cauchy theorem 中文意思是什麼
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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。 -
We reduce the cauchy problem of equations ( 8 ), ( 9 ) to an equivalent integral equations by the fundamental solution of a second order partial differential equation. then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution
先是通過一個二階偏微分方程的基本解，把imbq型方程組歸） ， p ）的初值問題轉化為等價的積分方程組，然後利用壓縮映射原理、解的延拓定理等證明了歸） ，問的初值問題的整體廣義解和整體古典解的存在唯一性 -
The proof of the generalized cauchy mean - value theorem with method of interpolation
利用插值法證明推廣的柯西中值定理 -
Based on the rolle mid - value theorem, by using determinant method, the lagrange mid - value theorem and cauchy mid - value theorem are obtained, and some new results are discovered
本文從羅爾中值定理出發，這用行列式理論，不僅證明了拉格朗日中值定理和柯西中值定理，還發現了一些新的結論。 -
Lagrange and cauchy differential mean value theorem on open interval are obtained based on generalized roll ' s theorem, which make it more expedient to study general character of function defined on open interval by means of derivative
摘要基於推廣的羅爾中值定理，得到有限開區間上的拉格朗日中值定理及柯西中值定理，使得利用導數研究開區間上函數的整體性態更為方便。 -
Using riemann - schwarz ' s symmetry principle of complex functions, the above problems are transformed into riemann - hilbert boundary problems. by combining the analysis of singularity of complex functions, generalized liouville ' s theorem, cauchy model integral and residue theorem, the general solutions of above problems are presented
創造性運用復變函數解析延拓原理，將上述問題轉化為riemann - hilbert邊值問題，結合復應力函數奇性主部分析方法、廣義liouville定理、 cauchy型積分和留數定理，獲得了上述問題的一般解答。 -
We also give out the notion of mild degenerate a - times integrated existence family, and prove that the wellposedness of the a - times abstract cauchy problems is equivalent to mild degenerate a - times integrated existence famliy generated by operator a where a satisfies with some conditions and degenerate a - times integrated semigroups mild generated by a. at last, we conclude the generation theorem of degenerate a - times integrated semigroups. and we prove that degenerate a - times integrated semigroups mild generated by a is equivalent to generated by a
我們也給出了mild退化-次積分存在族的概念。我們證明了， （ + 1 ） （ r ） -次抽象cauchy問題的適定性和閉線性運算元a在一定條件下， a的mild退化-次積分存在族以及a次生成退化的-次積分半群是等價的。最後，我們也給出了退化-次積分半群的生成定理。 -
Similarly, we prove that the c - wellposedness of the a - times abstract cauchy problems is equivalent to mild degenerate a - times integrated c - existence famliy mild generated by operator a where a satisfies with some conditions and degenerate a - times integrated semigroups mild generated by a. finally, we obtain the generation theorem of degenerate a - times integrated c - semigroups. and we prove that degenerate a - times integrated c - semigroups mild generated by a is equivalent to generated by a
我們同樣證明了（ + 1 ） （ r ） -次抽象cauchy問題的c -適定性和閉線性運算元a在一定條件下，其mild退化-次積分c存在族以及a次生成退化-次積分正則半群是等價的。我們也證明了退化-次積分正則半群的生成定理。 -
In the nineteenth century, when researchers began to pay attention to the analysis strictness in mathematics, cauchy put forward major series technique, which was confirmed highly effective in applying it to the convergence analysis of iterations. there are three kinds of convergence theorems which related to iterative method, a ) local convergence theorem, b ) semilocal convergence theorem, c ) global convergence theorem
對于迭代法收斂性的研究，數值工作者們做了大量的工作（見文後的參考文獻） ，但我們知道與迭代過程相關的收斂性定理通常有三種類型： a ）局部的； b ）半局部的； c ）全局的或整體的收斂性定理。 -
Cauchy residue theorem
柯渦數定理 -
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。 -
Cauchy integral theorem
柯錫分定理
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