發(fā)布時間：2018-11-23 06:49

【摘要】：復(fù)變函數(shù)是在研究電學(xué)、流體力學(xué)、空氣動力學(xué)、理論物理和熱力學(xué)中發(fā)展起來的。數(shù)學(xué)學(xué)科的其他分支和復(fù)變函數(shù)理論有著緊密的聯(lián)系。例如初等函數(shù)的本質(zhì)只有在復(fù)變函數(shù)中方能充分揭示。復(fù)變函數(shù)的應(yīng)用非常廣泛。在力學(xué)、工程力學(xué)及物理學(xué)的研究中,復(fù)變函數(shù)起到了關(guān)鍵的作用。本文的主要內(nèi)容分為四個小節(jié)。第一節(jié)首先介紹了雙解析函數(shù)理論的產(chǎn)生背景,發(fā)展以及國內(nèi)外研究現(xiàn)狀。其次介紹了Schwarz-Pick不等式以及有界解析零函數(shù)n階導(dǎo)數(shù)估計(jì)式的發(fā)展概況,最后闡述了本論文研究的內(nèi)容和意義。第二節(jié)主要研究了雙解析函數(shù)的卷繞數(shù)定理及其推論。本節(jié)首先介紹了一些相關(guān)的概念及性質(zhì),其次引用了雙解析函數(shù)的性質(zhì),類比解析函數(shù)的卷繞數(shù)定理,得到了雙解析函數(shù)的卷繞數(shù)定理,最后給出了雙解析函數(shù)卷繞數(shù)定理的三個推論。第三節(jié)主要研究了兩動點(diǎn)上雙曲導(dǎo)數(shù)下的Schwarz-Pick不等式。本節(jié)首先構(gòu)造了兩個解析映射,且證明了該解析映射符合Schwarz-Pick條件。其次給出了兩動點(diǎn)上雙曲導(dǎo)數(shù)下較強(qiáng)的Schwarz-Pick不等式,最后證明了兩動點(diǎn)上雙曲導(dǎo)數(shù)下更強(qiáng)的Schwarz-Pick不等式。第四節(jié)主要研究了有界零函數(shù)的n階導(dǎo)數(shù)估計(jì)問題。本節(jié)首先在已有的n階導(dǎo)數(shù)估計(jì)式的基礎(chǔ)上,得到了更精確的n階導(dǎo)數(shù)估計(jì)式。其次將文中得到的n階導(dǎo)數(shù)估計(jì)式與已有結(jié)論做了精確性對比,證實(shí)了本文估計(jì)式的精確性。
[Abstract]:Complex function is developed in the study of electricity, hydrodynamics, aerodynamics, theoretical physics and thermodynamics. Other branches of mathematics are closely related to the theory of complex function. For example, the essence of elementary functions can only be fully revealed in complex functions. Complex function is widely used. Complex function plays a key role in the study of mechanics, engineering mechanics and physics. The main content of this paper is divided into four sections. The first section introduces the background, development and research status of bianalytic function theory. Secondly, the development of Schwarz-Pick inequality and n-order derivative estimator of bounded analytic zero function is introduced. Finally, the content and significance of this paper are expounded. In the second section, we study the winding number theorem of bianalytic functions and its corollary. In this section, we first introduce some related concepts and properties, then we introduce the properties of bianalytic functions, compare the winding number theorems of analytic functions, and obtain the winding number theorems of bianalytic functions. Finally, three corollaries of the twin-analytic function winding number theorem are given. In the third section, we study the Schwarz-Pick inequality under the hyperbolic derivative of the two moving points. In this section, we first construct two analytic mappings and prove that the analytic mappings conform to the Schwarz-Pick condition. Secondly, the stronger Schwarz-Pick inequality under the hyperbolic derivative is given, and finally, the stronger Schwarz-Pick inequality under the hyperbolic derivative is proved. In the fourth section, the problem of n-order derivative estimation of bounded zero functions is studied. In this section, a more accurate estimate of n-order derivative is obtained based on the existing n-order derivative estimators. Secondly, the accuracy of the n-order derivative estimator obtained in this paper is compared with the existing results, which proves the accuracy of the estimator in this paper.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O174.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 胡琳;曾招云;;雙解析函數(shù)Schwarz問題的2種新解法[J];南昌大學(xué)學(xué)報(bào)(工科版);2012年04期

2 朱景文;劉詩煥;;雙解析函數(shù)的一點(diǎn)注記[J];井岡山大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年05期

3 張敏;苑文法;;雙曲度量下導(dǎo)數(shù)的Schwarz-Pick不等式(英文)[J];西安文理學(xué)院學(xué)報(bào)(自然科學(xué)版);2011年02期

4 任新安;;從調(diào)和函數(shù)看解析函數(shù)的性質(zhì)[J];數(shù)學(xué)教學(xué)研究;2010年07期

5 戴紹虞;潘一飛;;有界解析函數(shù)的n階導(dǎo)數(shù)估計(jì)[J];數(shù)學(xué)雜志;2010年02期

6 馮春強(qiáng);徐裕生;劉勇;苑文法;;有界函數(shù)的導(dǎo)數(shù)(英文)[J];紡織高校基礎(chǔ)科學(xué)學(xué)報(bào);2007年02期

7 林蓉;雙解析函數(shù)的傅里葉級數(shù)[J];三明高等�？茖W(xué)校學(xué)報(bào);2004年02期

8 王明華;雙解析函數(shù)的Riemann邊值逆問題(英文)[J];四川師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2003年02期

9 侯光仁;雙解析函數(shù)的幾個問題[J];延安大學(xué)學(xué)報(bào)(自然科學(xué)版);2002年04期

10 曾岳生;有界區(qū)域上雙解析函數(shù)的積分表示[J];懷化師專學(xué)報(bào);2002年02期

相關(guān)碩士學(xué)位論文 前3條

1 傅玉狀;解析函數(shù)與雙解析函數(shù)的相關(guān)問題研究[D];西安建筑科技大學(xué);2015年

2 李曉焱;雙解析函數(shù)與解析函數(shù)一些問題的研究[D];西安建筑科技大學(xué);2014年

3 苑文法;有界正則函數(shù)導(dǎo)數(shù)及系數(shù)估計(jì)[D];西北工業(yè)大學(xué);2002年

，

本文編號：2350669