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 之积
 the product of
 Using this method wecan compute the N-point DFT,Here N is the product of relative prime factors in {2,3, 4, 5, 7, 8, 9, 16} 可用来计算长度为N的离散傅里叶变换(DFT),其中N为集合{2,3,4,5,7,8,9,16}中互素因子之积。 短句来源 In this paper, we prove that each of the two systems of equations as the title has only the integer solution x=0. In other words, N=1 is the only integer such that the product of any two of 1,2,5, N or 1,5,10, N decreased by 1 is a perfect square. 本文证明了标题中所列的两个不定方程组均只有x=0的整解,从而证明了有且只有一个整数N=1使得1,2,5,N或1,5,10,N四数中任二数之积减去1后均为平方数. 短句来源 The zero-exponent of convergenceλ(f1f2) us of the product of any two linear independent solutionsf1(z), f2(z) of second linear differential equations and the growth ρ(f) of their solution have been investigated. Furthermore, The sufficient condition of λ (f1f2)=∞ and ρ (f) =∞ have been given. 研究了二阶线性微分方程两个线性无关解f_1（z）f_2（z）之积的零点收敛指数λ（f_1，f_2），以及其解的增长级ρ（f），给出了λ（f_1，f_2）＝∞和P（f）＝∞的充分条件。 短句来源 It is found that the product of the coupling coefficient η 1 and η 2 affects the gain curve. 发现两个耦合系数η1 与η2 之积的大小对增益曲线产生具体影响。 短句来源 If the function k(x,t) is split into the product of multiplification of H(x) and G(t),the general form of the solution to this equation is φ(x)=f(x)+αH(x),in which α is constant. 当k(x ,t)可以分离为两函数H(x)与G(t)之积时 ,该方程解的一般形式为 :(x) =f(x) +αH(x) ,其中α为常数。 短句来源 更多
 “之积”译为未确定词的双语例句
 Microwave dielectric properties of ε_r = 109.24,Qf = 8 650 GHz,τ_f = +243×10~(-6)/℃ were obtained for CNT(x = 0.39) ceramics sintered at 1 350 ℃ for 4 h. 在1 350℃烧结4 h,可制备出介电常数rε=109.24,品质因数与频率之积Qf=8 650 GHz,谐振频率温度系数τf=+243×10-6/℃的CNT(x=0.39)微波陶瓷。 短句来源 When x=0.1(mole fraction),the compacted ceramics were sintered at 1 150 ℃,and its dielectric properties were following:εr=84.7,τf=0.5,Q×f=8 452 GHz. 当x(Sn)=0.1(摩尔分数)时,其介电常数rε=84.7,频率温度系数fτ=0.5,品质因数与频率之积Q×f=8 452 GHz。 短句来源 when A∈GL ± 4(F), A is a product of three involutions iff rank (A-aI 4)≥2 or A is similar to B=aI 3a -3 for any a∈F, a 4≠1; 当A∈GL±4(F)时 ,A是 3个对合之积当且仅当对任意a∈F ,a4≠ 1 ,有rank(A-aI4) ≥ 2或A与B =aI3 a- 3 相似 ; 短句来源 when A∈GL ± 5(F), A is a product of three involutions iff rank (A-aI 5)≥2 and A is not similar to B=aI 3(- det A)I 2, for any ∈F,a 4≠1. 当A∈GL±5(F)时 ,A是 3个对合之积当且仅当对任意a∈F ,a4≠ 1 ,有rank(A-aI5) ≥ 2且A不与B =aI3 (-detA)I2 相似 . 短句来源 【Results】 The IP3 of control was(29.2±0.6)pmol/106 cells. V-PTEN/ V-actin,which was the gray degree multiply area of PTEN / the gray degree multiply area of actin,in control was 0.12±0.00.The apoptosis rate of control was(2.6±0.1)%. 结果对照组IP3含量为(29.2±0.6)pmol/106cells,PTEN蛋白与内参actin蛋白灰度和面积之积的比值V-PTEN/V-actin为0.12±0.00; 细胞凋亡率为(2.6±0.1)%。 短句来源 更多
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 the product of
 For char k = 0, it is shown that if n is odd, adj(X) is not the product of two noninvertible n × n matrices over k[xij], while for n even, only one special sort of factorization occurs. We show that ${\mathcal M}(G,R)$ is a symmetric tensor category, i.e., the motive of the product of two projective homogeneous G-varieties is a direct sum of twisted motives of projective homogeneous G-varieties. The classical Hecke identity gives the Fourier transform of the product of a homogeneous harmonic polynomial h times the Gaussian e-1/2>amp;lt;...>amp;gt;. The product of photocatalytic oxidation was detected by Fourier transform-Infrared. A new eco-hydrological index, expressed by the difference between precipitation and runoff divided by the product of precipitation and NDVI, was used in this study to represent the eco-hydrological functions of different catchments. 更多
 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)表示的一般正积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积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,湖底积有盐层之故。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,排除了存积的水,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。 << 更多相关文摘
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