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extremal

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extremal n.【數學】極值曲線，致極函數。

n. 【數學】極值曲線，致極函數。 “accessory extremal“ 中文翻譯：   配連極值“extremal arc“ 中文翻譯：   極值弧“extremal coding“ 中文翻譯：   極值編碼“extremal curve“ 中文翻譯：   極值曲線“extremal distance“ 中文翻譯：   極值距離“extremal distrbution“ 中文翻譯：   極值分布“extremal element“ 中文翻譯：   極值元素“extremal field“ 中文翻譯：   極值場“extremal function“ 中文翻譯：   極值函數“extremal graph“ 中文翻譯：   極端圖; 極圖“extremal length“ 中文翻譯：   極值長度“extremal point“ 中文翻譯：   極值點“extremal property“ 中文翻譯：   極值性質“extremal sensing“ 中文翻譯：   終極感測“extremal solution“ 中文翻譯：   極值解“extremal sport“ 中文翻譯：   極端運動片“extremal subset“ 中文翻譯：   端子集“extremal surface“ 中文翻譯：   極值曲面“extremal vector“ 中文翻譯：   極揣向量; 極端向量“relative extremal“ 中文翻譯：   相對極線“secondary extremal“ 中文翻譯：   配連極值“weak extremal“ 中文翻譯：   弱極值“analogue extremal system“ 中文翻譯：   模擬極值系統“constrained extremal problem“ 中文翻譯：   帶約束極值問題“extremadura“ 中文翻譯：   埃斯特雷馬杜拉; 度拉; 極端報“extremadouro“ 中文翻譯：   埃克斯特雷馬多羅

extreme

The first section of this paper gives a brief introduction about the basic concepts , terminology and symboles which are used in this paper . in section 2 , we give an accurate discussion about the structure of a kind of graphs in [ 6 ] and get the extremal graph . in the third section , we introduce a new concept - - - - implicit weighted degree and using it we give a condition on the existence of heavy cycles in weighted graphs 在本文的第一部分中，我們簡要介紹了論文中所涉及的一些概念，術語和符號；在第二部分中，我們對中圖的結構進行了精確的討論，給出了一個極圖；在第三部分，我們定義了一個新參數?隱賦權度，給出了賦權圖中重圈存在的隱賦權度條件；最后，在第四部分，我們給出了賦權圖中過兩點的重圈存在性的dirac型條件。

Only a few have studyed family of problems . we extend the work in [ 26 ] - [ 27 ] . first , under the classical assumption that ( t ) ( t ) , we consider the periodic boundary value problem , when / is independent of x ( t ) . second , under the case that ( t ) ( t ) , we consider the periodic boundary value problem and describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to periodic boundary value problems , when / depends on x ( t ) 氣t )這一項的邊值間題更是如此，基于此，我們把微分方程方面的結果推廣到時間模上.首先考慮在下解小于上解的情況下， f不含。 ( t )這一項的周期邊值問題，而后在下解大于上解的情況下，考慮了含有、 ( t )這一項的周期邊值問題，描述了一種構造性方法，構造了兩個單調序列其一致收斂到二階周期邊值問題的極值解

From these - two forms , we determine the automorphism group aut ( h ) of the ( 2n + 1 ) - dimensional heisenberg lie algebra h ( see theorem1 . 1 ) . moreover , some subgroups of aut ( h ) are obtained , such as the inner automorphism group , the central automorphism group , the involutional automorphism group , the first and the second extremal automorphism group 第一部分安排如下：首先給出了heisenberg李代數的兩種定義形式，由這兩種定義形式，我們得到了( 2n + 1 )維heisenberg李代數h的自同構群aut ( h ) (定理1 . 1 ) ；進而給出了aut ( h )的一些子群：內自同構群，中心自同構群，對合自同構群，第一類外自同構群，第二類外自同構群。

In this chapter , firstly , we apply a result of [ 20 ] to prove that for a class of quasisymmetric homeomorphisms with substantial boundary points , the maximal dilatation of the extremal quasiconformal extension equals the supremum of the ratios of the moduli of quadrilaterals , which improve the result of [ 148 ] 在本章中，我們首先利用了文[ 20 ]的結果，研究了單位圓周上一類具有本質邊界點的擬對稱同胚，證明了它的極值擬共形延拓的最大伸縮商等于四邊形模之比的上確界，改進了文148的有關結果

According to the quasi - invariance of the moduli of quadrilaterals under quasiconformal mappings , it is natural to think of approximating the maximal dilatation of the extremal quasiconformal mapping by the ratios of the moduli of quadrilaterals . a key problem is : is it true that the supremum of the ratios of the moduli of quadrilaterals equals the maximal dilatation of the extremal quasiconformal mapping 根據擬共形映射下四邊形模的擬不變性，利用四邊形模之比來逼近它是人們比較容易想到的方法，但關鍵的問題是四邊形模之比的上確界是否等于極值映射的最大伸縮商

Determining the extreme values and extremal functions of the analytic functions on d = { z $ c : z < 1 } is very important in the principles of univalent functions . baernstein [ 2 ] gave the conclusion by using koebe function as the extremal function , glenn schober [ 6 ] studied the classes such as s , p , k , s * of h ( d ) and represented these functions with integral formulations . wang jian [ 3 ] and others investigated the integral mean values Baernstein首先在單位圓上討論給出了以koebe函數作為極值函數的結論， glennschober對h ( d )中一些函數子類如s 、 p 、 k 、 s ~ *等作了研究，將這些子類上的函數用積分表達出來，王鍵結合baernstein ~ *函數的定義及glennschober的結論，定義了對稱集的概念并得出了一些函數類在其上的積分平均。

This chapter is devoted to the exposition of the basic theory of quasiconformal mappings , of the development and the research situation of the theory of extremal quasiconformal mappings and the theory of schwarzian derivatives ( including nehari families and the extremal set of schwarzian derivatives ) . the main results of this ph . d . dissertation are briefly introduced in this chapter 在這一章中，我們簡單介紹了擬共形映射的基本理論，擬共形映射極值問題、 schwarz導數理論(包括有關的nehari族與schwarz導數的極值集)的發展歷史與研究現狀，并對論文的主要結果給以簡單介紹。

In this chapter , we first recall the development and the research situation of the theory of uniquely extremal quasiconformal mappings , mainly introduce and analyse the significant results obtained by bozin v . , lakic n . , markovic v . and mateljevic m . [ 14 ] in 1998 . then we study the characteristics of uniquely extremal quasiconformal mappings , and obtain some criterions of uniquely extremality which are different from the results of [ 14 ] [ 14 ]關于唯一極值擬共形映射的研究成果，分析他們的這些極富創新意義的結果，在此基礎上我們主要研究了唯一極值擬共形映射的特征刻劃，得到了一些重要的和文[ 14 ]互不包含的刻劃唯一極值擬共形映射的結果。

In this thesis , we consider the following three aspects : first , we compute the bergman kernel functions with explicit formulas on generalized hna domains ; second , we obtain the explicit formulas for extremal maps and extremal values between the ball and the super - cartan domain of the first type ; finally , we give sufficient conditions and necessary conditions that holomorphic functions become bloch functions on super - cartan domains 在這篇論文中，我們討論了三個方面的內容：第一部分我們給出了四類廣義華羅庚域的bergman核函數的顯表達式；第二部分我們得到了第一類超cartan域與單位超球間的極值與極值映照；第三部分我們給出了四類超cartan域上全純函數是bloch函數的充分條件與必要條件。

And with the results of calculation obtained by the first - order gradient algorithms which is initial value of the neighboring extremal algorithms we can transform the problem into a face to point one , then a good result is attained by the neighboring extremal algorithms . in the end , the course of orbit transfers is depicted 利用梯度法對兩點邊值問題進行計算，將面對面的問題轉化為一個點對點問題，將所得結果作為鄰近極值法的初始值并進行精確計算。最后，描繪了最優變軌過程。

Combination of this lemma and the hamilton - connectivity involving neighborhood intersection obtains and improves or generalizes a series of classical results involving hamilton - connectivity , at the same time , we construct some extremal graphs to show the improved results to be the best possible ones . as for hamiltonicity , we omit the similar discussion 由于每一個偶階哈密爾頓連通圖是o -因子-臨界的，我們在最后一章中我們主要涉及哈密爾頓連通性，利用一個重要的引理，我們得到了一些新結果，并且改進了或推廣了一些經典結論。

The conclusion which , for a given non - extremal admissible control , another admissible control can be constructed such that the corresponding value of the objective functional decreases is proved , based on the result , an optimality condition is obtained and the strong variational method which solves optimal control problem is presented and the associated convergence result is proved also 證明了對任一非極值允許控制函數，均可構造另一允許控制函數，使最優控制問題相應的目標泛函值有一下降量。在此基礎上得到了最優控制問題最優性必要條件，并給出了求解該最優控制問題的強變分法及算法的收斂性結果。

In the fourth and fifth chapters of this paper , we discuss the schwarzian derivatives of analytic functions , the nehari families and the extremal set of schwarzian derivatives , and apply the obtained results to determine the inner radius of univalence of rectangles and hexagons with equal angles 在第四章和第五章中，對解析函數的schwarz導數和nehari族以及schwarz導數的極值集作了深入細致的研究，并且利用所得到的結果研究了矩形、等角六邊形的單葉性內徑問題。

Along with a price limit and capital requirement , the existence of a margin decrease the likelihood of a customer defaulting , a broker going bankrupt and systemic instability of the futures market . this paper applies sub - theories of generalized pareto distribution inherited from extreme value theory to examine the margin policy for price extremal movements 本文運用極值理論的廣義帕累托分布( gpd ) ,對以上證180指數和深證100指數為標的的股指期貨保證金進行了研究,并且將之與正態分布假設下的保證金水平進行比較。

Eventually , one may remove the large parameter a from the auxiliary problems by fredholm - riesz - schauder theory and extremal principle . thus the well - posedness and the regularity of the original problem will be obtained in a standard way . for the sake of convenience , we introduce some symbols 最后，利用跡定理和局部化技巧可以把問題在每個區域上的解拼起來，從而得到該類問題在整個一般區域上的hl弱解存在唯一性及解的高階正則性和高階模估計

In the family of quasiconformal mappings with given boundary correspondence , the extremal mapping must exist , but may be not unique . when is the extremal mapping unique , or what is the characteristic of uniquely extremal quasiconformal mapping is always the key problem 在這一章中，我們首先簡要回顧了對唯一極值擬共形映射研究的已有結果和最新進展，重點介紹了1998年bozinv . ， lakicn ， markovicv ，和mateljevic ： m

In this article , we study the infinite boundary value problems for first order nonlinear impulsive differential equations with “ supremum “ by means of the upper and lower solution method and the monotone iterative technique , and obtain the existence theorems for their extremal solutions 摘要應用上下解方法和單調迭代技術研究了帶有上確界的一階非線性脈沖微分方程無窮邊值問題，并獲得了其極值解的存在性結果。

The theory of extremal quasiconformal mappings is mainly concerned with the problems of existence and uniqueness of extremal quasiconformal mappings with given boundary correspondence and of the properties and characteristics of extremal quasiconformal mappings 擬共形映射極值理論主要討論給定邊界對應的擬共形映射族中極值映射的存在性、唯一性、及極值映射的性質與特征刻劃等問題。

Abstract : by applying the matrix rank method , in this note , the general expressions of the common least - square solutions to the matrix equations ax = c , xb = d is deduced , the extremal ranks of the common least - square solutions is obtained 文摘:通過使用矩陣秩方法,我們給出了矩陣方程組ax = c , xb = d的公共最小二乘解的通解表達式,以及公共最小二乘解的極大秩和極小秩