查询词典 monomial

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。

Research on monomial resources is generally interdisciplinary study or derived fromrelated sciences such as agrology, zoology and botany, geology, hydrology and climatology, geography, environmentalsciences, economics, national land economics, ecology, ergonomics and so forth.

单项自然资源研究各自从有关学科派生出来或与一些学科有着密切的相互联系和交叉，如：土壤学、动、植物学、地质学、水文和气候学、地理学、环境科学、经济学、国土经济学、生态学、人类生态学等。

The classical design is awarded most honors: style "2004" awarded the best seller in domestic monomial product for 5 years; style "3005" is the first one which fetched in the translucent aiguillette and started the market; our enterprise took the lead in attending France Lyons Underwear Fair with craft brother, 5 style of them is awarded with the international fashionable style.

经典设计屡获殊荣：其中"2004"款内衣连续5年销量在国内单个产品销量评比中名列第一；"3005"款在国内率先引进透明肩带设计，开创了市场先河；率先在同行业内参加世界级内衣盛会法国里昂内衣展，其中有5款产品被评为国际流行参考款式等。

Firstly, we get the necessary and sufficient conditions for Toeplitz operators that commutes with another such operator whose symbol is a monomial, meanwhile, we completely characterize when the mellin transform of the bounded function on the interval 0,1 is a rational function.

首先得到了以有界函数为符号的Toeplitz算子和以单项式函数为符号的Toeplitz算子可交换的充要条件，同时给出了0，1区间上的有界函数的Mellin变换为有理函数的充要条件。

We not only give explicitexpressions of monomial elements in the canonical basis but also representregions of them in "nice" forms which help us compute polynomial elementsin the canonical basis.

我们不仅给出了这种具体表达式，而且把它们对应的区域写成很好的形式，便于我们计算典范基中的多项式元素。

Marsh has proved that allmonomials are canonical basis elements for type 〓, he did not give concreteexpressions of monomial elements in canonical basis.

Marsh已经证明：对〓型量子群来说，所有单项式元素都属于典范基，但他并没有给出典范基中的单项式元素的具体表达式。

Our first main result is (see §9.1) 9.1. Theorem. Let a =∈〓.χ={i =｜〓=〓}, where 〓 is the unique longestelement in Weyl group of complex semi-simple Lie algebra for type 〓. Thencorresponding to 62 equivalence classes in χ for certain equivalent relation ～,we have 62 monomial elements in canonical basis, each of them correspondsto a region which consists of six independent inequalities.

我们的第一个主要结果是群的唯一最长元素，那么与χ的关于某种等价关系～的62个等价类对应，在典范基中有62个单项式元素，每个单项式元素对应一个由六个独立不等式构成的区域。

In particular, we compute Hochschild homology and cohomology groups of infinitedimensional path algebras and some of their quotient algebras, and we prove that for a general monomial algebra (not necessary finite-dimensional), all Hochschild cohomology groups of positive degrees vanish if and only if its Gabriel quiver is a finite tree.

特别地，我们计算了无限维路代数以及某些商代数的Hochschild同调群和上同调群，而且给出了一般单项代数的各正次Hochschild上同调群为零的充分必要条件，即它的Gabriel箭图是有限树。

The number of compound leaves, the number of leaflets and the total leaf area of bearing branches had highly significant positive monomial correlation with panicle width and volume.

结果母枝复叶数、小叶数、总叶面积与花穗宽度、花穗体积为显著或极显著正单相关，小叶数与穗坐果数为显著的正单相关，复叶数与单果重为显著的负相关。

Determined by the specific geological background of Longhetun, the characteristics of the soil resources show abundant calcium and leaning to alkaline. Monomial indexes to evaluate the revisal coefficient of soil adapted to karst mountains areas were screened out combined with the function of karst dynamics system and analysis of characters of each factor about fertility in soil. Predigestion model to soil revisal coefficient monomial assessment was established by successful importation of the content of nutrition elements in plant body, latent efficient elements in soil and available thickness of soil in the cranny of epikarst according to the characters that three carriers of soil, soil water and karst water supply nutrition to plants and two layers of foundation consist of surface soil and soil in epikarst cranny, and several types of soil revisal coefficient and weather-soil productive potentiality were calculated, the results show that the soil revisal coefficient was even more practical after modification than before, which make up of innovation of this study.

龙何屯特殊的地质背景条件决定了耕地土壤资源的富钙偏碱的特点，结合岩溶动力系统的作用，系统分析土壤中各肥力因子的特点，筛选出适宜岩溶石山区特点的土壤订正系数评价单项指标，针对研究区存在土壤、土壤水、岩溶水三种载体提供植物营养和表层土、土下表层岩溶带裂隙土两层空间基质的特点，成功引入植物体内营养元素含量、土壤元素隐性有效态含量及土下表层岩溶带裂隙土有效厚度等新参数指标，探讨建立了土壤订正系数单项指标评价简化模型，计算出龙何屯各耕地类型土壤订正系数和气候-土地生产潜力，结果显示修正后的土壤订正系数比修正前更符合实际，成为本研究的创新点。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐