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  product
     Spectral Invariant Subalgebras of Reduced Crossed Product C~*-algebras and Quasidiagonality of Roe Algebras
     交叉C~*-代数的谱不变子代数及Roe代数的拟对角性
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     Scientific Visualization System and HFFT Over Non-Tensor Product Domains
     科学计算可视化系统及非张量区域HFFT算法
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     ON THE PRODUCT OF N NON-HOMOGENEOUS LINEAR FORMS
     关于n个非齐次线性型之
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     ON POLAR·PRODUCT OPERATOR A~(*-1)A
     关于极·算子A~(*-1)A
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     THE UNION, PRODUCT OF MODELS AND HOMOGENEOUS MODELS
     模型的并、与齐次模型
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  integrable
     F(x)∈C′,G≠0.Then first order differential equationdydx-G′(x)G(x)y=Q(x)Ф(y+F(x)G(x))+G′(x)G(x)F(x)-F′(x)is integrable and possesses parameter formal general solution.
     F(x)∈C′,G≠0,则一阶微分方程dydx-G′(x)G(x)y=Q(x)Ф(y+F(x)G(x))+G′(x)G(x)F(x)-F′(x)可,且具有参数形式的通解.
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     The purpose of this paper is to study the approximation of operator Ln(f,x)=ρ_0~(m)A~(n)+sum from m=1 to n ρ_m~(n)(a_m~(n)cosmx+b_m~(n)sinmx) in the integrable function space R.
     本文研究引入的算子Ln(f,x)=ρ_0~(m)A~(n)+sum from m=1 to n ρ_m~(n)(a_m~(n)cosmx+b_m~(n)sinmx)在可函数空间R中的逼近。
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     A (3+1)-dimensional Integrable Sinh-Gordon-MKdV Equation
     一个(3+1)维可Sinh-gordon-MKdV方程
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     If f(x) is integrable on[a,b],then f(x) is also integrable over D[a≤x≤b;c≤y≤d].
     如果f(x)在[a,b]上可,则f(x)在D[a≤x≤b;c≤y≤d]上也可
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     Under the Bargmann constraint between the potentials and eigenfunctions, the spatial partq_(xx)+(λu+λ~2v-α)q=0 and the time part of the Lax pair of coupled Harry Dym equations are all non-linearized to be completely integrable systems in Liouville sense in the symplectic space (R~(2N), dp ∧dq).
     在位势与特征函数的Bargmann约束下,耦合Harry Dym方程族的Lax对的空间部分q_(xx)+(λu+λ~2v-α)q=0和时间部分均被非线性化为辛空间(R~(2n)dp∧dq)中的Liouville完全可系统。
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  “积”译为未确定词的双语例句
     Nonlinear Waves and Intrgrable Systems
     非线性波与可系统
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     Entranspy and Its Applications in Heat Transfer Optimization
     火及其在传热优化中的应用
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     Entranspy and Its Applications in Heat Transfer Optimization
     (火)及其在传热优化中的应用
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     On equations of multiplicative Number-theoretic functions
     论一类型性数论函数方程
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     PHYSICAL METHODS OF GROUP REPRESENTATION THEORY (Ⅲ) OUTER-PRODUCT REDUCTION COEFFICIENTS OF THE PERMUTATION GROUP AND CG COEFFICIENTS OF THE SU_n GROUP
     群表示论的物理方法(Ⅲ) 置换群外约化系数和SU_n群CG系数
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  product
In this paper we present an explicit formula for the twistors in the form of an infinite product of the universalR matrix ofUq(g).
      
These are analogous to "fusion rules" in tensor product decomposition and their derivation obtains from an analysis of theR-matrix.
      
In general, such a tensor product is no longer irreducible.
      
A fundamental question is how the irreducible components are embedded in the tensor product.
      
A special component of the tensor product is the so-called Cartan component Vλ+μ which is the component with maximal highest weight.
      
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  integrable
Quantum integrable systems and differential Galois theory
      
This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
      
This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
      
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
      
We prove a more general version of a result announced without proof in [DP], claiming roughly that in a partially integrable highest weight module over a Kac-Moody algebra the integrable directions from a parabolic subalgebra.
      
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  produit
La taille optimale pour la recolte depend du rapport prix de la nourriture/prix du produit (Vf/Vp).
      
Ils ont produit un nombre moyen de cystes de, respectivement, 184 +/- 38, 111 +/- 14 et 160 +/- 14 par ponte.
      
En Mediterranee, le pic de mue se produit en decembre-janvier et maijuin.
      
___TAGSTART___BR___TAGEND___Plusieurs groupes de crustaces ont produit de vastes ensembles d'especes dans les lacs anciens.
      
Acartia tonsa a produit deux types d'oeufs morphologiquement distincts, qui ont été identifiés comme oeufs immédiats et oeufs de diapause.
      
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  stagnate
This process proves that late imperial China was not stagnate society without "history," meanwhile, its pattern of development was clearly not identical to the Western style modernization progress.
      
In the solution of large linear systems, a condition guaranteeing that a minimal residual Krylov subspace method makes some progress, i.e., that it does not stagnate, is that the symmetric part of the coefficient matrix be positive definite.
      
There is a high risk for stone formation and obstruction with the HPI procedure because bile can stagnate in the ileocecum.
      
Residual andesitic to rhyodacite magmas may stagnate within the upper regions of the sialic Aegean crust and form relatively high level magma chambers beneath the southern volcanic centres of Santorini.
      
Volatile-rich parental magmas like Mount Shasta basalt probably tend to stagnate at deeper levels, crystallize early amphibole and produce comparatively calcic differentiates.
      
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In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in n-dimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the...

In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in n-dimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the given final region of states. Some conclusions are obtained from the maximum principle by using transversal conditions of optimal trajectories in terminal points, and the particular properties of the stated problem are pointed out. The case of linear dif-ferential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the rela-tions between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal loss-function J (x) is found and the connection between function J (x)and optimal vector control function u (x) is also stated. The methods proposed are practically the extension of the me-thods used by us for designing time optimal control systems as seen in [5, 6 ,7].Finally, an example is illustrated with optimal trajectories shown in phase plane.The necessary numerical data is calculated by an analog computer with high accuracy.

文中研究了具有公式(3)表示的一般正分泛函的最优控制系统的综合问题.在第一部分中研究了具有控制参数的一阶微分方程组.控制系统的终点状态为n维相空间内的某一逐段光滑边界的闭性区域Ω.文中指出了根据极大值原理和轨道终点的横截条件寻找引到Ω的所有最优轨迹的方法.这里详细地研究了具有二次泛函和被函数中不明显含有控制参数的质量指标泛函的线性方程情况.在文中第二部分研究了等损耗区的主要特性.指出了等损耗区与最优控制函数之间的关系.导出了求算最优损耗函数J(x)的偏微分方程,以及这一函数与最优控制函数u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的最优快速系统的综合方法的推广.文章最后举有例证.

Infolge der Fernwirkungen der Oberflachenzirkulation des Indischen Ozeans berwiegt also im Suezkanal in den 9 Monaten Oktober/Juni ein Wassertransport nach Norden vom Golf von Suez zum Mittelmeer, wobei am Kanalboden mehr oder minder weitreichende rucklaufige Bewegungen auftreten, die von der Salzanreicherung des Grossen Bittersees ausgehen. Im Vierteljahr Juli/September setzt sich bei ausgeglichenen Niveauverhaltnissen der Einfluss der vorherrschenden Nordwind durch und bewirkt einen Sudstrom, der zwar im nordlichen...

Infolge der Fernwirkungen der Oberflachenzirkulation des Indischen Ozeans berwiegt also im Suezkanal in den 9 Monaten Oktober/Juni ein Wassertransport nach Norden vom Golf von Suez zum Mittelmeer, wobei am Kanalboden mehr oder minder weitreichende rucklaufige Bewegungen auftreten, die von der Salzanreicherung des Grossen Bittersees ausgehen. Im Vierteljahr Juli/September setzt sich bei ausgeglichenen Niveauverhaltnissen der Einfluss der vorherrschenden Nordwind durch und bewirkt einen Sudstrom, der zwar im nordlichen Teile des Kanals nicht die ganze Wassersaule erfasst und hier offenbar von einem salzreichen, nach Norden gerichteten Bodenstrom unter lagert wird. (John Lee)

海水盐分之浓度,在各大洋中,平均皆在35‰上下,惟红海以地理关系,盐分特高,几达40‰,在红海湾内,且达43‰,然此尚不算大,苏彝士运河内之盐分,竟高至56‰,大概为世界盐分最高之海道矣。苏彝士运河盐分所以如此之高,盖因其中部有大苦湖,湖底有盐层之故。但自运河开凿后,因海水之流通,运河盐分已在逐年减低(水面盐分平均每年减低0.18‰,大苦湖底每年约减低0.30‰),而大苦湖底之盐层亦渐次溶消矣。

Since the year 1886, the Dupuit-Forchheimer theory and formulas for gravityflows toward wells and galleries have been broadly used in all nations of theworld. In these formulas, assumptions are made for underground flows fromfarther distances in horizontal directions at a constant rate toward wells andgalleries. According to the author's analysis, these assumptions are not consistentwith the actual conditions of flow, hence the formulas obtained therefrom are notrational, and the employment of these formulas...

Since the year 1886, the Dupuit-Forchheimer theory and formulas for gravityflows toward wells and galleries have been broadly used in all nations of theworld. In these formulas, assumptions are made for underground flows fromfarther distances in horizontal directions at a constant rate toward wells andgalleries. According to the author's analysis, these assumptions are not consistentwith the actual conditions of flow, hence the formulas obtained therefrom are notrational, and the employment of these formulas to investigate the general effectof surface drop or well diametre upon yield is devoid of rational foundations. According to the author's analysis, the flows toward wells or galleries areactually supplied vertically by draining the stored water above the free surface inthe course of its descending and enlarging. As the drainage of gravity water fromthe pores of soil particles in order to reduce the water content to that of filmshells takes one to two days, as the capillary water columns are interconnectedand mutually supplied sidewise, this vertical supply of water may maintain quite along time, yet the flow may not be absolutely steady. As regards vertical supply of water with unsteady regimen, equations of freesurface for flow pattern near galleries are deduced, corresponding to the Boussinesqpartial differential equation. Besides, the author has derived simplified equationsfor computing flows into wells and galleries. The latter, in comparison with theDupuit-Forchheimer formulas, gives a higher yield, while the free surface curve isreasonably tangent to the horizontal water table at a point which moves fartheraway as time goes on. J. Kozeny first pointed out the phenomenon that the water depth in the groundon the wall will not be further lowered when it reaches one half of the depthbefore pumping. The author hereby proposes a theoretical proof of it on the basisof theorem of least work. Based upon these theories, formulas are proposed for maximum possible yieldof wells and galleries dug to horizontal impervious strata, to be used in prelimi-nary estimations for hydro-geological workers.

1886年以来,杜布义-福熙罕默(Dupuit-Forchheimer)的井流及沟流的理论与计算用公式被世界各国广泛地应用着。公式假设地下水从远处沿着水平方向以定率流向井内或沟内,按作者分析这种假设并不符合实际情况,因之所得公式也不合理,用这些公式来推论水位降落或井径对於出水率的影响也没有合理的凭据。作者推论,井流或沟流的水实际上是从水面线以上,在其降落并扩大的过程中,排除了存的水,沿着直垂方向所供应着的。因为从土壤颗粒的空隙间排除重力水,使减为薄膜水,每需时一两天,而水面上的毛细管水又是横向贯通并互相接济着,所以垂直供水可以维持很久,而潜流也决不会绝对稳定。根据这垂直供水的不定汉条件引出了沟流的水面线公式,结果符合蒲薪奈斯克的偏微分方程式。另外,作者又拟具了简化的井流及沟流计算用公式。这些公式和杜氏-福氏公式比较,所得出水率较大,而水面线则合理地切於静水线,切点随着时程向远处移动。柯臣尼(J.Kozeny)最早指出井边地内水深不会低於静水深一半的现象,本文中作者根据最小工作定律试拟了理论的证明以支持之。根据这些理论,引出了从静水中抽水时井流、沟流最大可能出水率的公式,以供水文地质工作者初步估算...

1886年以来,杜布义-福熙罕默(Dupuit-Forchheimer)的井流及沟流的理论与计算用公式被世界各国广泛地应用着。公式假设地下水从远处沿着水平方向以定率流向井内或沟内,按作者分析这种假设并不符合实际情况,因之所得公式也不合理,用这些公式来推论水位降落或井径对於出水率的影响也没有合理的凭据。作者推论,井流或沟流的水实际上是从水面线以上,在其降落并扩大的过程中,排除了存的水,沿着直垂方向所供应着的。因为从土壤颗粒的空隙间排除重力水,使减为薄膜水,每需时一两天,而水面上的毛细管水又是横向贯通并互相接济着,所以垂直供水可以维持很久,而潜流也决不会绝对稳定。根据这垂直供水的不定汉条件引出了沟流的水面线公式,结果符合蒲薪奈斯克的偏微分方程式。另外,作者又拟具了简化的井流及沟流计算用公式。这些公式和杜氏-福氏公式比较,所得出水率较大,而水面线则合理地切於静水线,切点随着时程向远处移动。柯臣尼(J.Kozeny)最早指出井边地内水深不会低於静水深一半的现象,本文中作者根据最小工作定律试拟了理论的证明以支持之。根据这些理论,引出了从静水中抽水时井流、沟流最大可能出水率的公式,以供水文地质工作者初步估算之用。

 
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