• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    SEVERAL UNIQUENESS THEOREMS OF ALGEBROID FUNCTIONS ON ANNULI?

    2016-04-18 05:44:46YangTAN譚洋SchoolofAppliedMathematicsBeijingNormalUniversityZhuhai519087China
    關(guān)鍵詞:誤工施工隊(duì)崗位培訓(xùn)

    Yang TAN(譚洋)School of Applied Mathematics,Beijing Normal University,Zhuhai 519087,China

    ?

    SEVERAL UNIQUENESS THEOREMS OF ALGEBROID FUNCTIONS ON ANNULI?

    Yang TAN(譚洋)
    School of Applied Mathematics,Beijing Normal University,Zhuhai 519087,China

    E-mail:shutongtan@sina.com

    AbstractIn this paper,we discuss the uniqueness problem of algebroid functions on annuli,we get several uniqueness theorems of algebroid functions on annuli,which extend the Nevanlinna value distribution theory for algebroid functions on annuli.

    Key wordsthe Nevanlinna theory;multiple values;the uniqueness of algebroid functions on annuli

    2010 MR Subject Classi fi cation34M10;30D35

    ?Received September 9,2014;revised June 16,2015.Project Supported by the Natural Science Foundation of China(11171013).

    1 Introduction

    In 1926,Nevanlinna[1]proved the following famous fi ve-value theorem:

    For two nonconstant meromorphic functions f(z)and g(z)on the complex plane C,

    if they have the same inverse images(ignoring multiplicities)for fi ve distinct values,

    then f(z)≡g(z).

    After this wonderful work,the uniqueness theory of meromorphic functions in C attracted many investigations[2-5].As the extension of meromorphic functions,the uniqueness of algebroid functions in the complex plane C is an important subject in the value distribution theory.The uniqueness problem of algebroid functions was firstly considered by Valiron,afterwards some scholars got several uniqueness theorems of algebroid functions in the complex plane C[6-13].In 2005,Khrystiyanyn and Kondratyuk proposed the Nevanlinna theory for meromorphic functions in multiply connected domains[14,15].In 2009,Cao and Yi[16]investigated the uniqueness of meromorphic functions sharing some values and some sets on annuli.Thus it is interesting to consider the uniqueness problem of algebroid functions in multiply connected domains.In this paper,we mainly study doubly connected domain.We assume that the readers are familiar with the Nevanlinna theory of meromorphic functions and algebroid functions[17-27].By the doubly connected mapping theorem[28]each doubly connected domain is conformally equivalent to the annulus A(R1,R2)={z:R1<|z|<R2},0≤R1<R2≤+∞.We only consider two cases:

    In the latter case the homothetyreduces the given domain to the annulusThus,in two cases every annulus is invariant with respect to the inversion

    2 Basic Notions and De finitions

    Let Av(z),Av?1(z),···,A0(z)be a group of holomorphic functions which have no common zeros and de fi ne on the annulus

    Then irreducible equation(2.1)de fines a v-valued algebroid function on the annulus(1<R0≤+∞).

    Let W(z)be a v-valued algebroid function on the annulususe the notations:

    where wj(z)(j=1,2,···,v)is a one-valued branch of W(z),n1(t,W)is the counting function of poles of the function W(z)in{z:t<|z|≤1}and n2(t,W)is its counting function of poles in{z:1<|z|≤t}(both counting multiplicity);is the counting function of poles of the functionis its counting function of poles in{z:1<|z|≤t}(both ignoring multiplicity);is the countingfunction of poles of the functionwith multiplicity≤k(or>k)in{z:t<|z|≤1},each point counts only once;is the counting function of poles of the functionwith multiplicity≤k(or>k)in{z:1<|z|≤t},each point counts only once.nx1(t,W)and nx2(t,W)are the counting function of branch points of the function W(z)in {z:t<|z|≤1}and{z:1<|z|≤t},respectively.Nx(r,W)is the density index of branch point of W(z)on the annulus

    Let W(z)be an algebroid function on the annulusif there are λ branches of W(z)which take a(∞)as the value in z0point,then we have the fractional power series

    n0(r,a)=where n0(r,a)is the counting function of zeros of W(z)?a on the annulus(counting multiplicity).If there are λ branches of W(z)which take∞as the value in z0point,then we have the fractional power series

    n0(r,∞)=n0(r,W)=where n0(r,∞)is the counting function of poles of W(z)on the annulus(counting multiplicity).z=z0is a branch point of λ?1 degree of W(z)on its Riemann Surfacedenotes the branch points of W(z)on its Riemann Surface on the annulus

    Let W(z)be a v-valued algebroid function which be determined by(2.1)on the annulusWhen a =∞,N0(r,W)=are the counting function of zeros of W(z)?a and ψ(z,a)on the annulus

    De finition 2.1Let W(z)be an algebroid function on the annulus+∞),the function

    is called the Nevanlinna characteristic of W(z).

    De finition 2.2Let W(z)be an algebroid function on the annulus+∞),we denote the de fi ciency of a∈C=C∪{∞}by

    and denote the reduced de fi ciency by

    3 Some Lemmas

    Lemma 3.1(see[14])Let f be a nonconstant meromorphic function on the annulus

    where 1≤r<R0.

    Lemma 3.2([14],Jensen theorem for meromorphic function on annuli)Let f be a nonconstant meromorphic function on the annulus

    where 1≤r<R0.

    Lemma 3.3Let W(z)be a v-valued algebroid function which is determined by(2.1)on the annulus

    ProofFirst,we have

    So,from above determinant we know that J(z)is a holomorphic function on the annulus.In fact,by(2.2),if there are λ branches of W(z)which take a∈C as the value in z0point,then there areitems including the factorin J(z)(τ is the multiplicity of zero),that is:z0is a zero of J(z),the multiplicity of z0isat least.That is to say,the branch points of λ?1 degree of W(z)are zeros of λ?1 degree of J(z)atleast.So(3.1)is true.By substitutinginto J(z),using Lemma 3.2,we get

    So we have

    Lemma 3.4(the first fundamental theorem for algebroid function on annuli)Let W(z)be a v-valued algebroid function which is determined by(2.1)on the annulusR0≤+∞),a∈C,

    ProofBy Viete theorem,we have

    Using Lemma 3.2,we get

    Among them

    because

    So

    Lemma 3.5(the second fundamental theorem for algebroid function on annuli)Let W(z)be a v-valued algebroid function which is determined by(2.1)on the annulusR0≤+∞),ak(k=1,2,···,p)are p distinct complex numbers(finite or in finite),then we have

    N1(r,W)is the density index of all multiple values including finite or in finite,every τ multiple value counts τ?1,and

    ProofLet ak∈C(k=1,2,···,p),wj=wj(z)(j=1,2,···,v)are v branches of W(z),by the following identity

    Ck=[(a1?ak)(a2?ak)···(ak?1?ak)(ak+1?ak)···(ap?ak)]?1,w′(z)is the derivative of w(z)and satisfies the following equation

    By(3.4),

    Among them,

    So we have

    Let

    So we get

    其次,在施工前期,管理人員對(duì)公路工程的具體施工設(shè)計(jì)和人員安排無(wú)法做到合理調(diào)配,導(dǎo)致在施工現(xiàn)場(chǎng)工作人員崗位不定,現(xiàn)場(chǎng)混亂,工序復(fù)雜,工期拖延,最終出現(xiàn)延工、誤工的現(xiàn)象[3]。而且部分施工隊(duì)的進(jìn)度控制意識(shí)薄弱,無(wú)法按照施工計(jì)劃在規(guī)定時(shí)間內(nèi)完成施工任務(wù)。個(gè)別施工隊(duì)為加快工程進(jìn)度,隨意增加施工人員,而部分施工人員由于沒(méi)有接受專業(yè)崗位培訓(xùn),匆忙上崗,造成部分已經(jīng)完工的工程質(zhì)量不合格,因無(wú)法通過(guò)質(zhì)量驗(yàn)收而必須返工,不僅拖延工期更增加了施工成本。

    By(3.9),(3.10),(3.11)

    Combining(3.6),(3.7),(3.8),(3.12)and using Lemma 3.4 we have

    And because

    Then

    By(3.13)and above formula

    Because N0(r,W)≤T0(r,W)+O(1),so(3.14)can be rewritten as the following

    So we get(3.16).By substituting(3.16)into(3.15)we have

    By(3.17)and Lemma 3.3,we get(3.3).

    The remainder of the Second Fundamental Theorem is the following formula,

    outside a set of finite linear measure,if r?→R0=+∞;while

    outside a set E of r such that

    We notice that the following formula is true,

    Lemma 3.6(the Cartan theorem for algebroid function on annuli)Let W(z)be a v-valued algebroid function which is determined by(2.1)on the annulusthen we get

    ProofLet a be a finite complex number,then we have[2,22]

    By(2.1)

    We integrate(3.21)on α from 0 to 2π and by(3.20),

    By(3.23),(3.24)and(3.25),

    By(3.26)and(3.27),(3.19)is true.

    Lemma 3.7Let W(z)be a v-valued algebroid function which be determinated by(2.1)on the annulusif the following conditions are satis fied

    then W(z)is an algebraic function.

    So we have

    Because therefore

    So we get

    On the other hand,there is the following formula by Viete theorem of algebraic equation

    where(α1,α2,···,αv?j)is the combination of taking v?j numbers from(1,2,···,v),(?1)αis 1 or-1,which depends onbeing even permutation or odd permutation.Now everyby(3.34),

    The right hand side of(3.35)has nothing to do with number j,so any(1<R0≤+∞)

    Then we get

    So according to(3.33)and(3.37),we have

    According to(3.38)and(3.39),we have

    By the conditions of Lemma 3.7 and above formula,all meromorphic functions fjk(z)(0≤j,k≤v)which satisfy the following conditions

    By references[14,15]and[22],all functions fjk(z)are rational functions,because A0(z),A1(z),···,Av(z)can’t have nonconstant common factor,so all Aj(z)(j=1,2···v)must be polynomials.Then W(z)degenerates an algebraic function.

    Remark 3.8Let W(z)be an algebroid function on the annulus+∞)and let a be a complex number.We useto denote the set of zeros of W(z)?a with multiplicity no greater than k,in which each zero is counted only once.

    Remark 3.9Now let W(z)be a v-valued algebroid function which is determined by(2.1)on the annulusbe aμ-valued algebroid function which is determined by the following equation on the annulus

    Without loss of generality,letdenotes the counting function of the common values of=a with multiplicity≤k on the annulus+∞),each point counts o︿nly once.And let

    4 Main Results

    Furthermore let

    and

    where m and n are positive integers in(1,2,···q)and b is an arbitrary complex number.If

    By De finition 2.2

    Because

    By De finition 2.2 we have

    From(4.6)and(4.7)

    From(4.4),(4.5)and(4.8)we get

    From(4.1)

    So we can deduce that

    Thus we have

    where

    By similar discussion we get

    where

    By(4.9),(4.10)and Remark 3.9

    R(?,ψ)denotes the resultant of ?(z,W)and ψ(z,W),it can be written as the following

    It can be written in another form

    So we know that R(?,ψ)is a holomorphic function,using Lemma 3.2,

    Then we get

    By the conditions of Theorem 4.1,we know that W(z)andtake the same values with multiplicity≤kjabout q distinct aj,each point counts only once,at the same time we getFrom(4.11),(4.12)and Remark 3.9

    Hence

    From Lemma 3.7 we know that this is not true.Therefore we complete the proof of Theorem 4.1.

    Set

    where m and n are positive integers in(1,2,···,q).If

    ProofSince δ0(aj,W)≥the assertion follows from Theorem 4.1.

    If

    where m is positive integer in(1,2,···q),then we have

    ProofLetting m=n,Corollary 4.3 immediately follows from Corollary 4.2.

    If

    ProofLetting m=4v+1,Corollary 4.4 immediately follows from Corollary 4.3.

    (ii)If q=8v and kj>1 then

    (iii)If q=7v and kj>2 then

    ProofWe note that

    Corollary 4.5 immediately follows from Corollary 4.4.

    Thus from Corollary 4.5 we obtain the theorem as following.

    References

    [1]Nevanlinna R.Einige eindeutigkeitss?tze in der theorie der meromorphen funktionen.Acta Math,1926,48(3/4):367-391

    [2]Yi H X,Yang C C.Uniqueness Theory of Meromorphic Function.Beijing:Science Press,1995

    [3]Ueda H.Unicity theorems for meromorphic or entire functions.Kodai Math,1980,3(3):457-471

    [4]Zhang Q C.The uniqueness of meromorphic functions with their derivatives.Kodai Math,1998,21(2):179-184

    [5]Bhoosnurmath S S,Dyavanal R S.Uniqueness and value-sharing of meromorphic functions.Comput Math Appl,2007,53(8):1191-1205

    [6]Sun D C,Gao Z S.On the operations of algebroid functions.Acta Math Sci,2010,30B(1):247-256

    [7]Sun D C,Gao Z S.Uniqueness theorem for algebroid functions.Journal of South China Normal University,2005,(3):80-85

    [8]Yi H X.On the multiple values and uniqueness of algebroid functions.Engineering Math,1991,8(4):1-8

    [9]Cao T B,Yi H X.On the uniqueness theory of algebroid functions.Southeast Asian Bull Math,2009,33(1):25-39

    [10]He Y Z.On the algebroid functions and their derivatives(I).Acta Mathematica Sinica,1965,15(2):281-295

    [11]He Y Z.On the algebroid functions and their derivatives(II).Acta Mathematica Sinica,1965,15(4):500-510

    [12]He Y Z.On the multiple values of algebroid functions.Acta Mathematica Sinica,1979,22(6):733-742

    [13]Xuan Z X,Gao Z S.Uniqueness theorems for algebroid functions.Complex Var Elliptic Equ,2006,51(7):701-712

    [14]Khrystiyanyn A Ya,Kondratyuk A A.On the Nevanlinna theory for meromorphic functions on annuli(I).Matematychni Studii,2005,23(1):19-30

    [15]Khrystiyanyn A Ya,Kondratyuk A A.On the Nevanlinna theory for meromorphic functions on annuli(II).Matematychni Studii,2005,24(2):57-68

    [16]Cao T B,Yi H X,Xu H Y,et al.On the multiple values and uniqueness of meromorphic function on annuli.Comput Math Appl,2009,58(7):1457-1465.

    [17]Sun D C,Gao Z S.Value Distribution Theory of Algebroid Functions.Beijing:Science Press,2014

    [18]Hayman W K.Meromorphic Functions.Oxford:Oxford University Press,1964

    [19]Yang L.Value Distribution Theory.Beijing:Science Press,1982

    [20]Tsuji M.Potential Theory in Modern Function Theory.Tokyo:Maruzen,1959

    [21]He Y Z,Gao S A.On algebroid functions taking the same values at the same points.Kodai Math,1986,9(2):256-265

    [22]He Y Z,Xiao X Z.Algebroid Functions and Ordinary Di ff erential Equations in the Complex Domain.Beijing:Science Press,1988

    [23]He Y Z,Li Y Z.Some results on algebroid functions.Complex Variables Theory Appl,2001,43(3/4):299-313

    [24]Sun D C,Gao Z S.On the operations of algebroid functions.Acta Math Sci,2010,30B(1):247-256

    [25]Liu H F.On the uniqueness of algebroid functions and their derivatives.Acta Math Sci,2014,34A(5):1296-1303

    [26]Wang S M.On the fundamental theorems for reducible algebroid functions.Acta Math Sci,2014,34A(5):1219-1227

    [27]Jiang Y B,Gao Z S.Uniqueness of algebroid functions concerning CM shared values.Acta Math Sci,2014,34A(4):796-801

    [28]Axler S.Harmonic functions from a complex analysis viewpoint.Amer Math Monthly,1986,93(4):246-258

    猜你喜歡
    誤工施工隊(duì)崗位培訓(xùn)
    加入倫敦施工隊(duì)
    審計(jì)誤工補(bǔ)貼背后的故事
    拆錯(cuò)房子
    分析影響社區(qū)護(hù)士崗位培訓(xùn)效果的相關(guān)因素
    警惕村集體誤工支出亂象
    試論農(nóng)民工誤工賠償?shù)臉?biāo)準(zhǔn)的適用范圍爭(zhēng)議
    法制博覽(2017年30期)2017-01-27 14:08:06
    村集體誤工支出管理與賬務(wù)處理
    驚蟄
    全科醫(yī)師崗位培訓(xùn)中神經(jīng)病學(xué)的教學(xué)體會(huì)
    編輯有感——基于崗位培訓(xùn)和編輯實(shí)踐的感悟
    国产成年人精品一区二区| 国产免费一级a男人的天堂| 99热6这里只有精品| 一边摸一边抽搐一进一小说| 久久99热这里只有精品18| 久久精品国产亚洲av香蕉五月| 国产精品无大码| av在线亚洲专区| 国产激情偷乱视频一区二区| 国产在视频线在精品| 国产片特级美女逼逼视频| or卡值多少钱| 免费av毛片视频| 精品一区二区三区人妻视频| 看黄色毛片网站| 亚洲av不卡在线观看| 午夜福利视频1000在线观看| 国产精品日韩av在线免费观看| 久久国产乱子免费精品| 熟女电影av网| 亚洲欧美成人精品一区二区| 真实男女啪啪啪动态图| 中文资源天堂在线| 免费av观看视频| 久久精品国产99精品国产亚洲性色| 可以在线观看的亚洲视频| 国产人妻一区二区三区在| 久久天躁狠狠躁夜夜2o2o| 在线观看午夜福利视频| 国产成人a∨麻豆精品| 久久久久久久午夜电影| 亚洲自拍偷在线| 午夜福利在线观看免费完整高清在 | 国产熟女欧美一区二区| 亚洲精华国产精华液的使用体验 | 联通29元200g的流量卡| 老司机福利观看| 最新在线观看一区二区三区| 成人av在线播放网站| 午夜激情欧美在线| 精品久久久久久久久久久久久| 国产综合懂色| 又爽又黄无遮挡网站| 国产人妻一区二区三区在| 非洲黑人性xxxx精品又粗又长| 亚洲欧美清纯卡通| 天天躁日日操中文字幕| 黄色视频,在线免费观看| 成人漫画全彩无遮挡| 99九九线精品视频在线观看视频| 久久精品国产99精品国产亚洲性色| 欧美zozozo另类| 18禁在线播放成人免费| АⅤ资源中文在线天堂| 亚洲av.av天堂| 成人国产麻豆网| 村上凉子中文字幕在线| 精品人妻偷拍中文字幕| 成人特级黄色片久久久久久久| 色5月婷婷丁香| 日韩欧美免费精品| 哪里可以看免费的av片| 男女下面进入的视频免费午夜| 人人妻人人澡欧美一区二区| 国产亚洲精品久久久久久毛片| 两性午夜刺激爽爽歪歪视频在线观看| 啦啦啦韩国在线观看视频| 免费av观看视频| h日本视频在线播放| 黄色配什么色好看| 国产免费男女视频| 日日摸夜夜添夜夜添av毛片| 欧美绝顶高潮抽搐喷水| 白带黄色成豆腐渣| 久久精品91蜜桃| 色哟哟哟哟哟哟| 麻豆久久精品国产亚洲av| 日本-黄色视频高清免费观看| 日本黄大片高清| 久久热精品热| 欧美+亚洲+日韩+国产| 久久精品91蜜桃| 寂寞人妻少妇视频99o| 亚洲经典国产精华液单| 国产精品国产高清国产av| 内射极品少妇av片p| 精品久久久久久久人妻蜜臀av| 国产 一区 欧美 日韩| 欧美3d第一页| 97超级碰碰碰精品色视频在线观看| 日韩 亚洲 欧美在线| 51国产日韩欧美| 亚洲四区av| 男插女下体视频免费在线播放| 国产成人a∨麻豆精品| 少妇猛男粗大的猛烈进出视频 | 亚洲欧美日韩高清在线视频| 国产精品久久电影中文字幕| 免费看日本二区| 麻豆av噜噜一区二区三区| aaaaa片日本免费| 一级黄片播放器| 欧美3d第一页| 九九爱精品视频在线观看| 晚上一个人看的免费电影| 国产在视频线在精品| 国产伦精品一区二区三区四那| 国产激情偷乱视频一区二区| 国产免费男女视频| 在线天堂最新版资源| 国产精品一区二区性色av| 亚洲精品在线观看二区| 国产蜜桃级精品一区二区三区| 国产亚洲91精品色在线| 国产高清有码在线观看视频| 男插女下体视频免费在线播放| 欧美色欧美亚洲另类二区| 又爽又黄a免费视频| 国产亚洲精品av在线| 老熟妇乱子伦视频在线观看| 国产成人精品久久久久久| av天堂在线播放| 在线免费观看的www视频| 久久精品综合一区二区三区| 亚洲aⅴ乱码一区二区在线播放| av女优亚洲男人天堂| 欧美成人精品欧美一级黄| 久久久a久久爽久久v久久| 国产午夜精品论理片| 变态另类成人亚洲欧美熟女| 欧美日本亚洲视频在线播放| 日韩制服骚丝袜av| 成年女人永久免费观看视频| 国产成人a∨麻豆精品| 成人性生交大片免费视频hd| 国产69精品久久久久777片| 欧洲精品卡2卡3卡4卡5卡区| 国产高清三级在线| 真人做人爱边吃奶动态| 国产精品一区二区三区四区免费观看 | 精品少妇黑人巨大在线播放 | 韩国av在线不卡| 亚洲第一电影网av| 青春草视频在线免费观看| 欧美绝顶高潮抽搐喷水| 精品一区二区三区人妻视频| 国产精品久久久久久亚洲av鲁大| 日日啪夜夜撸| 男女下面进入的视频免费午夜| 九色成人免费人妻av| 少妇裸体淫交视频免费看高清| 卡戴珊不雅视频在线播放| 久久久色成人| 欧美成人免费av一区二区三区| 亚洲第一电影网av| 美女被艹到高潮喷水动态| 国产精品国产高清国产av| ponron亚洲| 黄片wwwwww| АⅤ资源中文在线天堂| 校园人妻丝袜中文字幕| 国产片特级美女逼逼视频| 欧美极品一区二区三区四区| 亚洲不卡免费看| 日韩一区二区视频免费看| 国产黄片美女视频| av在线观看视频网站免费| 波多野结衣高清作品| 两个人视频免费观看高清| 久久午夜亚洲精品久久| 国产69精品久久久久777片| 国内精品久久久久精免费| 天天一区二区日本电影三级| 亚洲精品在线观看二区| 哪里可以看免费的av片| 97热精品久久久久久| 久久人人爽人人片av| 亚洲图色成人| 可以在线观看毛片的网站| 国产精品99久久久久久久久| av福利片在线观看| 国产午夜福利久久久久久| 波多野结衣高清无吗| 亚洲成人精品中文字幕电影| 99热只有精品国产| 校园人妻丝袜中文字幕| 欧美在线一区亚洲| 久久综合国产亚洲精品| 亚洲欧美日韩卡通动漫| 嫩草影院入口| 久久天躁狠狠躁夜夜2o2o| 69人妻影院| 色播亚洲综合网| 一个人观看的视频www高清免费观看| 欧美zozozo另类| 欧美成人一区二区免费高清观看| 国产高清有码在线观看视频| 我要看日韩黄色一级片| 国产精品爽爽va在线观看网站| 男女边吃奶边做爰视频| 露出奶头的视频| 中文字幕熟女人妻在线| 嫩草影院精品99| or卡值多少钱| 给我免费播放毛片高清在线观看| 国产人妻一区二区三区在| 免费看av在线观看网站| 天堂网av新在线| 99久久九九国产精品国产免费| 不卡一级毛片| 在线观看一区二区三区| 久久久久久久午夜电影| 18禁裸乳无遮挡免费网站照片| 久久久久国内视频| 99在线视频只有这里精品首页| 麻豆精品久久久久久蜜桃| 晚上一个人看的免费电影| 欧美最黄视频在线播放免费| 中国美白少妇内射xxxbb| 内射极品少妇av片p| 中文亚洲av片在线观看爽| 成人av一区二区三区在线看| avwww免费| 日本a在线网址| 麻豆乱淫一区二区| 久久亚洲国产成人精品v| 自拍偷自拍亚洲精品老妇| 91久久精品国产一区二区三区| 最近在线观看免费完整版| 国产av一区在线观看免费| 日韩精品中文字幕看吧| 午夜a级毛片| 女人十人毛片免费观看3o分钟| 欧美色欧美亚洲另类二区| 亚洲av中文字字幕乱码综合| 亚洲成人久久性| www日本黄色视频网| 欧美一区二区国产精品久久精品| 午夜免费激情av| 欧美丝袜亚洲另类| 日本一本二区三区精品| 白带黄色成豆腐渣| 美女免费视频网站| 狠狠狠狠99中文字幕| 亚洲成a人片在线一区二区| 免费人成在线观看视频色| 你懂的网址亚洲精品在线观看 | 女人十人毛片免费观看3o分钟| 男女视频在线观看网站免费| 久久午夜福利片| 亚洲美女搞黄在线观看 | 黑人高潮一二区| 嫩草影院新地址| 乱系列少妇在线播放| 亚洲国产精品久久男人天堂| 欧美日韩综合久久久久久| 亚洲精品色激情综合| 亚洲欧美中文字幕日韩二区| 麻豆国产97在线/欧美| 久久综合国产亚洲精品| 精品一区二区三区视频在线| 久久久久精品国产欧美久久久| 久久亚洲国产成人精品v| 婷婷精品国产亚洲av在线| 九九久久精品国产亚洲av麻豆| 少妇裸体淫交视频免费看高清| 亚洲欧美日韩高清专用| 成人亚洲精品av一区二区| 亚洲丝袜综合中文字幕| 小说图片视频综合网站| 97人妻精品一区二区三区麻豆| 长腿黑丝高跟| 俺也久久电影网| 欧美高清性xxxxhd video| 欧美+日韩+精品| 男人舔奶头视频| 变态另类丝袜制服| 国产精品久久视频播放| 国产v大片淫在线免费观看| 国产探花极品一区二区| 国产男靠女视频免费网站| 淫秽高清视频在线观看| 少妇人妻精品综合一区二区 | 人妻少妇偷人精品九色| av在线老鸭窝| 日本-黄色视频高清免费观看| 久久久久久久久久黄片| 午夜福利视频1000在线观看| 丝袜喷水一区| 色哟哟哟哟哟哟| 99在线人妻在线中文字幕| 99久久精品国产国产毛片| 成年女人毛片免费观看观看9| 赤兔流量卡办理| 国产伦在线观看视频一区| 亚洲成人av在线免费| 1000部很黄的大片| 日本色播在线视频| 亚洲最大成人av| 国产黄色视频一区二区在线观看 | 国产一区二区三区av在线 | 国产精品久久视频播放| 久久精品国产亚洲av天美| 国产成人freesex在线 | 亚洲成a人片在线一区二区| 亚洲国产日韩欧美精品在线观看| 国产精品一区二区性色av| 免费不卡的大黄色大毛片视频在线观看 | 久久这里只有精品中国| 日本爱情动作片www.在线观看 | 日本黄色视频三级网站网址| 我的女老师完整版在线观看| 两个人视频免费观看高清| 精品一区二区三区av网在线观看| 国产一级毛片七仙女欲春2| 国产精品久久久久久精品电影| 夜夜爽天天搞| 久久久久久久亚洲中文字幕| 国产午夜福利久久久久久| 波多野结衣高清作品| 国产精品嫩草影院av在线观看| 中文字幕人妻熟人妻熟丝袜美| 在线a可以看的网站| 国产精品免费一区二区三区在线| 亚洲四区av| 欧美日本视频| 亚洲真实伦在线观看| 俄罗斯特黄特色一大片| 美女高潮的动态| 内射极品少妇av片p| 在线观看一区二区三区| 性插视频无遮挡在线免费观看| 国产乱人偷精品视频| 成人av一区二区三区在线看| 一级毛片久久久久久久久女| 亚洲图色成人| 成人特级黄色片久久久久久久| 久久久久久久久久黄片| 1024手机看黄色片| 人妻丰满熟妇av一区二区三区| 日本黄大片高清| 精品久久国产蜜桃| 国产成人aa在线观看| 人人妻人人看人人澡| 亚洲美女黄片视频| 一个人免费在线观看电影| 亚洲人成网站在线播| 寂寞人妻少妇视频99o| 97在线视频观看| 亚洲国产精品成人久久小说 | 国产色爽女视频免费观看| 国产高清不卡午夜福利| 亚洲av免费在线观看| 毛片女人毛片| 国产精品一区二区免费欧美| 全区人妻精品视频| 久久久成人免费电影| 男女视频在线观看网站免费| 精品久久久久久成人av| 久久久久国产精品人妻aⅴ院| 五月伊人婷婷丁香| 岛国在线免费视频观看| 成年免费大片在线观看| 国产精品亚洲美女久久久| 国产男靠女视频免费网站| 美女xxoo啪啪120秒动态图| 麻豆乱淫一区二区| 中文资源天堂在线| 欧美日本亚洲视频在线播放| 超碰av人人做人人爽久久| 色视频www国产| 内射极品少妇av片p| www日本黄色视频网| 最近中文字幕高清免费大全6| 中出人妻视频一区二区| 人妻夜夜爽99麻豆av| 听说在线观看完整版免费高清| 亚洲av不卡在线观看| 国产极品精品免费视频能看的| 国产中年淑女户外野战色| 国产av麻豆久久久久久久| 精品人妻偷拍中文字幕| 男女之事视频高清在线观看| 99久久成人亚洲精品观看| 欧美日韩在线观看h| 成人av在线播放网站| 尾随美女入室| 一区福利在线观看| 简卡轻食公司| 少妇高潮的动态图| 亚洲18禁久久av| aaaaa片日本免费| 婷婷精品国产亚洲av| 亚洲熟妇中文字幕五十中出| 桃色一区二区三区在线观看| 插逼视频在线观看| 欧美性猛交╳xxx乱大交人| 国产91av在线免费观看| 99视频精品全部免费 在线| 精品久久久久久久久av| 一级av片app| 国产免费一级a男人的天堂| 在线观看美女被高潮喷水网站| 中文字幕人妻熟人妻熟丝袜美| 欧美一区二区精品小视频在线| 美女xxoo啪啪120秒动态图| 日本在线视频免费播放| 午夜福利在线观看免费完整高清在 | 黄色欧美视频在线观看| 国产精品久久久久久亚洲av鲁大| 亚洲欧美日韩卡通动漫| 成人美女网站在线观看视频| av中文乱码字幕在线| 亚洲五月天丁香| 亚洲欧美成人精品一区二区| 色噜噜av男人的天堂激情| 国产精华一区二区三区| 看黄色毛片网站| 欧美日本视频| 色在线成人网| 中国美女看黄片| 国产精品电影一区二区三区| 亚洲自拍偷在线| videossex国产| 真人做人爱边吃奶动态| 久久久久久伊人网av| 国产69精品久久久久777片| 在线天堂最新版资源| 久久久精品94久久精品| 亚洲不卡免费看| 男女啪啪激烈高潮av片| videossex国产| 色5月婷婷丁香| 久久久久久久久久黄片| 成人二区视频| 熟女电影av网| or卡值多少钱| 亚洲美女搞黄在线观看 | 国产欧美日韩一区二区精品| 久久久久免费精品人妻一区二区| 高清日韩中文字幕在线| 欧美色欧美亚洲另类二区| 网址你懂的国产日韩在线| 亚洲国产欧美人成| 亚洲图色成人| 蜜臀久久99精品久久宅男| 1024手机看黄色片| 插逼视频在线观看| 亚洲高清免费不卡视频| 国产精品电影一区二区三区| 亚洲欧美成人综合另类久久久 | 亚洲成av人片在线播放无| 免费高清视频大片| 国产在视频线在精品| 人人妻人人澡人人爽人人夜夜 | 97热精品久久久久久| 亚洲第一电影网av| 一级毛片aaaaaa免费看小| 国内揄拍国产精品人妻在线| 少妇人妻精品综合一区二区 | 日本撒尿小便嘘嘘汇集6| 精品福利观看| 激情 狠狠 欧美| 亚洲在线自拍视频| 色综合亚洲欧美另类图片| 中文字幕免费在线视频6| 日本与韩国留学比较| 日本一二三区视频观看| 两性午夜刺激爽爽歪歪视频在线观看| 国产精品一及| 麻豆精品久久久久久蜜桃| 亚洲中文字幕日韩| 99国产精品一区二区蜜桃av| 免费一级毛片在线播放高清视频| 午夜a级毛片| 麻豆乱淫一区二区| 国产一级毛片七仙女欲春2| 亚洲国产精品成人综合色| 亚洲精华国产精华液的使用体验 | 国产精品av视频在线免费观看| 久久99热6这里只有精品| 91午夜精品亚洲一区二区三区| 亚洲最大成人手机在线| 亚洲经典国产精华液单| 99在线人妻在线中文字幕| 亚洲国产精品久久男人天堂| 色在线成人网| 在线看三级毛片| 91久久精品电影网| 18禁裸乳无遮挡免费网站照片| av在线亚洲专区| 在线免费十八禁| 人妻制服诱惑在线中文字幕| 97在线视频观看| 国产在线精品亚洲第一网站| 丰满的人妻完整版| 午夜精品国产一区二区电影 | 亚洲av一区综合| 在线国产一区二区在线| 五月玫瑰六月丁香| 日韩欧美国产在线观看| 亚洲成人中文字幕在线播放| 99热这里只有是精品在线观看| 日本免费一区二区三区高清不卡| 亚洲va在线va天堂va国产| 亚洲经典国产精华液单| 成人午夜高清在线视频| 特级一级黄色大片| 美女xxoo啪啪120秒动态图| 午夜免费男女啪啪视频观看 | 免费观看精品视频网站| 黑人高潮一二区| 国产aⅴ精品一区二区三区波| 久久久久久久久大av| 亚洲图色成人| 日本 av在线| 中文字幕免费在线视频6| 91av网一区二区| 麻豆av噜噜一区二区三区| 亚洲精品在线观看二区| 乱系列少妇在线播放| 国产女主播在线喷水免费视频网站 | 久久精品夜夜夜夜夜久久蜜豆| 亚洲成a人片在线一区二区| 嫩草影视91久久| 亚洲人与动物交配视频| 大型黄色视频在线免费观看| 亚洲欧美日韩高清专用| 亚洲第一区二区三区不卡| 日韩亚洲欧美综合| 悠悠久久av| 欧美xxxx性猛交bbbb| 一区二区三区高清视频在线| 能在线免费观看的黄片| 一进一出抽搐gif免费好疼| 国产精华一区二区三区| 亚洲国产高清在线一区二区三| 美女内射精品一级片tv| 黄色配什么色好看| 亚洲av一区综合| 91狼人影院| 免费观看人在逋| 精品少妇黑人巨大在线播放 | 国产亚洲精品综合一区在线观看| 有码 亚洲区| 啦啦啦韩国在线观看视频| 日韩三级伦理在线观看| 天堂影院成人在线观看| 日韩精品有码人妻一区| 欧美高清性xxxxhd video| 色噜噜av男人的天堂激情| 一卡2卡三卡四卡精品乱码亚洲| 91av网一区二区| 最新在线观看一区二区三区| 亚洲精品日韩在线中文字幕 | 一进一出抽搐动态| 国内少妇人妻偷人精品xxx网站| 日本一二三区视频观看| 欧美日韩综合久久久久久| 成人无遮挡网站| 亚洲人成网站在线播放欧美日韩| 国产精品久久视频播放| 婷婷精品国产亚洲av| 国产精品久久久久久av不卡| 久久鲁丝午夜福利片| 我要搜黄色片| 日韩国内少妇激情av| 男女之事视频高清在线观看| 日韩,欧美,国产一区二区三区 | 人人妻人人澡人人爽人人夜夜 | a级毛片免费高清观看在线播放| 99热这里只有是精品50| 香蕉av资源在线| 亚洲天堂国产精品一区在线| 亚州av有码| 国产色婷婷99| АⅤ资源中文在线天堂| 国产 一区 欧美 日韩| 精品一区二区免费观看| 校园春色视频在线观看| 欧美日韩精品成人综合77777| 又爽又黄无遮挡网站| 亚洲成人精品中文字幕电影| 亚洲成a人片在线一区二区| 国产精品久久久久久亚洲av鲁大| 国产麻豆成人av免费视频| 日本免费一区二区三区高清不卡| 国产欧美日韩一区二区精品| 三级国产精品欧美在线观看| 亚洲av免费高清在线观看| 人妻夜夜爽99麻豆av| 国产片特级美女逼逼视频| 人妻夜夜爽99麻豆av| 在线免费十八禁| 久久热精品热| 在线免费观看不下载黄p国产| 嫩草影视91久久| 非洲黑人性xxxx精品又粗又长| 波多野结衣高清无吗| 国产日本99.免费观看| 国产三级在线视频| 男人狂女人下面高潮的视频| 国产精品无大码| 欧美成人精品欧美一级黄| 少妇被粗大猛烈的视频| 老司机福利观看| 久久精品国产亚洲av香蕉五月| 欧美国产日韩亚洲一区| 香蕉av资源在线| 亚洲av成人精品一区久久| 国产一区二区亚洲精品在线观看| 免费一级毛片在线播放高清视频| 黄色视频,在线免费观看| 国产精品一区二区三区四区免费观看 | 内地一区二区视频在线|