fourier theorem 中文意思是什麼
fourier theorem
解釋
傅里葉定理-
The following topics are covered in the course : complex algebra and functions ; analyticity ; contour integration, cauchy ' s theorem ; singularities, taylor and laurent series ; residues, evaluation of integrals ; multivalued functions, potential theory in two dimensions ; fourier analysis and laplace transforms
本課程包含下列各項主題：復數代數與函數；可解析性；輪廓積分；柯西定理；奇異性，泰勒與羅倫茲級數，留數，積分的運算；多值函數，二維的勢能理論；傅立葉分析與拉普拉斯轉換。 -
Discussion question : produce a plausible justification of nyquist ' s theorem based on the fourier analysis information given in the lecture
討論問題：請根據課文中給出的傅里葉分析知識證明尼奎斯特定理。 -
Thus the resistance factor and vibration modes of the soil layer are obtained and used to analysis the pile response. by considering the interaction between the soil layer and the pile with boundary condition of continuity of displacement and equilibrium of force at the interface of soil layer and pile, the dynamic equilibrium equation of pile is solved and an analytical solution for the pile response in frequency domain is yielded, which is used to define complex stiffness and mobility at the level of the pile head. based on the convolution theorem and inverse fourier transform, a semi - analytical solution of velocity response in time - domain subjected to a semi - sine exciting force is given
首先通過引入勢函數方法對土體位移進行分解，從而將土體動力平衡方程解耦，求解得到了土層的振動模態和阻抗因子，然後利用該解以小應變條件下樁土接觸面上力平衡和位移連續條件來考慮樁土耦合作用，求解樁的動力平衡方程，得到了樁頂的頻域響應解析解、復剛度和速度導納，利用卷積定理和傅里葉逆變換，求得了半正弦脈沖激振力作用下樁頂速度時域響應半解析解。 -
The traditional beam propagation algorithm based on fast fourier transform fails to give right results due to the limitation of the sampling theorem
由於取樣定理的限制，常規的基於快速傅里葉變換（ fft ）光束傳輸模擬演算法不能進行任意焦距聚焦光束的傳輸過程的模擬。 -
Integral theorem of fourier
傅里葉積分公式 -
We apply this condition and elementary properties of fourier series to prove a uniqueness theorem for periodic solutions of a class of second order nonlinear ordinary differential systems
我們應用這個條件和傅立葉級數的基本性質證明了二階非線性常微系統周期解的唯一性定理。 -
The main work and achievements are summarized as follows : according to the spectrum analysis theory, the simple formula of the power spectrum between the excitation and the response is obtained. then the time - domain statistical properties of the structural response are acquired through fourier inverse transform, and cauchy ' s residue theorem is applied to solving the integral of fourier inverse transform, the structural dynamic reliability is calculated in terms of possion hypothesis based on first passage failure
主要研究內容如下：從譜分析理論出發，得到了激勵與響應功率譜之間的簡明關系式，由fourier逆變換得到響應的時域特徵，利用cauchy留數理論處理fourier逆變換的積分式，基於首超破壞的possion假設計算結構系統的動力可靠性，並在此基礎上進行結構優化設計，奠定了確定性模型的基礎。
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