、KB型油封、VB型油封、TA型油封、SA型油封、KA型油封、VA型油封、IDI型密封圈、UN型密封圈、UHS型密封圈、OSI型密封圈、UPH型密封圈、YX型密封圈、YA型密封圈、QY型密封圈、KY型密封圈、O型密封圈、矩形密封圈、星型密封圈、L型领圈、DKB型防尘圈、DKI型防尘圈、DKBI型防尘圈、AF型防尘圈、DH型防尘圈、DHS型防尘圈、V型夹布橡胶组合封、U型夹布橡胶密封圈、J型无骨架油封、组合垫圈、支撑环、耐磨导向环、尼龙割套、挡圈、梅花型联轴器缓冲垫、菱型联轴器缓冲垫、橡胶缓冲体、橡胶支架等多种材质密封件。

Firstly, this paper describes the history and state of the research to the minimal polynomial and the characteristic polynomial and then gives the main methods and its computational complexities for computing the characteristic polynomial and of a constant matrix, the characteristic polynomial of a polynomial matrix and the minimal polynomial of a polynomial.

本文先叙述了对最小多项式和特征多项式的国内外的研究历史和现状，然后给出了已有的计算常数矩阵特征多项式、多项式矩阵的特征多项式和常数矩阵最小多项式的主要算法及其复杂性。

I plant main products are: 1, GB1235-76 series O-ring, GB34521-82 series O-ring, with other hydro-rubber O-ring; 2, U-shaped ring, Y-shaped ring, Yx - Seal, X-ring, J-ring, drum-shaped ring, Lei-ring, ring various geometric shapes electrical transformer ring; 3, HG4-692-67 series skeleton SEAL, JB2600-80 Series skeleton SEAL, China imported machinery supporting oil seal; 4, various models of standard high-pressure hose Telegraph textile, 5, all kinds of plastic strips, Jiaobang, anti-tip circle, JB982-77 series combined seal gaskets, shock absorption pad , Standards and non-standard items, Zapin production; 6, users can also be designed in accordance with the specific product design, I plant to design, test and manufacture a product.

GB1235-76系列O型密封圈、GB34521-82系列O型密封圈、其它液压气动用O形橡胶密封圈；2、U形密封圈、Y形密封圈、Yx形密封圈、X形密封圈、J形密封圈、鼓形密封圈、蕾形密封圈、各种几何图形电器密封圈、变压器密封圈；3、HG4-692-67系列骨架油封、JB2600-80系列骨架油封、国产进口机械配套油封；4、各种型号规格高压钢线纺织胶管；5、各种胶条、胶棒、防尖圈、JB982-77系列组合密封垫圈、减震垫，标准与非标准件、杂品的生产；6、还可根据用户自行设计的特异性产品图样，我厂给予设计、试验并加工制作成产品。

Structured packing which has wire mesh packing, sheet packing nets, rolling-hole packing, corrugated plate packing, etc.; bulk packing are: Powell ring, ladder ring, Intalox ring, flat ring, conjugate ring, the British park , double convex ring, ring ohm, V-ring, ring 84 inside the arc and so on; experimental filler: Q net ring packing, rolling-hole ring packing, Seater, Central and so on, column has: Tortoise net, float valve, connectors , Nagarze, blister, plate, tray, distribution devices, such as demister.; Products sold throughout the country, exported to Southeast Asia.

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First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按&序&最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

The first chapter, main instead " duo-ring " condition of " every maximal left ideal is GW-ideal " condition,study strongly regularities of GP-V-ring on this condition.lt is shown that (1) R is strongly regular iff R is left GP-V-ring whose maximal left ideals are GW-ideal.(2)R is strongly regular iff R is left GP-V-ring whose maximal right ideals are GW-ideal. The second chapter, generalize some results of GP-V-ring to GP-V-ring, discuss regularity of GP-V-ring.It is shown that (1) R is left self-injective regular with non-zero socle iff R is left GP-V -ring with Soc = Soc and R contains an injective maximal left ideal.(2)R is regular ring and every maximal essential left ideal is ideal iff R is left GP-injective left GP-V -ring and every maximal essential left ideal is ideal.

第一章主要将"duo-环"条件替换成"每一极大左理想是GW-理想"条件，研究在此条件下，GP-V-环的强正则性，证明了：(1)R是强正则环当且仅当R是左GP-V-环且R的每一极大左理想是广义弱理想；(2)R是强正则环当且仅当R是左GP-V-环且R的每一极大右理想是广义弱理想，第二章，主要将GP-V-环上一些结果推广到GP-V′-环上，讨论GP-V′-环的正则性，证明了：(1)R是左自内射正则环且Soc≠0当且仅当R是包含内射极大左理想的GP-V′-环，且Soc=Soc；(2)R是正则环且每一极大本质左理想是理想当且仅当R是左GP-内射的左GP-V′-环且每一极大本质左理想是理想。

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Finally, it investigate QF-ring with right gpm-injective, and obtain the following theorem:Theorem The following statements are equivalent:(1) R is quasi-Frobeniusean ring:(2) R is right noetherian, left pm-injective ring, right pm-injective ring;(3) R is right noetherian, left pm-injective ring, right GP-injective ring;(4) R is right noetherian, left gpm-injective ring, right gpm-injective ring;(5) R is right noetherian, right gpm-injective ring and each right minimal ideal is right annihilator.

最后用右gpm-内射对QF环进行研究，得到了如下定理：定理下列条件等价：(1) R是quasi-Frobeniusean环；(2) R是右Noether，左pm-内射环，右pm-内射环：(3) R是右Noether，左pm-内射环，右GP-内射环；(4) R是右Noether，左gpm-内射环，右gpm-内射环；(5) R是右Noether，右gpm-内射环且每个极小右理想是右零化子。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。