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fourier-series
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  fourier级数
     With the nonlinear material constitutive relation was considered,the single-freedom vibration control equation of nonlinear material cable under concentrated load was presented. And then the vibration displacement of cable was analyzed by Fourier-series,the formula for its vibration was deduced with L-P method,finally the vibrational peculiarity between nonlinear material and linear material was compared.
     在考虑非线性材料本构关系的基础上,建立了非线性材料悬索在集中荷载作用下的单自由度振动控制方程,把悬索的振动位移利用Fourier级数展开,再采用L-P法求得了非线性材料悬索在集中荷载作用下的振动近似解,把非线性材料悬索的振动特性与线性材料悬索的振动特性进行了比较分析。
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     In process of finding the Fourier-series expansion of the function, usually get some different result,for example the sine-series and the cosine-series. To choice proper examples and explain them exactly in teaching,it will play important role on the students comprehend the meaning of this type of topic and the not uniqueness of Fourier series of the function.
     在求函数的Fourier级数时, 经常遇到将函数在区间 [0, α] 上展成Fourier级数、正弦级数或余弦级数 在教学中恰当地举例及讲解, 学生不但能正确理解这类题目的含义, 而且对函数的Fourier级数展开式的不唯一性也有充分的认识
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     The generalized Fourier-series method was used to derive the impact responses formula of an unrestrained planar frame structure when subjected to an impact of a moving rigid-body. By using these formula,the analytic solutions of dynamic responses of the contact-impact system can be obtained.
     运用广义Fourier级数方法推导了无约束平面框架结构受运动刚体冲击时的瞬态动力响应公式,利用这些公式得到冲击系统动力响应解析解.
短句来源
     The Fourier-series method is adopted to analyze the responses of an unrestrained bar under a rigid axial impact. The rigid response of the bar is separated directly from its total response of the bar and the relationship and affecting factors between the rigid displacement and elastic displacement of the bar is investigated.
     用Fourier级数方法推导了无约束自由杆承受运动刚体纵向冲击作用下的响应,将刚性位移直接由总位移中分离出来,并分析了无约束自由杆的刚性位移与弹性位移的关系及其影响因素。
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  “fourier-series”译为未确定词的双语例句
     A“modified double Fourier-Series”filtering method is presented and applied to the separationof meso-scale waves from satellite sounding data.
     本文提出一种“修正的双傅氏级数”滤波方法,应用卫星资料个例,与 Barnes 带通滤波法进行了对比试验。
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  相似匹配句对
     Demonstrations on Fourier Optics
     付里叶光学教学演示
短句来源
     Chirp Fourier Transformer
     Chirp傅里叶变换器
短句来源
     On the convergence of Fourier-U seriers
     关于Fourier—U级数的收敛性
短句来源
     Starting from the Fourier Series
     从Fourier级数讲起
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     On L-convergence and Approximation of Fourier Series
     关于Fourier级数的L~1收敛及逼近问题
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  fourier-series
For simplicity, however, all numerial results presented and discussed throughout paper are dealing with a single harmonic of such Fourier-series expansions.
      
This is achieved by suitably expanding the lateral surface boundary conditions in the form of appropriate Fourier-series.
      
The mathematical centerpiece of the Fourier-series method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it.
      
The Fourier-series method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule.
      
Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines.
      
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Using the x,y,p coordinates,and neglecting the small terms in thesteady state vorticity equation, we have(?)taking two layer baroclinic model,as Sawyer and Bushby,we let(?)in whichA(p)=(p_0+p_1-2p)/(p_0-p_1),(3)where p_0=1000mb and p_1=200mb.Introducing (2) to (1) and integrating from p=p_0 to p=p_1 under thefollowing bundary conditions(?)We obtain(?)where H=(RT_0)/g is the height of the homogeneous atmosphere,and η=η(x,y) is the topography of the earth's surface.For the distribution of vertical velocity,we...

Using the x,y,p coordinates,and neglecting the small terms in thesteady state vorticity equation, we have(?)taking two layer baroclinic model,as Sawyer and Bushby,we let(?)in whichA(p)=(p_0+p_1-2p)/(p_0-p_1),(3)where p_0=1000mb and p_1=200mb.Introducing (2) to (1) and integrating from p=p_0 to p=p_1 under thefollowing bundary conditions(?)We obtain(?)where H=(RT_0)/g is the height of the homogeneous atmosphere,and η=η(x,y) is the topography of the earth's surface.For the distribution of vertical velocity,we assume ω(x,y,p)=B(p) (?)(x,y)+C(p) ω_0(x,y),(5)whereB(p)=1-A(p)~2,C(p)=(p-p_1)/(p_0-p_1).(6)Introducing (2) and (5) to (1),multiplying A(p),and then integratingit with respect to p from p_0 to p_1,we find(?)Using again the relations of (2) and (5) and the geostrophic approximationin (Ⅰ)(1),taking steady state and then eliminating (?) from it with (10),we have(?)whereC_1=[R/(gc_p)]ln[p_0/(?)],M=[(4f~2)/(p_0-p_1)][1/(C_2RΓ_p)],C_2=(1/2)[(p_0+3p_1)/(p_0-p_1)]-[(4p_0p_1)/(p_0-p_1)~2]ln[(2p_0)/(p_0+p_1)].The motion is considered as consisting of small perturbations superim-posed upon a basic zonal current (?)+A(p)U_T,and taking geostrophic app-roximation,wo obtained the two required equations:(?)in which β is the variation of Coriolis parameter with latitude.We used the equation (9) and (10) to a rectangular reigon with a mar-ginal cyclicity and with a length equal to that of the latitud circle at 45°and take 1 day as the time unit and the radius of 45° latitude circle aslength unit.By means of Fourier analysis,the solution may be written inthe following form(?)where the topographical influence function Φ_0 and the heating influencefunction Φ_h are respectively defined by the Fourier series (?)As the equation was linearzed, we can put Q_m=0 to find the topographiceffect, and put η=0 to find the effect of heat sources and sinks;whenboth Q_m≠0 and η≠0,we can find the combined influences of heat sour-ces and sinks and topography.For case of winter,we take (?)=15m/s and U_t=13m/s.In the unitsdescribed above,we find (?)=2.87×10~(-1),β=2π,M=231,β/(?)=21.9.We have constructed separately the flow patterns respectively due tothe thermal effect,the topographical effect and the combined effect of themon the westerlies.By examining these patterns we may state the followingpoints on the formation of mean troughs and ridges and jet stream:(1)For the case Q_m=0.There is a trough to the downstream ofmountains and a ridge over the mountains created by the forced ascent ofthe westerly current over the topography.The Tibetan Platean is importanton the formation of the Asiatic mean troughs and ridges.(fig.1) Consi-dering the combined effect of the mountains of Rocky and Greenland,theposition and intensity of the computed mean trough and ridge (fig.6) iswell in agreement with the observation.(fig.4,10) However the effect ofthe forced ascent of the westerly current over the mountains does notgive a jet stream.(2)For the case η=0.Through dynamic processes the large-scaleheat sources and sinks show even larger influences than that of the moun-tains on the midtropospheric flow.The 500 mb trough is located west ofthe heat source,and the ridge west of the heat sink.The jet stream isformed at the south-western part of the heat source.The perturbationpattern of heating and cooling (fig.2,7) is in better agreement with theobserved one than that due to topography.(3)The flow pattern obtained by considering both heat sources andsinks and topography (fig.3,9) is in good agreement with the observedones.The agreement with observation is much better than any one of thefactors considered alone.

本文第二部分根据简单的两层斜压模式,用小扰动分别解出地形、热源的常定扰动和地形与热源的共同扰动.作者得到西藏高原对于东亚平均槽、脊的形成具有一定的作用.洛矶山加上格林兰高地后更能解释北美槽、脊的形成.在夏季由于西风带的北移,只有地形作用也使得平均槽的强度和位置发生变化.热源的扰动作用对平均槽的生成具有更显著的作用,冬季的西风急流和夏季小槽的生成都和热源扰动更有直接的关系.考虑了热源和地形的共同作用后所得的扰动流型更接近了实现.由此作者提出热源和地形作用通过动力过程在大气环流中相互制约的统一性.

Denote by σ_n~α(f; x) the n-th Cesàro mean of order a for the Fourier series of f(x) and write R_N(f,α;x)=sum from n=N to ∞ |σ_n~α(f;x)-σ_(n+1)~α(f;x)|. The object of this note is to estimate R_N(f,α;x), the main results obtained can be stated as follows: Theorem 1. If (x)∈Lip 1, then the relation holds uniformly in x. Theorem 2. If f (x)∈Lip 1, then for 0<α≤1, the relation R_N(f,α;x)=0((log N)/N~α) holds uniformly in x. Moreover, for almost all x, there give Theorem 3. If f (x)∈kw~((r))(r<1), then there holds...

Denote by σ_n~α(f; x) the n-th Cesàro mean of order a for the Fourier series of f(x) and write R_N(f,α;x)=sum from n=N to ∞ |σ_n~α(f;x)-σ_(n+1)~α(f;x)|. The object of this note is to estimate R_N(f,α;x), the main results obtained can be stated as follows: Theorem 1. If (x)∈Lip 1, then the relation holds uniformly in x. Theorem 2. If f (x)∈Lip 1, then for 0<α≤1, the relation R_N(f,α;x)=0((log N)/N~α) holds uniformly in x. Moreover, for almost all x, there give Theorem 3. If f (x)∈kw~((r))(r<1), then there holds uniformly good, for almost every x, there holds R_N(f,α;x)=O(1/N~r),α=1 or α≥2. Furthermore these results can not be improved without changing the conditions.

§1.导言设f(x)~1/2α_0+sum from n=1 to ∞(α_ncos nx++b_nsin nx),帕蒂于[1]中证明了: 定理A.设f(x)是一个周期2π的可积周期函数。{λ_n}是一个凸的数列,它满足∑n~(-1)λ_n<∞。则当x_0是f(x)的勒贝格点时,级数1/2α_0λ_0+sum from n=1 to ∞λ_n(α_ncos nx_0+b_nsin nx_0)是

The shallow elliptical shell has different curvature in two principal directions, and is more complicate in analysis than spherical shell. Practical methods are available to compute the maximum bending moments and membrane direct forces when the shell is uniformly loaded. But from the viewpoint of shell design, the effective method to determine maximum twisting moments and membrane shear forces about the corners of shell are urgently needed. In the present paper, using the technique of substituting a double...

The shallow elliptical shell has different curvature in two principal directions, and is more complicate in analysis than spherical shell. Practical methods are available to compute the maximum bending moments and membrane direct forces when the shell is uniformly loaded. But from the viewpoint of shell design, the effective method to determine maximum twisting moments and membrane shear forces about the corners of shell are urgently needed. In the present paper, using the technique of substituting a double Fourier series by a double Fourier integral, simple formulas for the twisting moments and for the membrane shear forces are obtained readily. The accuracy of formulas and the rapid convergency of the series involved are fully discussed and proved to be satisfied.

本文用化二重Fourier级数为二重Fourier积分的方法,考虑了矩形底椭球面扁壳在角点附近扭矩和薄膜剪力的简化计算。在角点上的扭矩和薄膜剪力为全壳最大,它们的公式(3.1)和(3.14)也很容易进行计算。对角点附近的扭矩和薄膜剪力也得到了收敛很快的级数,并对级数的收敛性作了严格的证明。对于球面扁壳这种特殊情况,本文的结果与文献[4]的结果一致。

 
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