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 为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法，我们为您准备了出自英文原文的大量英语例句，供您参考。 
Like the truncations of the Taylor expansion, the truncations of a chromatic expansion at t = t0 of an analytic function f(t) approximate f(t) locally, in a neighborhood of t0.


It is available for the case that the sign of f(x) changes frequently or the derivative f'(x) does not exist in the neighborhood of the root, while the Newton method is hard to work.


One allows the appearance of eight limit cycles in the neighborhood of infinity, which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.


Neighborhood union of independent sets and hamiltonicity of clawfree graphs


Let G be a graph, for any u∈V(G), let N(u) denote the neighborhood of u and d(u)=N(u) be the degree of u.

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 A new approach to tail buffeting is made by studying the problem of a thin airfoil performing a periodic oscillation of small amplitude in the presence of an interface across which the flow undergoes a constant change indensity and velocity. A general solution to the problem is found. Lift and moment for some speical cases are obtained in simple forms and are plotted in Fig. 3 and 4 for the two basic modes of oscillation: bending and torsion. A typical application to flutter analysis is made and it is found... A new approach to tail buffeting is made by studying the problem of a thin airfoil performing a periodic oscillation of small amplitude in the presence of an interface across which the flow undergoes a constant change indensity and velocity. A general solution to the problem is found. Lift and moment for some speical cases are obtained in simple forms and are plotted in Fig. 3 and 4 for the two basic modes of oscillation: bending and torsion. A typical application to flutter analysis is made and it is found that tail flutter at low speeds is possible for the tail lying in the neighborhood of the interface produced by the wing.  本文对尾翼顫振給了一个完全新的研究。用平行于气流的速度不連續面代替机翼及其遺迹,考慮在不連續面附近以微振幅周期振动的薄翼剖面,求得了問題的一般解。对于某些重要的情形,建立了翼剖面弯曲和扭曲振动时升力和力矩公式。典型例題指出:当翼剖面与速度不連續面间的距离小于半翼弦时,翼剖面可能在低速范圍內發生弯曲扭曲顫振。  In at least one case where3 the potential folw in the neighborhood of the outherdoge of the boundarylayer varies rapidly,the boundarylayer theory has not been well undorstood,The interest in this problem led the author to the study of the laminar flow of a viscous incomperssible fluid over a curved surface whose curvature,as has been found previously,displays rathor large effects on the natrre of boundarylayer flow.The specific point to be investigated here is th question as to how to join the bundarylayer... In at least one case where3 the potential folw in the neighborhood of the outherdoge of the boundarylayer varies rapidly,the boundarylayer theory has not been well undorstood,The interest in this problem led the author to the study of the laminar flow of a viscous incomperssible fluid over a curved surface whose curvature,as has been found previously,displays rathor large effects on the natrre of boundarylayer flow.The specific point to be investigated here is th question as to how to join the bundarylayer with the potential flow.On the basis of the fact that the viscous that,in the neighborhood of the outer edge of boundarylayer,the velocity in the main stream dirction u should asymptotcally approach that in the main stream.  利用一种严格的边界層外缘条件重新计算了不可压縮非粘性流体繞二維曲面的运动,求出曲度对表面剪力与速度剖面的影响。墨菲曾首次研究此題,其结果与本文的結果比較,在質与量上均有出入,因此說明如何准确連結边界層与势流对此类問題的重要性。 結果还表明凸面曲度使表面剪应力較平面的剪应力小,也使边界層內的速度比平面的小。反之,凹面曲度使表面剪应力較平面的大,也使边界層的速度比平面的大。又曲度对表面剪应力的影响小,对速度剖面影响大。  In the first part of this paper we consider the partial differential equation as a generalized EulerPoisson equation:(?) (1.1)where β,β′are constants, and a(x,y),b(x,y),c(x,y),d(x,y)are all regularfunctions in Hadamard's sense.Therefore x=y is the singular line of thecoefficients.The behaviors of the solutions of(1.1)in the neighborhood ofthe singular line x=y are described by introducing the concepts of“index”and the“regular part”:Let ρ be a constant and υ(x,y)be a regularfunction(υ(x,x)≠0)such thatu(x,y)=(xy)~ρυ(x,y)is... In the first part of this paper we consider the partial differential equation as a generalized EulerPoisson equation:(?) (1.1)where β,β′are constants, and a(x,y),b(x,y),c(x,y),d(x,y)are all regularfunctions in Hadamard's sense.Therefore x=y is the singular line of thecoefficients.The behaviors of the solutions of(1.1)in the neighborhood ofthe singular line x=y are described by introducing the concepts of“index”and the“regular part”:Let ρ be a constant and υ(x,y)be a regularfunction(υ(x,x)≠0)such thatu(x,y)=(xy)~ρυ(x,y)is a solution of(1.1),then the constant ρ is said to be the“index”andρ(x,y)the“regular part”of the solution.It is shown that all the possibleindexes must satisfy the indicial equation(?)and if F(ρ+1)≠0,then the normal derivative of the regular part on thesingular line x=y is determined completely by the value itself,i.e.(?)The regular part υ(x,y)satisfies the equation of a particular form of(1.1),in which γ=0,and therefore it is sufficient to study the equation of theform(?) (?) (3.2)We define the singular Cauchy prob em as follows:to find a functionυ(x,y)continuous together with its first derivatives and twice differentiablein the region ACBD(cf.figure 1 p.518),and satisfying the equation(3.2)in the region ACBD,except the singular line AB,on which it takes anygiven regular funtion u_0(2x)as its initial value.We give the existence proof of such singular Cauchy problem in thegeneral case(β+β′≠0),and it follow that,the solution of the equation(1.1)may,in general,be expressed as.(?)where ρ_1 and ρ_2 are different roots of the indicial equation;or(?)where ρ_1 is the double root of indicial equation.The second part of this paper,deals with the singular equation in space,especially the equation of the following form:(?) (15.5)where A_σ is any linear operator which (?)epends only on the variables σ==(σ_1,…,σ_n),such that,the Cauchy problem for the associated regular equation(?) (15.6)and the initial data(?)has a unique soluion υ(x,σ_,…,σ_n).The solution of singular Cauchy problem for equation(15.5),with initial data(?)can be expressed by υ(x,σ_1,…,σ_n)in the form(?)where K(τ,t)is a kernel well defined by the operator(?)For example,the kerne for EulerPoissonDarboux operator(?)is(?). The same method can be applied to solve the Cauchy problem for thegeneralized Chapligin equation(?)(where K(t)is an increasing function,and K(0)=0),with initial data(?)The solution is given explicitly by(17.12).(p.550).  本文的第一部分研究了含奇线方程的解在奇线附近的性质;引进了“指数”的概念,从而给出了关于这类方程的“奇型郭西问题”的正确提法;并且通过一种特殊的积分征分方程的研究,证明了这种“奇型郭西问题”的解的存在性,并且给出其近似解法;最后,就一般的情形,给出了方程一般解的表达式,从而说明了在β+β′<0时,郭西问题的多解性。本文的第二部分研究了空间含奇面方程(?)其中 A_σ是任一祇与变元σ=(σ_1…,σ_n)有关的算子,并且关于(15.5)的奇型郭西问题的解可以用关于方程(不合奇面)(?)(15.6)的郭西问题的解表示出来。同样的方法可用来解决空间却普里金方程(17.1)的郭西问题。   << 更多相关文摘 
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