Posting two-Frank Li (999069322)

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Two-Loop Electroweak Corrections to $Delta r$

where the factor ∆q describes all the quantum corrections in the low energy eﬀective theory (i.e. QED corrections). At one-loop order these corrections have been computed a long time ago [ 10]. Recently also the two-loop result for ∆q has been obtained [ 11]. Taking it into account, the error of GF is nowadays dominated by the experimental error of τµ measurement3 .
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This equation however gets quantum corrections. In fact in the l.h.s. of (3) there appear contributions coming from both short and long distance. It the r.h.s. these contributions should be separately absorbed in GF and the matrix element OF respectively. In order to make this in the most easiest and elegant way the factorization theorem is used. In order to separate the short and long distance dynamics at the level of a single Feynmans diagram we use the large mass expansion procedure [ 12]. Namely, given the graf F , then asymptotically F ∼ S · T (H ) , (4)

二联体亲子鉴定英语

二联体亲子鉴定英语Duplex Parentage Testing: Understanding the Process and Its Applications.Duplex parentage testing, also known as diploid genotyping, is a highly specialized form of genetic testing that aims to establish the biological relationship between two individuals, typically a child and a putative parent. This process involves the analysis of genetic markers present in the DNA of the individuals involved to determine if they share a common genetic heritage. This article will delve into the details of duplex parentage testing, its scientific principles, applications, and ethical considerations.Scientific Principles of Duplex Parentage Testing.Duplex parentage testing relies on the principles of Mendelian inheritance and modern genetic technology. It typically involves the examination of multiple geneticmarkers, such as single nucleotide polymorphisms (SNPs) or short tandem repeats (STRs), which are passed down from parents to their children. These markers are present in specific locations on the DNA, known as loci. By comparing the genetic markers of the putative parent and child, scientists can determine if there is a genetic match, indicating a biological relationship.The process begins with the collection of DNA samples from the individuals involved. These samples can be obtained through a variety of methods, including buccal swabs, blood samples, or even saliva. Once collected, the DNA is isolated and amplified using polymerase chain reaction (PCR) or other similar techniques. This process produces enough DNA material for detailed analysis.Applications of Duplex Parentage Testing.Duplex parentage testing has a wide range of applications in various scenarios. Some of the most common uses include:1. Paternity Testing: This is one of the most common reasons for seeking duplex parentage testing. It involves determining whether a man is the biological father of a child. Paternity testing can be used in cases of disputed paternity, for example, when a child is born out of wedlock or when a man questions his parental status.2. Maternity Testing: Although less common, duplex parentage testing can also be used to establish maternity, or the biological relationship between a woman and her child. This is particularly useful in cases where the biological mother is unknown or disputed.3. Sibling Relationships: Duplex parentage testing can also be used to determine whether two individuals are siblings. This is achieved by comparing the genetic markers of the potential siblings with each other and with those of their putative parents.4. Adoption: In the context of adoption, duplex parentage testing can help to establish the biological relationship between an adoptive parent and child, orbetween siblings who were separated at birth.Ethical Considerations.While duplex parentage testing offers valuable information in resolving questions of biological relationships, it also raises ethical considerations. One of the most significant ethical issues is the privacy and confidentiality of test results. Strict protocols must be followed to ensure that test results are shared only with the authorized parties and that they are not misused or misinterpreted.Another ethical concern is the potential impact of test results on individuals and families. Positive results can confirm biological relationships, but negative results can cause emotional distress and even family breakdowns. It is, therefore, crucial that testing is conducted with the full knowledge and consent of all parties involved, and that they are provided with appropriate support and counseling throughout the process.Conclusion.Duplex parentage testing is a powerful tool that can provide valuable insights into biological relationships. It relies on the principles of Mendelian inheritance and modern genetic technology to analyze genetic markers and establish whether individuals share a common genetic heritage. From paternity testing to adoption and sibling relationships, duplex parentage testing has a wide range of applications. However, it is crucial to approach this testing with caution, respecting the privacy and confidentiality of test results and providing appropriate support and counseling to all parties involved.While duplex parentage testing can offer answers to complex biological questions, it is only one piece of the puzzle. It is essential to remember that genetic relationships are not the sole determinant of family ties. Emotional, cultural, and social factors play an equally important role in defining our sense of family and belonging. In this sense, duplex parentage testing shouldbe seen as a tool to complement other forms of evidence and understanding, rather than a replacement for them.。

Many--body aspects of positron annihilation in the electron gas

derivatives of known properties of electron gas or electron–positron mixtures, and their quality has been tested only in the case of a positron–neutral atom bound system [11]. So far there have not been many attempts to formulate a microscopic many–body theory that deals with an inhomogeneous electron gas. A ﬁrst move to this direction was made by Stachowiak and Boro´ nski [12], who studied the case of a spherical inhomogeneity in jellium. Most of the many–body aspects of positron annihilation rates are reﬂected in a single number, namely the value of the electron–positron distribution function, g IB (r ), at the origin. (As a convention, we shall label all two–body quantities that involve one positron (“impurity”) and one electron (“background”) with a superscript IB.) The annihilation rate of a positron in homogeneous electron gas can be written in the form [13], 1 12 = 3 g IB (0) × 109 sec−1 , τ rs (1.1)

TWO OU-IANG TYPE NONLINEAR INTEGRAL INEQUALITIES AND APPLICATION

1
Introduction
In 1998, Yan g [1] obtaine d a gen eralization of O u- Ian g ine qu ality as follows: Lemm a 1.1 Let ϕ ∈ C ( R + , R+ ) be an increasing fun ct ion w ith ϕ ( ∞) = ∞ , ψ ∈ C ( R+ , R + ) be a non decrea sing fu nction and c be a non negat ive con sta nt. If u, f ∈ C ( R + , R+ ) an d Z
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Main Results
Theorem 2.1 Let u, f , g ∈ C ( R + , R+ ) , an d p ≥ q , c be non n egat ive const ant s. If
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f ( s )ds ∈ D om( G − 1 ).
Th e ine quality p lay s an imp ortant role in th e stud y of lin ear diﬀere ntial equ ations. In [2,3], it was ge ne raliz ed to the c ase of n variab les. S ome inte gral ine qu alities sim ilar to [1] we re obtain ed by Li [4]. In this pap e r, a n ew inte gral in equ ality is given ﬁrstly by an elem entary in equ ality an d the n by a ge ne ralization of th e ne w integral in equ ality. F in ally an exam ple is give n to ind icate th e app lic ation of th e ineq uality.

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二次订货策略在单周期产品逆向供应链中的应用_侯云章

2005年11月系统工程理论与实践第11期　文章编号:1000-6788(2005)11-0035-06二次订货策略在单周期产品逆向供应链中的应用侯云章1,戴更新2,于庆东2(1.南京大学工程管理学院,江苏南京210093;2.青岛大学国际商学院,山东青岛266071)摘要:　在单周期产品逆向供应链中,为了研究二次订货策略的协调机制,将零售商面临的需求划分为两个阶段,在每个阶段中分别进行订货,以利润最大化为目标建立了目标函数.采用数值方法分析了供应链的总体收益,并对二次订货和一次订货进行了比较.数值算例表明二次订货策略能够显著提高供应链尤其是零售商的收益,可以有效的协调逆向供应链系统.关键词:　逆向物流;二次订货;报童问题;供应链协调中图分类号:　F273 文献标识码:　A The Application of Two Ordering Opportunities in Single-periodProducts of Reverse Supply Chain ManagementHOU Yun-zhang1,DAI Geng-xin2,YU Qing-dong2(1.School of Management Science and Engineering,Nanjing University,Nanjing210093,China;2.International Business College,Qingdao University,Qingdao266071,China)Abstract:　To study the coordination of t wo ordering opportunities in sin gle-period product reverse suppl y chain,theretailer's total demand is divided into two periods,products are ordered in each period respectively,and anoptimization function aiming at maximizing total profits has been established.Then the total profit of the reverse supplychain has been analyzed by the use of the numerical method,and the results of one ordering opportunity with those oft wo ordering opportunities under different parameters have been compared.The results show that t wo orderingopportunities tactics can remarkably improve the profit of reverse supply chain,especially the retailer,and caneffectively coordinate the reverse supply chain system.Key words:　reverse logistics;two orderin g opportunities;newsboy problem;supply chain coordination近些年来,随着社会环保意识和可持续发展意识的加强,逆向物流逐渐引起人们的重视.所谓逆向物流,美国物流管理协会将其定义为“计划、实施和控制原料、半成品库存、制成品和相关信息,高效和成本经济地从消费点到起点的过程,从而达到回收价值和适当处置的目的”.逆向物流的发展促使了逆向供应链的产生,V.Daniel R.Guider Jr[1]认为逆向供应链是指为了从客户手中回收使用过的产品所必需的一系列活动,其目的是对回收品进行处置,或者再利用夏绪辉等人[2]结合国际上对逆向物流和逆向供应链的研究,也给出了逆向供应链的概念.在对逆向供应链中单个节点库存控制的研究中,针对需求计划的长短可以分为单周期和多周期两种类型,Vlachos等人[3]借助于经典的报童问题对单周期、单库存点的存储问题进行了较为详细的研究,针对物品回收的处理策略,文中提出了六种解决方案,以最大化利润为目标函数建立了报童问题模型,得出了各自的订货策略.但是,文中的假设和大多数的报童模型一样,均只有一次订货,然而,在实际应用中单周期产品的订货机会常常不止一次[4,5],零售商常常在销售季季末再进行一次订货.基于此,本文在文献[3]收稿日期:2004-10-24资助项目:国家自然科学基金(70171045) 作者简介:侯云章(1979-),男,山东临沂人,南京大学工程管理学院博士生,主要研究领域为物流与供应链管理,演化管理理论;E-mail:qdhyzhang@;戴更新(1970-),男,安徽人,博士,副教授,硕士生导师,主要研究领域为电子商务与物流、运作管理;于庆东(1962-),男,山东龙口人,博士,教授,博士生导师,主要研究领域为可持续发展技术经济学、管理系统工程.的基础上,考察了二次订货策略下整个逆向供应链的收益,并对二次订货和一次订货条件下的供应链收益进行了分析.1　系统的描述与假设本文考察了一个简单的二级供应链系统,即单个零售商、单个供应商在零售商分别采用一次订货和二次订货策略时的期望收益.在二次订货情况下将零售商的整个计划周期为两个阶段(见图1所示):第一次订货完全依据对需求的预测,而真正的需求在第二次订货时被了解到.设两次订货量分别为Q 1,Q 2,在每个阶段开始,订货量都已经到达,两个阶段的需求分别用x ,y 表示,两者分别服从均值为μ1,μ2,方差为σ1,σ2的正态分布,第二阶段的订货量与第一阶段的紧密相关,第一阶段的订货如果有剩余,则转入第二阶段继续使用,第二阶段的剩余物品则进行降价销售.x ～N (μ1,σ1)y ～N (μ2,σ2)阶段一　Q 1阶段二　Q 2图1　零售商的计划周期划分另外假设:1)阶段一、阶段二的需求相互独立;2)零售商以价格c 从供应商处订购产品,以固定的零售价p 销售,而供应商的生产成本为c M ;3)零售商所售的货物有一个常数的返回率r (0≤r <1);并且无论是零售商还是供应商,他们对顾客的返回货物以及季末剩余货物均做同样的处理:即以价格s 进行降价销售,并且总可以销售完毕;以f (·),F (·)分别表示两个阶段需求的密度函数和分布函数.为不失一般性,有p >c >c M >s .2　二次订货下模型的建立和求解本节对零售商和供应商在信息不共享而采用二次订货策略时的收益进行分析.2.1　阶段一模型分析根据1中假设,首先分析第一阶段中零售商的收益函数:①如果需求x >Q 1,则零售商收益为p (1-r )Q 1+srQ 1;②如果需求x ≤Q 1,则零售商收益为p (1-r )x +srx .零售商的总收益为:π2R ,1(Q 1)=∫Q 1[(1-r )p +rs ]xf (x )d x +∫+∞Q1[(1-r )pQ 1+srQ 1]f (x )d x -cQ 1.进一步化简,得:π2R ,1(Q 1)=[(1-r )p +rs ]∫Q 1xf (x )d x +Q 1(1-F (Q 1))-cQ1.(1)对(1)式求极值,由 π2R ,1 Q 1=0得:F (Q 1)=1-c(1-r )p +rs.令K 1=1-c (1-r )p +rs,则Q ＊1=F -1(K 1).(2)将(2)代入(1)得π2R ,1(Q ＊1)=[(1-r )p +rs ]∫Q＊1xf (x )d x .2.2　阶段二模型分析首先假设零售商仅有一次订货机会,我们对其收益进行分析,以Q ＊2s 表示最优订货量,则:①如果需求y >Q 2,则零售商收益为p (1-r )Q 2+srQ 2;②如果需求y ≤Q 2,则零售商收益为p (1-r )y +s [Q 2-(1-r )y ].于是,总收益函数为:π(Q 2)=∫Q 2[(1-r )py +s (Q2-(1-r )y )]f (y )d y +∫+∞Q2[(1-r )pQ2+srQ 2]f (y )d y -cQ 2.进一步化简得:36系统工程理论与实践2005年11月π(Q 2)=(1-r )(p -s )∫Q 2yf (y )d y -Q 2F (Q 2)+[(1-r )p +rs -c ]Q2.(3)对(3)求极值,由 π Q 2=0得F (Q 2)=(1-r )p +rs -c(1-r )p +rs -s .令K 2=(1-r )p +rs -c (1-r )p +rs -s ,则Q ＊2s =F -1(K 2).将Q ＊2s 代入(3)得收益π(Q ＊2s )=(1-r )(p -s )∫Q＊2s 0yf (y )d y .当零售商有两次订货机会时,为表示的方便,此处引入两个变量:v =max (0,Q 1-Q ＊2s ),w =max (0,Q 1-x ),于是,阶段二的实际订货量Q ＊2表示为如下的分段函数:Q ＊2=0w ≥Q ＊2s (4.1)Q ＊2s -w0<w <Q ＊2s　(4.2)Q ＊2sw =0　(4.3)(4)对各条件下的收益进行分析:①式(4.1)即第一阶段的剩余品完全满足第二阶段的需求,故第二阶段的订货量为0,此时第二阶段的收益为:(π2R ,2,1|Q 1)=π(w )+c w =[(1-r )p +rs ]w +(1-r )(p -s )∫wyf (y )d y -wF (w ). ②当0<w <Q ＊2s ,则第二阶段还要进行补充订货Q ＊2s -w ,使其总量达到Q ＊2s ,此时收益为:(π2R ,2,2|Q 1)=π(Q ＊2s)+c w =c w +(1-r )(p -s )∫Q＊2syf (y )d y . ③当w =0,则第二阶段订货量为Q ＊2s ,故零售商收益(π2R ,2,3|Q 1)=π(Q ＊2s)=(1-r )(p -s )∫Q ＊2syf (y )d y .2.3　供应链总收益分析及求解2.3.1　Q 1的求解通过以上分析,由w 的定义,给定Q ＊1即可得出x 的表达式,于是,条件(4.1)可以变为0≤x ≤v ,条件(4.2)即v <x ≤Q 1,条件(4.3)即Q 1≤x ≤+∞,因此,零售商的总收益函数可表示为:(π2R |Q 1)=(π2R ,1|Q 1)+(π2R ,2|Q 1)=[(1-r )p +rs ]∫Q1xf (x )d x +Q 1(1-F (Q 1))-c Q 1+∫v(π2R ,2,1|Q 1)f (x )d x +∫Q 1v(π2R ,2,2|Q 1)f (x )d x +∫+∞Q1(π2R ,2,3|Q 1f (x )d x .(5)式(5)的求极值问题,容易想到通过对Q 1求偏导来解决,但实际上这种方法解决起来相对麻烦,同时,求解Q 1的解析解几乎难以完成.可以看出,式(5)是关于Q 1的一元函数,而(π2R ,2,1 Q 1),(π2R ,2,2 Q 1),(π2R ,2,3 Q 1)均是Q 1的积分函数,给定Q 1,式(5)相对较容易求得,故考虑采用数值方法来得到数值解,从而可分析问题的实质含义,实际上数值方法是经常被用来做辅助决策分析的[6].2.3.2　Q 2的求解给定Q ＊1,由式(4)可得:E (Q 2)=∫Q ＊1v(Q＊2s-w )f (x )d x +∫+∞Q ＊1Q ＊2s f (x )d x .(6)同时,将Q ＊1代入(5)得到零售商的期望总收益.当Q 1、Q 2求出后,即可得出供应商的期望收益:37第11期二次订货策略在单周期产品逆向供应链中的应用(π2M|Q1,Q2)=(c-c M)(Q1+Q2).此时,供应链总体收益为:(π2T|Q1,Q2)=(π2M|Q1,Q2)+(π2R|Q1).(7)3　一次订货下模型的建立和求解本节分别讨论在一次订货情况下,供应商和零售商不合作和进行完全合作时,供应链的总体收益. 3.1　不合作情况下供应链收益分析由1中假设,销售季季末没有售完的以及顾客的返回品均进行降价销售,以变量u表示整个销售季的需求,可得零售商的期望收益为:π1R(Q)=∫Q0[(1-r)pu+s(Q-(1-r)u)]f(u)d u+∫+∞Q[1-r)pQ+srQ]f(u)d u-cQ,(8)此时,供应商的收益为:(π1M|Q)=(c-c M)Q. 故在一次订货情况下,当两者不合作时,整个供应链的总收益为:π1T(Q)=π1R(Q)+(π1M|Q).(9) 3.2　合作情况下供应链收益分析现假设供应商和零售商的信息完全共享,令Q′表示此时的订货量,则两者的总收益为:π′1T(Q′)=∫Q′0[(1-r)pu+s(Q′-(1-r)u)]f(u)d u+∫+∞Q′[(1-r)pQ′+srQ′]f(u)d u-c M Q′.(10) 定理　一次订货情况下,完全合作时总收益大于不合作时供应链总收益.证明　由(9)式,对其求极值,由π1R Q=0得:F(Q)=(1-r)p+rs-c (1-r)p+rs-s;同理,由式(10)可得:F(Q′)=(1-r)p+rs-c M (1-r)p+rs-s,由假设c>c M,故可得F(Q′)>F(Q),因此Q′>Q.令函数g(Q)=π1T(Q),对Q求偏导,得:g Q=(1-r)p+rs-c-(1-r)(p-s)F(Q),由假设p>c>c M>s,故函数g(Q)是关于Q的单调增函数,因此π′1T(Q′)>π1T(Q),即证.4　数值算例通过以上分析,本节给出数值算例,采用数值分析的方法,分析不同参数情况下一次订货和二次订货的期望订货以及期望收益.1)首先分析不同参数下,零售商采用一次和二次订货策略时的期望收益和期望订货.设零售商面对的市场需求为服从μ=100,σ=9的正态分布,其订购价格c=5,卖价p=10,阶段一和阶段二的需求分别为μ1=μ2=μ2,σ1=σ2=σ2,另外,供应商的生产成本为c M=4.表1给出了商品的返回率r=0.1,0.2,s=2,3,4情况下的零售商的各个阶段的订货量,以及供应链中期望收益.在以上的数值算例中,我们规定了μ1,μ2,σ1,σ2的值,实际上,如果零售商的二次订货时间不受制约的话,换句话说,如果零售商可以任意划分需求的两个阶段,其收益也会带来不同的变化,表2给出了在r =0.2,s=2的情况下,当μ1取不同的值时,零售商的订货量以及期望总收益:由表1和表2可以得出如下结论:38系统工程理论与实践2005年11月1)二次订货情况下,零售商的期望收益明显大于仅有一次订货机会时的期望收益,而订货量小于仅有一次订货机会时的平均订货量;相反,由于在二次订货情况下零售商的订货量偏少,供应商的期望收益相比一次订货时有所下降,但是供应链总收益明显增加.2)随着r 的增加,当s 保持不变时,无论是二次订货还是一次订货,零售商的期望收益明显减少,订货量也有下降趋势;供应商的期望收益与整个供应链的总收益均随之减少.3)随着s 的增加,当r 保持不变时,无论是二次订货还是一次订货,零售商的期望收益明显增加,订货量也有上升趋势;供应商的期望收益与整个供应链的总收益均随之增加.4)当总需求不变,第一阶段的需求增加时,零售商的总收益增加,第一阶段的订货量增加,第二阶段的订货量呈下降趋势,但总的订货量成不规则变化.当μ1=0.8μ时,零售商可以获得最大收益327.95,且订货量为101.1;此时供应商的收益并未达到最大,而供应链的总收益达到最大.表1　不同参数下零售商的订货量以及供应链期望收益一次订货(不合作时)二次订货r s Q 1π1R π1M π1R +π1M Q 1Q 2Q 1+Q 2π2R π2M π2R +π2M0.12101.9394.71101.89496.6077.623.7101.3402.12101.32503.440.13104.2409.79104.24514.0378.025.0103.0415.71103.01518.720.14108.0427.02108.00535.0281.625.1106.7429.82106.72536.540.22100.7317.09100.70417.7978.521.9100.4323.80100.44424.240.23103.3341.19103.29444.4878.623.7102.3346.70102.33449.030.24107.3367.61107.30474.9179.325.8105.1371.23105.11476.34表2　不同的阶段划分下零售商订货量和供应链中期望收益μ1=0.3μμ1=0.4μμ1=0.5μμ1=0.6μμ1=0.7μμ1=0.8μμ1=0.9μQ 164.372.578.582.487.892.497.2Q 236.628.521.918.413.58.76.2Q 1+Q 2100.9101.0100.4100.8101.3101.1103.4π2R 315.83322.25323.80325.50327.21327.95325.16π2M80.7280.880.3280.6481.0480.8882.72π2R +π2M396.55403.05404.12406.14408.25408.83407.882)分析当供应商的生产成本c M 分别为2.5,3,3.5,4时整个供应链的收益,取r =0.2,s =2,其他参数同1),表3给出了在不同的生产成本下供应链的总收益,可见:①在一次订货情况下,供应链完全合作时的收益总大于不合作时的收益;②在二次订货情况下,无论生产成本多大,供应链收益总大于一次订货情况下不合作时的收益;③当生产成本较高时,采用二次订货策略时,供应链的期望收益可以超过一次订货策略下的完全合作时的总收益.表3　一次订货和二次订货策略下供应链总收益c M2.533.54一次订货且不合作568.84518.49468.14417.79一次订货完全合作581.59526.2472.33419.61二次订货580.7530.15479.6424.2439第11期二次订货策略在单周期产品逆向供应链中的应用40系统工程理论与实践2005年11月5　结论在单周期产品供应链管理(包括正向和逆向)的研究中,常常借助于经典的报童模型,限制了订货机会只有一次,然而在实际生活中,多次订货情况并不少见.本文研究了在逆向供应链中,当零售商对剩余品和回收品采用降价处理策略时,分别采用一次和二次订货策略时供应链的总收益,以及不同参数下零售商采用二次订货策略时的期望收益和期望订货,并分析了供应商和整个供应链的收益.数值算例表明二次订货明显提高了零售商和整个供应链的收益,同时零售商的订货数量同一次订货机会时相比趋于减少,并且,当供应商的生产成本较大时,采用二次订货可以使供应链总收益大于一次订货完全合作时的总收益.因此,在完全竞争市场,零售商通过二次订货可以不采用合作策略而获得较大收益;相反,在垄断市场下供应商可以将提供二次订货机会作为供应链协调的方法,以此提高供应链的总收益,这样的协作可能比完全信息共享在实际运用中更容易操作.本文的进一步研究可以从以下几个方面进行:1)对回收品进行多手段处理时,特别是当回收品进行再加工时,联合二次生产进行研究;2)价格对市场的需求弹性,对零售商的零售价格的灵敏度分析显得更具实际意义,这些将在后续文章中进行研究.本文的研究不仅丰富了库存论的内容,同时,对逆向供应链协作提供了有益的指导.参考文献:[1]　V.Daniel R.Guider Jr,Luk N Van Wasssenhove.The reverse supply chain[J].Harvard Business Review,2002,80(2):25-26.[2]　夏绪辉,刘飞,曹华军,高全杰.逆向供应链及其管理系统研究[J].现代集成技术.2003(4):87-90.Xia Xuhui,Liu Fei,Cao Huajun,Gao Quanjie.Research on the reverse supply chain and management system[J].Manufacture Information Engineering of China.2003(4):87-90.[3]　Dimitrios Vlachos,Rommert Dekker.Return handling options and order q uantities for single period products[J].European Journalof Operational Research,2003,151:38-52.[4]　Amy Hing-Ling Lau,Hon-Shiang Lau.Decision models for single-period products with two ordering opportunities[J].InternationalJournal of Production Economics,1998,55:57-70.[5]　Hon-shiang Lau,Amy Hing-Ling Lau.Reordering strategies for a newsboy-t ype product[J].European Journal of OperationalResearch1997,103:557-572.[6]　姚忠.退货策略在单周期产品供应链中的作用[J].系统工程理论与实践,2003,23(6):69-73.Yao Zhong.The role of the returns policies in the supply chain of the single-period products[J].System Engineering Theory and Practice.2003,23(6):69-73.。

非线性泛函的分数漫疗方程解说明书

Solution for a Space-time Fractional DiffusionEquationQiyu Liu1, and Longjin Lv2,*1College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China 2Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China*Corresponding authorAbstract—This work focuses on investigating the solutions for a generalized fractional diffusion equation. This equation presents space and time fractional derivatives, includes an absorbent term and a linear external force, takes a time-dependent diffusion coefficient into account, and subjects to the natural boundaries and the general initial condition. We obtain explicit analytical expressions in terms of the Fox H functions for the probability distribution. In addition, we analyze the first passage time and the second movement distribution for the case characterized by the absence of absorbent term and external force for a semi-infinite interval with absorbing boundary condition.Keywords-anomalous diffusion; fractional diffusion; green function; fox functionI.I NTRODUCTIONAnomalous diffusion is one of the most ubiquitous phenomena in nature [1]. It is present in a wide variety of physical situations. For instance, surface growth, transport of fluid in porous media [2], two-dimensional rotating flow [3], subrecoil laser cooling [4], diffusion on fractals [5], or even in multidisciplinary areas such as econophysics [6-8]. The properties concerning these equations have also been investigated. For instance, in [9] boundary values problems for fractional diffusion equations are studied, in [10] a fractional Fokker-Planck equation is derived from a generalized master equation, in [11] the behavior of fractional diffusion at the origin is analyzed and a connection between the Fox H functions and the fractional diffusion equations was investigated in [12]. Also a generalization of Brownian motion to multidimensional anomalous diffusion is considered by using fractional differential equation in [13, 14]. Analytical solution of fractional Navier–Stokes equation is investigated by using modified Laplace decomposition method in [15]. In [16] the maximum principles for solutions of the linear fractional diffusion equations are derived, in [17], the regional controllability for the Riemann–Liouville time fractional diffusion systems is analysed, in [18] a harmonic analysis of random fractional diffusion-wave equations is done, in [19] the Cauchy problem for fractional diffusion equations is discussed, and second order accuracy finite difference methods for space-fractional partial differential equations are proposed in [20]. The space-time fractional nonlinear Schrödinger equation is solved by mean of on the fractional Riccati expansion method [21]. Analytical solution of time-fractional Drinfeld-Sokolov-Wilson system is obtained by using residual power series method [22].In this direction, we dedicate this work to investigate a fractional diffusion equation which employs space and time fractional derivatives by taking a time-dependent diffusion coefficient, an absorbent or sources term and an external force into account. More precisely, we focus our attention on the following equation(,)()(,)[()(,)]()(,)tx t dt D t t x tt xtF x x t dt a t t x txγμρρμρρ∂∂∂∂∂'''=-⎰'''---⎰∂(1)With 01γ<…, 02μ<…, where D(t) is a time dependent diffusion coefficient, F(x) is an external force, a(t) is a time dependent absorbent term, which may be related to a reaction diffusion process. Here we use the Caputo operator for the fractional derivative with respect to time t and the Riesz-Weyl operator for the fractional derivative with respect to spatial x [23] and we work with the positive spatial variable x. Later on, we will extend the results to the entire real x-axis by the use of symmetry (in other words, we are working with /||xμμ∂∂). The presence of the reaction term like the one presents in the above equation may be useful to investigate several situations by choosing an appropriated a(t). For example, catalytic processes in regular, heterogeneous, or disordered systems [24, 25].The plan of this work is to start by considering (1) without external force and absorbent term. Then we consider (1) in the presence of the absorbent term 1()/()a t atββ-=Γwithout external force. After that we incorporate the external force ()F x x=-K in our analysis. In all the above cases, (1) satisfies to the generic initial condition (,0)()x xρρ= (()xρ is a given function), and the natural boundary condition(,)0tρ±∞=. The remainder of this paper goes as follow. In Sec.2, we obtain the exact solutions for the previous cases. In Sec.3, we present our conclusions.II.S OLUTION FOR THE F RACTIONAL D IFFUSION E QUATION Let us start our analysis by considering (1) in the absence of the external force and the absorbent term. Thus (1) reads2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2017)(,)()(,).t x t dt D t t x t t x γμγμρρ'''=-∂∂∂∂⎰ (2)Notice that for 1, 2γμ==, (2) reduces to the usual diffusion equation taking memory effect into account, which can be obtained from a dichotomous random process [26]. By applying the Laplace and Fourier transforms, and employing Riesz representation for the spatial fractional derivatives, we may simplify (2), which is an integral order differential equation, to the following algebraic equation1ˆˆˆ(,)(,0)()||(,),s k s s k D s k k s γγμρρρ--=- (3)where(,){(,)}(,)st x s x t x t e dt ρρρ∞-==⎰ L ,(){()}()st D s D t D t e dt Ds α∞--===⎰L , and ˆ(,){(,)}(,)ikx k t x t x t e dx ρρρ+∞--∞==⎰F . Then, (3) can be solved by the Green function method [27]. So we have(,)(,)(,0).x t dx x x t x ρρ+∞-∞'''=-⎰G(4)Applying the Fourier and Laplace transform in (4), weobtain the solution which is given byˆˆ(,)(,)(,0),k s k s k ρρ= G (5)1(,),()||s k s s Ds k γγμ-=+ G(6)where ˆ(,0)k ρis the Fourier transform of the initial condition and (,)k t Gis the Green function of (2) in the Fourier-Laplace space. Applying the inverse of Laplace transform, we obtain,1(,)(||),k t E D k tμγαγα++=-G (7)where ,()E x αβis the Mittag-Leffler function. In order to perform the inverse of Fourier transform, we express (,)k t Gin the terms of Fox function, i.e. (1)()(1)()(,(1)),,(,())(,(1)),,(,())[|]p q a A a A p m np q b B b B q H x ⋯⋯ [28]. So (7) can be written as follows11(0,1)12(0,1),(0,)(,)[|||].k t H D k t μγαγα++=G (8)This solution recovers the usual one for (,)(2,1)μγ= and for 2μ≠ it extends the results found in [29]. Note that the Mellin transform of the Fourier transform of f (x ) is an even function{[()]()}(){[()]()}()2()(){()}(1).2c f x k z f x k z zz cos f x z π==Γ-M F F M (9)We first evaluate the Mellin transform of (8) to find the Mellin transform of (,)x t G . The Mellin transform then only need to be inverted to find Fourier inverse, (,)x t G . To find the Mellin transform of (8), we note the Mellin transform of a Fox function is given by [30](,)11(,)()11()(1){[|]},(1)()p p q q m na j j j j j j m nzp qb z q p j m j j j n j j b z a z Hax ab z a z αββαβα==-=+=+∏Γ+∏Γ--=∏Γ--∏Γ+M (10)when the following conditions are met110,q mj j j j δβα===->∑∑(11)11110,p qnmj jjj j j n j j m A ααββ==+==+=-+->∑∑∑∑(12)1|()|,2arg a A π<(13)111[()]()[()].jj j m j n jjb a min z min βα≤≤≤≤--<<R R R(14)By applying this procedure, we obtain (see Figure I)11(1,),(1,)2123111111/(0,)(1,)(,)222||(,)[|].2()x x t Dt γαγαμμμμγαμμμ++--+-G(15)FIGURE I. THE BEHAVIOR OF GREEN FUNCTION (,)x t G IN (15) ISILLUSTRATED BY CONSIDERING 1/2)(,)Dt x t γαμ+G VERSUS1/||2()x Dt γαμ+ FOR TYPICAL VALUES OF γα+ AND μIn Figure I, we show the behavior of the above equation for typical values of μ, γ and α. Note that the Green function obtained here leads to an anomalous spreading of the initial condition due to the presence of the spatial and time fractional derivatives and a memory effect. This feature can be verified, for simplicity, by analyzing the second movement of (15) for particular case μ=2. For this case, it is given by202()()(1)t x dt t t D t γγ'''<>=-Γ+⎰ (16)For the initial condition (,0)()x x ρδ=and the diffusion coefficient 1()/()D t Dt αα-=Γ. Figure II shows the behavior of <x 2> versus t , which illustrates how (16) evolves on the time by considering, for simplicity, D =1 for typical values of γ and α.FIGURE II. THE BEHAVIOR OF < X 2> VERSUS TIn Figure II, we can see for small time <x 2> is dominated by the initial distance, and for large time the rate of <x 2> is less than that of the intermediate time. This behaviors are verified in turbulent processes [31]. At this point, by submitting (15) andthe initial condition (,0)()x x ρρ= into (4), we can get thesolution for (2), which is given by11(1,),(1,)2123111111/(0,)(1,)(,222(,)||[|]().2()x t x x dx x Dt γαγαμμμμγαμμμρρ++--+∞+-∞-='-'⎰(17)The result obtained here can be rated to several resultspresented in [10, 12, 32].In this direction, by using the previous result and the method of images [27], we may find the solution when the boundary condition is defined in a semi-infinity interval, i.e.(0,)(,)0t t ρρ=∞=. In particular, the solution taking this boundary condition into account, in the absence of theabsorbent term and external force, is given by11(1,),(1,2123111111/(0,,)(,)22211(1,,)2123111111/(0,)(1,)(,222||(,)[|]2()||[|]2()x x t H Dt x HDt γαγαμμμμγαμμμγαγαμμμμγαμμμξρξ++--+-++--+--=+-(18)For the initial condition (,0)()x x ρδξ=-. This result extends results found in [33, 34] and the first passage time distribution for the system governed by this case, using the definition(,)()x t t dx tρ∞∂=-∂⎰F employed in [35], is given by11(1,),(1,)2123111111/(0,)(1,)(,)222()[|],2()t Dt γαγαμμμμγαμμμξ++--+-=F (19) Which has the asymptotic behavior 1()/()~1/t t γαμ++F forlarge time. In Figure III, the behavior of the first passage time distribution ()t Fin (19) is illustrated by considering [/(2())]()t μγα+F versus 1//(2())Dt γαμξ+, for typical values of γ + α and μ.FIGURE III. THE BEHAVIOR OF THE FIRST PASSAGE TIMEDISTRIBUTION ()t F IN (19)Let us go back to (1) and consider 1()/()a t at ββ-=Γ . Then,(1) reads100(,)()(,)()(,).()t ta x t dt D t t x t dt t t x t t x γμβγμρρρβ-∂∂∂''''''=---Γ∂⎰⎰ (20)By using the Laplace and Fourier transforms, at the same time employing Riesz representation for the spatial fractional derivatives, we have1ˆˆˆˆ(,)(,0)()||(,)()(,),s k s s k D s k k s a s k s γγμρρρρ--=-- (21)where ()D s Ds α-= , ()a s as β-= and ˆ(,0)k ρis the Fourier transform of the initial condition. The solution of this equation,for simplicity, by considering ˆ(,0)1k ρ=, is given by1ˆ(,).()||()s k s s D s k a s γγμρ-=++ (22)Then, we employ the procedure presented in [36], where an explanation of how to get the series expansion in terms of Fox H function can be found. By applying this procedure, we obtain()110()ˆ(,).(||)j j j j a s k s s D k γααβγαμρ++--∞++=-=+∑ (23)Applying the inverse of Laplace transform on the above equation, we can obtain(),()1011(,1)12(0,1)((),)0()ˆ(,)(||)!()[|||].!j j j j j j j j at k t E D k t j at H D k t j βγμγαγαβαβγμγαβγγαρ+∞++-+=+∞+--++=-=--=∑∑ (24)Then, following the same procedure as in the first case tofind the Fourier inverse of ˆ(,)k t ρ, we have 11(1,),(1(),)2123111111/(0,)(1,)(,222(,)||[|].2()j j j j x t x Dt γαγαβγβγμμμμγαμμμρ+++∞-++-++-==(25) Note that the result got here for a bi-fractional reaction diffusion equation recovers the solution for the usual one. Let us incorporate the external force ()F x x =-K into the previous calculations. For this case, (1) reads100(,)()(,)[(,)]()(,).()ttx t t a dt D t t x t x x t dt t t x t x x γγμβμρρρρβ-∂∂∂∂∂∂=''''''-+--Γ⎰⎰K (26)Following the procedure employed above to the casewithout external forces, we also use the Fourier and Laplace transforms to simplify our study. By using these integral transforms, (26) can be simplified to()||101()||ˆ(,)(.!()D s k n n D s k s k s e n s n a s μμγμγρμμ-∞-==++∑ K K K (27)By applying the inverse of Laplace transform on (27) asabove, we can obtain10(0,)11(,1)000(),1[()]||ˆ(,)[|]!! (()).j tn n j j j a t t k k t dt H t n j t E n t t βγμααγγβρμμ+∞∞-==+'--''=''⨯--∑∑⎰D K K (28)Here, we used the property of the Laplace transform ofconvolution formula, i.e. []f g f g *=⋅L , where0()()tf g dt f t t g t '''*=-⎰.In order to get the solution, we need to get the inverse ofFourier transform of (,)k t G. Therefore, we only need to perform the inverse of Fourier transform on10(0,)11(,1)||[|]n D k t H μααμ-'K . Following the same procedure employed in the first case, we have1(1,)(0,)1100,111/11(,1)22111(,)(1,222||||{[|]}[()|]2n n D k t x H Dt αμααμμμαμμ---''K F K (29)and1(1,)(0,)111/221110(,)(1,)00222(),1||(,)[(|]2 (()).j n tn j j j x x t dt Dt E n t t αβγμμμαγγβμρμ+∞∞-==+=''⨯--∑∑⎰K K(30)The above equation in the absence of absorbent term recovers the results found in [37], i.e. a (t )=0. Note that the solution of (26) in the absence of absorbent term is a stationary one given in terms of the L évy distribution. This feature is a characteristic of the presence of the spatial derivatives in the diffusion equation which changes the probability for a jump length (see [38] and references therein).III. S UMMARY AND C ONCLUSIONSWe have worked out a generalized diffusion equation which presents space and time fractional derivatives and takes an absorbent term and the external force into account. We have first analyzed the case characterized by the absence of external forces and the absorbent term. For this case, we have obtained the exact solution and expressed it in terms of a Fox function. Furthermore, we have considered the second moment for this case and obtained the first passage time distribution by taking the boundary conditions (0,)(,)0t t ρρ=∞= into account. Then we consider (2) with an absorbent term a (t )=at β-1/ Γ(β). Subsequently, we have incorporated the external force ()F x x =-K to the previous situations in which the absorbentterm is present. For the third case, we have also discussed the stationary solution which emerges from α(t)=0. In this sense, the present results may be considered as an extension to a broad context of the analysis for the time fractional diffusion equations. Finally, we expect that the results obtained here may be useful to the discussion of the anomalous diffusion systems where fractional diffusion equations play an important role.A CKNOWLEDGMENTWe would like to thank the Natural Science Foundation of Zhejiang (Grant No. LY17A010020) for partial financial support and be grateful to the anonymous referees for useful comments and suggestions.R EFERENCES[1]J. Bouchaud and A. Georges, "Anomalous diffusion in disordered media:statistical mechanisms, models and physical applications," Physics reports, vol. 195, pp. 127-293, 1990.[2]H. Spohn, "Surface dynamics below the roughening transition," Journalde Physique I, vol. 3, pp. 69-81, 1993.[3]T. H. Solomon, E. R. Weeks and H. L. Swinney, "Observation ofanomalous diffusion and Lévy flights in a two-dimensional rotating flow," Phys Rev Lett, vol. 71, p. 3975, 1993.[4] F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, "Subrecoil laser cooling and Lévy flights," Phys Rev Lett, vol. 72, p. 203, 1994.[5]J. Stephenson, "Some non-linear diffusion equations and fractaldiffusion," Physica A: Statistical Mechanics and its Applications, vol.222, pp. 234-247, 1995.[6]V. Plerou, P. Gopikrishnan, L. A. N. Amaral, X. Gabaix, and H. E.Stanley, "Economic fluctuations and anomalous diffusion," Phys Rev E, vol. 62, p. R3023, 2000.[7]L. Longjin, F. Ren and W. Qiu, "The application of fractional derivativesin stochastic models driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, vol. 389, pp. 4809-4818, 2010.[8]L. Lv, J. Xiao, L. Fan, and F. Ren, "Correlated continuous time randomwalk and option pricing," Physica A: Statistical Mechanics and its Applications, vol. 447, pp. 100-107, 2016.[9]R. Metzler and J. Klafter, "The random walk's guide to anomalousdiffusion: a fractional dynamics approach," Physics reports, vol. 339, pp.1-77, 2000.[10]R. Metzler and T. F. Nonnenmacher, "Space-and time-fractionaldiffusion and wave equations, fractional Fokker-Planck equations, and physical motivation," Chem Phys, vol. 284, pp. 67-90, 2002.[11] B. West, M. Bologna and P. Grigolini, Physics of fractal operators:Springer Science & Business Media, 2012.[12] F. Mainardi, G. Pagnini and R. K. Saxena, "Fox H functions in fractionaldiffusion," J Comput Appl Math, vol. 178, pp. 321-331, 2005.[13]V. V. Uchaikin, "Multidimensional symmetric anomalous diffusion,"Chem Phys, vol. 284, pp. 507-520, 2002.[14]L. Lv, F. Ren, J. Wang, and J. Xiao, "Correlated continuous time randomwalk with time averaged waiting time," Physica A: Statistical Mechanics and its Applications, vol. 422, pp. 101-106, 2015.[15]S. Kumar, D. Kumar, S. Abbasbandy, and M. M. Rashidi, "Analyticalsolution of fractional Navier-Stokes equation by using modified Laplace decomposition method," Ain Shams Engineering Journal, vol. 5, pp.569-574, 2014.[16]M. Al-Refai and Y. Luchko, "Maximum principle for the fractionaldiffusion equations with the Riemann-Liouville fractional derivative and its applications," Fract Calc Appl Anal, vol. 17, pp. 483-498, 2014. [17] F. Ge, Y. Chen and C. Kou, "Regional controllability analysis offractional diffusion equations with Riemann-Liouville time fractional derivatives," Automatica, vol. 76, pp. 193-199, 2017. [18]V. V. Anh and N. N. Leonenko, "Harmonic analysis of randomfractional diffusion--wave equations," Appl Math Comput, vol. 141, pp.77-85, 2003.[19]S. D. Eidelman and A. N. Kochubei, "Cauchy problem for fractionaldiffusion equations," J Differ Equations, vol. 199, pp. 211-255, 2004. [20]Y. Takeuchi, Y. Yoshimoto and R. Suda, "Second order accuracy finitedifference methods for space-fractional partial differential equations," J Comput Appl Math, vol. 320, pp. 101-119, 2017.[21] E. A. Abdel-Salam, E. A. Yousif and M. A. El-Aasser, "AnalyticalSolution of the Space-Time Fractional Nonlinear Schrödinger Equation,"Rep Math Phys, vol. 77, pp. 19-34, 2016.[22]H. M. Jaradat, S. Al-Shara, Q. J. Khan, M. Alquran, and K. Al-Khaled,"Analytical solution of time-fractional Drinfeld-Sokolov-Wilson system using residual power series method," IAENG International Journal of Applied Mathematics, vol. 46, pp. 64-70, 2016.[23]I. Podlubny, Fractional differential equations vol. 198: Academic press,1998.[24]P. A. Alemany, D. H. Zanette and H. S. Wio, "Time-dependentreactivity for diffusion-controlled annihilation and coagulation in two dimensions," Phys Rev E, vol. 50, p. 3646, 1994.[25] B. J. West, P. Grigolini, R. Metzler, and T. F. Nonnenmacher,"Fractional diffusion and Lévy stable processes," Phys Rev E, vol. 55, p.99, 1997.[26]P. Allegrini, P. Grigolini and B. J. West, "Dynamical approach to Lévyprocesses," Phys Rev E, vol. 54, p. 4760, 1996.[27]H. Feshbach and P. M. Morse, Methods of theoretical physics: McGraw-Hill Interamericana, 1953.[28] A. M. Mathai and R. K. Saxena, "The H function with applications instatistics and other disciplines," 1978.[29]R. Metzler, E. Barkai and J. Klafter, "Anomalous diffusion andrelaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach," Phys Rev Lett, vol. 82, p. 3563, 1999.[30]H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-functions of oneand two variables, with applications: South Asian Publishers, 1982. [31]G. Boffetta and I. M. Sokolov, "Relative dispersion in fully developedturbulence: the Richardson's law and intermittency corrections," Phys Rev Lett, vol. 88, p. 094501, 2002.[32][32] F. Mainardi, Y. Luchko and G. Pagnini, "The fundamental solutionof the space-time fractional diffusion equation," Fract Calc Appl Anal, vol. 4, pp. 153-192, 2001.[33]G. Rangarajan and M. Ding, "Anomalous diffusion and the first passagetime problem," Phys Rev E, vol. 62, p. 120, 2000.[34]L. Lv, J. Xiao, L. Zhang, and L. Gao, "Solutions for a generalizedfractional anomalous diffusion equation," J Comput Appl Math, vol. 225, pp. 301-308, 2009.[35]H. Risken, Fokker-Planck Equation: Springer, 1996.[36]T. Langlands, "Solution of a modified fractional diffusion equation,"Physica A: Statistical Mechanics and its Applications, vol. 367, pp. 136-144, 2006.[37]R. Metzler, E. Barkai and J. Klafter, "Anomalous transport in disorderedsystems under the influence of external fields," Physica A: Statistical Mechanics and its Applications, vol. 266, pp. 343-350, 1999.[38] A. Schot, M. K. Lenzi, L. R. Evangelista, L. C. Malacarne, R. S. Mendes,and E. K. Lenzi, "Fractional diffusion equation with an absorbent term and a linear external force: Exact solution," Phys Lett A, vol. 366, pp.346-350, 2007.。

最优化理论与算法完整版课件

几何规划动态规划不确定规划：随机规划、模糊规划等
多目标规划对策论等
随机过程方法
统计决策理论马氏过程排队论更新理论仿真方法可靠性理论等
TP SHUAI
统计学方法
回归分析群分析模式识别实验设计因子分析等
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Ring signatures without random oracles

Ring Signatures without Random OraclesSherman S.M.Chow1,Joseph K.Liu2,Victor K.Wei3and Tsz Hon Yuen31Department of Computer ScienceCourant Institute of Mathematical SciencesNew York University,NY10012,USAschow@2Department of Computer ScienceUniversity of BristolBristol,UKliu@3Department of Information EngineeringThe Chinese University of Hong KongShatin,Hong Kong{kwwei,thyuen4}@.hkAbstract.Since the formalization of ring signature by Rivest,Shamirand Tauman in2001,there are lots of variations appeared in the liter-ature.Almost all of the variations rely on the random oracle model forsecurity proof.In this paper,we propose a ring signature scheme basedon bilinear pairings,which is proven to be secure against adaptive chosenmessage attack without using the random oracle model.It is one of theﬁrst in the literature to achieve this security level.Keywords:Ring Signature,Random Oracle Model,Bilinear Pairings1IntroductionA ring signature scheme(for examples[1],[7],[9],[14],[16],[19],[23]and[24]) allows members of a group to sign messages on behalf of the group without revealing their identities,i.e.signer anonymity.In addition,it is not possible to decide whether two signatures have been issued by the same group member. Diﬀerent from a group signature scheme(for examples,[12],[10]and[3]),the group formation is spontaneous and there is no group manager to revoke the identity of the signer.That is,under the assumption that each user is already associated with a public key of some standard signature scheme,a user can form a group by simply collecting the public keys of all the group members including his own.These diversion group members can be totally unaware of being conscripted into the group.Ring signature schemes could be used for whistle blowing[19],anonymous membership authentication for ad hoc groups[9]and many other applications It is the full version of the paper in ASIACCS06.The comment of[5]is correct for the previous version of this paper only.2Sherman S.M.Chow,Joseph K.Liu,Victor K.Wei and Tsz Hon Yuen which do not want complicated group formation stage but require signer anonymity. For example,in the whistle blowing scenario,a whistleblower gives out a secret as well as a ring signature of the secret to the public.From the signature,the public can be sure that the secret is indeed given out by a group member while cannotﬁgure out who the whistleblower is.At the same time,the whistleblower does not need any collaboration of other users who have been conscripted by him into the group of members associated with the ring signature.Hence the anonymity of the whistleblower is ensured and the public is also certain that the secret is indeed leaked by one of the group members associated with the ring signature.Ring signature scheme can be used to derive other primitives as well.It had been utilized to construct non-interactive deniable ring authentication[20], perfect concurrent signature[21]and multi-designated veriﬁers signature[18].Many reductionist security proofs used the random oracle model[4].Several papers proved that some popular cryptosystems previously proved secure in the random oracle are actually provably insecure when the random oracle is instan-tiated by any real-world hashing functions[11,2].All of the existing schemes are either relying on the random oracle assumption or not giving rigorous secu-rity proof[23].Therefore ring signatures provably secure in the standard model attract a great interest.It is natural to ask whether there is practical ring signature scheme provably secure without random oracles.In this paper,we provide an aﬃrmative answer by constructing a ring signature scheme whose security is reducible to a new type of Diﬃe-Hellman problem without random oracles.1.1ContributionsIn this paper,we propose a ring signature scheme that is proven to be secure against adaptive chosen message attack without relying on the random oracle assumption[4].It is one of theﬁrst in the literature.Its construction is based on bilinear pairings.We give a rigorous security proof.We extend the q-Strong Diﬃe-Hellman Problem[6]into the(q,n)-Disjunctive Strong Diﬃe-Hellman Problem.The security of our proposed ring signature scheme is reduced to this hard problem.In addition,we show the generic construction of ring signature scheme.1.2Previous WorkRing signature scheme wasﬁrst formalized by Rivest et.al.in[19].There are many pairing-based ring signature schemes.Ring signature schemes from pairing-based short signature were proposed in[7]and[25].With the help of pairing,ID-based ring signature was introduced in[24]and ID-based threshold ring signature scheme was introduced in[13].To the best of authors’knowledge,the most eﬃcient(ID-based or non-ID-based)ring signature scheme from bilinear pairings is[14],which requires only a constant number of pairings computation(zero in signing and two in veriﬁcation).Ring Signatures without Random Oracles3 Among all the above schemes,only the one proposed in[23]is claimed to be provably secure without using the random oracle model.However,there is no formal security proof for this claim.For the remaining ring signature schemes, none of them can be proven secure without using the random oracle assumption.A recent and parallel work by Bender,Katz and Morselli[5]has proposed new formal deﬁnitions of security for ring signature schemes.They also propose a solution for any number of users based on general assumptions,and an eﬃcient construction for two users.Both constructions do not rely on random oracles. They do not propose any eﬃcient solution for n>2users.OrganizationThis paper is organized as follow:The next section contains preliminaries about the underlying cryptographic primitive used in this paper.In Section3,we review the deﬁnition of secure ring signature schemes.In section4we show the generic construction of ring signature scheme.Then we propose our new ring signature instantiation in Section5and give the security proofs.Finally,we conclude the paper in Section6.2PreliminariesBefore presenting our results,we review the deﬁnitions of groups equipped witha bilinear pairings and a related assumption.2.1Bilinear PairingsHere we follow the notation in[8].Let G1and G2be two(multiplicative)cyclic groups of prime order p.Let g1be a generator of G1and g2be a generator of G2.We also letψbe an isomorphism from G2to G1,withψ(g2)=g1,andˆe be a bilinear map such thatˆe:G1×G2→G T with the following properties:1.Bilinearity:For all u∈G1,v∈G2and a,b∈Z,ˆe(u a,v b)=ˆe(u,v)ab.2.Non-degeneracy:ˆe(g1,g2)=1.putability:There exists an eﬃcient algorithm to computeˆe(u,v).2.2Diﬃe-Hellman ProblemWe introduce the following problem:Deﬁnition1((q,n)-DsjSDH).The(q,n)-Disjunctive Strong Diﬃe-Hellman Problem in(G1,G2)is deﬁned as follow:Given h∈G1,g,g x∈G2,distinct a i∈Z∗p and Universal One-Way Hash Functions(UOWHF)H i(·)for1≤i≤n, distinct nonzero mτfor1≤τ≤q andσi,τfor1≤i≤n,1≤τ≤q,satisfying:ni=1σ(xa i+H i(mτ))i,τ=h4Sherman S.M.Chow,Joseph K.Liu,Victor K.Wei and Tsz Hon Yuenfor allτ.Output m∗and(σ∗i,γi),for1≤i≤n such that they satisfy:ni=1σ∗i(xa i+H i(m∗)+γi)=hand H i(m∗)+γi=H i(mτ)for all i andτ.We say that the(q,n,t, )-DsjSDH assumption holds in(G1,G2)if no t-time algorithm has advantage at least in solving the(q,n)-DsjSDH problem in(G1,G2).Notice that if n=1,the(q,1)-DsjSDH Assumption without hash is equiva-lent to the q-CAA Assumption[22].By Theorem1of[22],the q-SDH’Assump-tion is equivalent to the q-CAA Assumption.The q-SDH Assumption[6]implies the q-SDH’Assumption.3Security DeﬁnitionHereafter we review the deﬁnition and the security notion of ring signature schemes.Letλs∈N be a security parameter and m∈{0,1}∗be a message.Deﬁnition2(Ring Signature Scheme).A ring signature scheme is a triple (G,S,V)where–(ˆs,P)←G(1λs)is a probabilistic polynomial time algorithm(PPT)which takes as input a security parameterλs,produces a private keyˆs and a public key P.–σ←S(1λs,ˆs,L,m)is a PPT which accepts as inputs a security parameter λs,a private keyˆs,a set of public keys L including the one that correspond to the private keyˆs and a message m,produces a signatureσ.–1/0←V(1λs,L,m,σ)is a PPT which accepts as inputs a security parameter λs,a set of public keys L,a message m and a signatureσ,returns1or0 for accept or reject,respectively.We require that V(1λs,L,m,S(1λs,ˆs,L, m))=1for any message m and any private keyˆs which is generated by G(1λs)and any set public keys L including the one that correspond to the private keyˆs.For simplicity,we usually omit the input of security parameter when using S and V in the rest of the paper.L may include public keys based on diﬀerent security parameters.The security of the signature scheme deﬁned above is set to the smallest one among them.G may also be extended to take the description of key types.The security of a ring signature scheme consists of two requirements,namely Signer Ambiguity and Existential Unforgeability.They are deﬁned as follows. Deﬁnition3(Signer Ambiguity).Let L={P1,···,P n}where each key isgenerated as(ˆs i,P i)←G(1λs i)for someλsi ∈N.Letλs=min(λs1,···,λsn).Aring signature scheme is said to be unconditionally signer ambiguous if,for anyRing Signatures without Random Oracles5 L,any message m,and any signatureσ←S(ˆs,L,m)whereˆs∈{ˆs1,···,ˆs n},any unbound adversary E accepts as inputs L,m andσ,outputsˆs with probability 1/n.It means that even all the private keys are known,it remains uncertain that which signer out of n possible signers actually generates a ring signature. Existential Unforgeability.For ring signature,we would like to consider the security model for existential unforgeability.It models the adaptive chosen mes-sage attack.For a ring signature scheme with n public keys,the existential unforgeability is deﬁned as the following game between a challenger and an ad-versary A:1.The challenger runs algorithm G.Let L={P1,···,P n}be the set of n publickeys in which each key is generated as(ˆs i,P i)←G(1λs i)for someλsi ∈N.Letλs=min(λs1,···,λsn).A is given L and the public parameters.2.A can adaptively queries the signing oracle q S times.SO(m):On input anymessage m,returns a ring signatureσ←S(ˆs i,L,m),such that V(L,m,σ) =1.3.Finally A outputs a tuple(m∗,σ∗).A wins if V(L,m∗,σ∗)=1and m∗is never been queried to SO.Denote Adv A be the probability that A wins in the above game,taken over the coinﬂips of A and the challenger.Deﬁnition4.A ring signature scheme is(t,q S, )-existentially unforgeable un-der an adaptive chosen message attack if no PPT adversary A runs in time at most t,with at most q S queries to SO,and Adv A is at least .Note that our security model is similar to the“Unforgeability againstﬁxed-ring attacks”as in[5].We say that a ring signature scheme is secure if it satisﬁes the Signer Am-biguity and Existential Unforgeability.4Generic ConstructionWe use Cramer,Damg˚ard,and Shoenmaker[15]:A ring signature is a non-interactive zero-knowledge(NIZK)proof of the following disjunction:SP K{x:∨1≤i≤n(x,y i)∈R i}(M)(1) where R i={(x i,y i)}is the sk-pk relation of the i-th user,and SP K is a signature of proof of knowledge notion from[10].Generic instantiation of NP statement:Groth,Ostrovsky,and Sahai[17] gave an eﬃcient NIZK proof of general NP statement.The size of the proof is O(λs|C|),whereλs is the security parameter,and|C|is the size of the NP circuit.The complexity is O(λs)λs-bit exponentiations.6Sherman S.M.Chow,Joseph K.Liu,Victor K.Wei and Tsz Hon Yuen The circuit size of the NP circuit(1)is O(|R|),assuming all R i has the same size.Typically,|R|=O(λs)λs-bit exponentiations,i.e.|R|=O(λs(logλs)2) for all major sk-pk relations.Therefore,the proof size of(1)instantiated by the method in[17]is O(λ2s(logλs)2)bits.By[15],we have the following theorem:Theorem1.The above generic ring signature is secure provided each compo-nent signature is secure.5Our InstantiationWe construct a fully secure ring signature scheme in the standard model using the DsjSDH assumption.Let(G1,G2)be bilinear groups where|G1|=|G2|=p for some prime p.Let the message to be signed be m∈Z∗p.(Explicitly,the domain can be extended to anyﬁnite string{0,1}∗using a collision resistant hash function H:{0,1}∗→Z∗p.)The scheme is as follows:Setup.Select a pairingˆe:G1×G2→G T.Let h,g1be a generator of G1,g2 be a generator of G2andψ(g2)=g1.Deﬁne H i(·)be universal one-way hash functions(UOWHF)for1≤i≤n.The public parameters are(ˆe,h,g1,g2,H1, ...,H n).Key Generation.For user i,he picks elements x i,y i∈R Z∗p which are the secret keys.The corresponding public keys are u i,v i∈G2where u i=g x i2,v i=g y i2.Signing.Assume the signer wants to form a ring signature of n users{(u1,v1), ...,(u n,v n)}with his own public keys at index t.To sign a message m:1.For i∈{1,...,n}\t,he picks z i∈R Z∗p and computesσi=g z i1.2.He picks R i∈R Z∗p for1≤i≤n.Heﬁnds w∈G1such thath=w·[i∈{1,...,n}\t (ψ(u i·g H i(m)2·v R ii)z i)],3.He computesσt=w1/(x t+H i(m)+R t y t)by his secret keys x t,y t.4.The signature is{(σ1,R1),···,(σn,R n)}.Veriﬁcation.Given a signature{(σ1,R1),···,(σn,R n)}from a set of users {(u1,v1),...,(u n,v n)}for message m,the veriﬁer accepts if the following holds:ni=1[ˆe(σi,(u i·g H i(m)2·v R ii))]=ˆe(h,g2)Remark:Collision resistant hash function is suﬃcient for the scheme instead of UOWHF.The former is considered more eﬃcient than the latter.Ring Signatures without Random Oracles7 5.1Security AnalysisThe correctness of the scheme is straightforward.Theorem2.Our ring signature scheme is unconditionally signer ambiguous.Proof.For i∈{1,...,n}\t,σi’s are random since z i’s are randomly picked.σt can be considered as in the form of g1z t as g1is the generator and hence such z t always exists.It is determined byσi’s by the equation,soσt is also uniformly distributed.Also the R i’s are also randomly picked.To conclude,the distribution of the components of the signature generated by our scheme is independent of what is the group of participating signer,for any message m and any set of users associated to the ring signature.Theorem3.Suppose the(q,n,t , )-DsjSDH assumption holds in(G1,G2). Then our ring signature scheme with n users is(t,q S, )-secure against existential forgery under an adaptive chosen message attack provided that:q S≤q,t≤t −Θ(q S nT)and ≥2( +q S/p)where T is the maximum time for an exponentiation in G1and G2.Proof.Suppose the adversary A can forge the basic ring signature scheme with n users.We construct an algorithm S that uses A to solve the(q,n)-DsjSDH problem.Initialization.S is given the DsjSDH tuple:h,g,g z,a i,H i,ˆmτ,ˆσi,τfor 1≤i≤n,1≤τ≤q.Then B sets g2=g,g1=ψ(g2).Sﬂips a fair coin c mode and setups as follows:1.If c mode=1,S randomly picks y,b1,...,b n∈Z∗p,and sets public key of useri(u i,v i)=(g za i,g yb i).2.If c mode=2,S randomly picks x,b1,...,b n∈Z∗p,and sets public key of useri(u i,v i)=(g xb i,g za i).Denote the set of public keys as L.B gives(h,g1,g2,L,H1,...,H n)to A. Simulating SO.For theτ-th SO query,S generates a signature for a message mτ.S computes m i,τ=H i(mτ)andˆm i,τ=H i(ˆmτ).1.If c mode=1,checks if there exist i∈{1,...,n}such that g za i=g−m i,τ.Ifso,then S can compute z and answer the(q,n)-DsjSDH problem.At this point S successfully terminates the simulation.Otherwise,for all1≤i≤n,B computes R i,τ=(ˆm i,τ−m i,τ)/yb i.In the unlikely that R i,τ=0,S reportsfailure and aborts.S returns the signature(ˆσi,τ,R i,τ)for1≤i≤n.Then the signature satisﬁes:ni=1[ˆe(ˆσi,τ,(u i·g H i(mτ)2·v R i,τi))]8Sherman S.M.Chow,Joseph K.Liu,Victor K.Wei and Tsz Hon Yuen=ni=1[ˆe(ˆσi,τ,(u i·g H i(mτ)+yb i R i,τ2))]=ni=1[ˆe(ˆσi,τ,(u i·gˆm i,τ2))]=ni=1[ˆe(ˆσi,τ,g za i+H i(ˆmτ)2)]=ˆe(h,g2)2.If c mode=2,for all1≤i≤n,B computes R i,τ=(xb i+m i,τ)/ˆm i,τ.Computeσi,τ=ˆσ1/R i,τi,τ.S returns the signature(σi,τ,R i,τ)for1≤i≤n.Then the signature satisﬁes:ni=1[ˆe(σi,τ,(u i·g H i(mτ)2·v R i,τi))]=ni=1[ˆe(σi,τ,(g xa i+H i(mτ)2·v R i,τi))]=ni=1[ˆe(ˆσ1/R i,τi,τ,(gˆm i,τR i,τ2·v R i,τi))]=ni=1[ˆe(ˆσi,τ,g(H i(ˆmτ)+za i)2)]=ˆe(h,g2)Hence S generates valid signatures for mτfor both cases.Simulation Deviation.It can be shown easily that any pairwise statistical distance among(1)Real World,(2)Ideal World-1where c mode=1,and(3) Ideal-World-2where c mode=2,is negligible.The proof is similar to the proof in Theorem2and thus omitted.Extraction.Finally,A outputs a signature(σ∗i,R∗i)for1≤i≤n for message m∗and wins if it passes the veriﬁcation and m∗is never been queried to SO. Denote m∗i=H i(m∗).There are two cases:1.With c mode=1:Conditioned on the above event,denote 1,1as the condi-tional probability of A’s delivered ring signature satisfying H i(m∗)+R∗i yb i=H i(ˆmτ)∀i,τ.Then S computesγi=R∗i yb i and returns(σ∗i,γi)for1≤i≤nas the solution to the(q,n)-DsjSDH problem.2.With c mode=2:Conditioned on the above event,denote 2,2as the condi-tional probability of A’s delivered ring signature satisfying H i(m∗)+R∗i za i=H i(ˆmτ)for some i,τ.Therefore for some i,τ,we have:H i(m∗)+R∗i za i=H i(mτ)+R i,τza iRing Signatures without Random Oracles9z=H i(m∗)−H i(mτ) a i(R i,τ−R∗i)Then the(q,n)-DsjSDH problem is solved.Notice that for c mode=1,S aborts if A issued a signature query mτ=ˆmτ.This happens with probability at most q S/p.Suppose A can forge the ring signature with probability .Due to the negligible statistical distance between the two ideal worlds and the real world,we have 1,1+ 2,2= /2−q S/p.Summarizing with the signer ambiguity,we have:Theorem4.The ring signature is secure if the(q,n,τ, )-DsjSDH assumption holds in(G1,G2).Remark.The above ring signature instantiation and proofs specialized to the short signature in[6]when n=1,with the modiﬁcation that the message is hashed before use.6ConclusionIn this paper,we propose a ring signature scheme that is proven to be secure without using the random oracle model.Its construction is based on bilinear pair-ings.It is theﬁrst instantiation in the literature to achieve the security of signer ambiguity and existential unforgeability with formal rigorous proofs.Further-more,we generalize the q-SDH Problem into(q,n)-Disjunctive SDH Problem. The security of our proposed scheme is reducible to this hard problem.Acknowledgments.The authors would like to thank the anonymous referees of the ASIACCS06and Dr.Jonathan Katz for the discussion.References1.M.Abe,M.Ohkubo,and K.Suzuki.1-out-of-n Signatures from a Variety of Keys.In Y.Zheng,editor,Advances in Cryptology-ASIACRYPT2002,Proceedings, volume2501of Lecture Notes in Computer Science,pages415–432.Springer,2002.2.M.Bellare,A.Boldyreva,and A.Palacio.An Uninstantiable Random-Oracle-Model Scheme for a Hybrid-Encryption Problem.In C.Cachin and J.Camenisch, editors,Advances in Cryptology-EUROCRYPT2004,Proceedings,volume3027 of Lecture Notes in Computer Science,pages171–188.Springer,2004.3.M.Bellare,D.Micciancio,and B.Warinschi.Foundations of Group Signatures:Formal Deﬁnitions,Simpliﬁed Requirements,and a Construction Based on General Assumptions.In E.Biham,editor,Advances in Cryptology-EUROCRYPT2003, Proceedings,volume2656of Lecture Notes in Computer Science,pages614–629.Springer,2003.4.M.Bellare and P.Rogaway.Random oracles are practical:A paradigm for designingeﬃcient protocols.In Proc.1st ACM Conference on Computer and Communica-tions Security,pages62–73.ACM Press,1993.10Sherman S.M.Chow,Joseph K.Liu,Victor K.Wei and Tsz Hon Yuen5. 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ING的结构和功能

REVIEWThe ING family tumor suppressors:from structure to functionAlmass-Houd Aguissa-Toure´•Ronald P.C.Wong •Gang LiReceived:29June 2010/Revised:31July 2010/Accepted:10August 2010/Published online:29August 2010ÓSpringer Basel AG 2010Abstract The INhibitor of Growth (ING)proteins belong to a well-conserved family which presents in diverse organisms with several structural and functional domains for each protein.The ING family members are found in association with many cellular processes.Thus,the ING family proteins are involved in regulation of gene tran-scription,DNA repair,tumorigenesis,apoptosis,cellular senescence and cell cycle arrest.The ING proteins have multiple domains that are potentially capable of binding to many partners.It is conceivable,therefore,that such pro-teins could function similarly within protein complexes.In this case,within this family,each function could be attributed to a speciﬁc domain.However,the role of ING domains is not deﬁnitively clear.In this review,we sum-marize recent advances in structure–function relationships in ING proteins.For each domain,we describe the known biological functions and the approaches utilized to identify the functions associated with ING proteins.Keywords ING ÁTumor suppressor ÁProtein domain ÁPHD ÁNLSIntroductionThe ﬁrst member of INhibitor of Growth (ING)family was found in 1996by a strategy based on subtractivehybridization between cDNAs from a normal mammary cell line and seven breast cancer cell lines followed by a subsequent in vivo selection for cDNA fragments capable of promoting neoplastic transformation [1].This gene is called ING1which encodes a 33-kDa protein (p33ING1b).Fluorescent in situ hybridization and radiation hybrid mapping linked ING1to the cytogenetic marker SHGC-5819at 13q34[2,3].The ING1gene has three exons and can be alternatively spliced to generate p47ING1a,p33ING1b,p27ING1d,and p24ING1c;the last of these results from an internal initiation at the ﬁrst ATG within exon 2[4–8].Since this discovery,four additional ING genes (ING2-5)encoding proteins and several splicing isoforms of ING2[9]and ING4[10]have been identiﬁed.By homology search of p33ING1b complementary cDNA sequence,the ING2(known as ING1L )gene was cloned [11].In 2003,ING3encoding a 46.8-kDa protein (p47ING3)with a C-terminal plant homeodomain (PHD)ﬁnger motif was subsequently identiﬁed through a com-putational domain search [12].The same year,the two newest members of the ING family,ING4and ING5were identiﬁed through a computational sequence homology search for expressed sequence tag clones with a PHD ﬁnger motif [13].ING family and biological functionsThe ING family proteins regulate a wide variety of cellular processes.The inhibition of ING1using antisense expres-sion constructs promotes cell transformation in cell lines and tumor formation in vivo,and blocks cells in the G1phase of the cell cycle when expressed ectopically [1].Also,studies have indicated that ING proteins are involved in cell cycle checkpoints and cell cycle progression [14,15].A.-H.Aguissa-Toure´ÁR.P.C.Wong ÁG.Li (&)Department of Dermatology and Skin Science,Jack Bell Research Centre,Vancouver Coastal Health Research Institute,University of British Columbia,2660Oak Street,Vancouver,BC V6H 3Z6,Canada e-mail:gangli@interchange.ubc.caCell.Mol.Life Sci.(2011)68:45–54DOI 10.1007/s00018-010-0509-1Cellular and Molecular Life SciencesING1expression is signiﬁcantly repressed in44%of human primary breast cancers and100%of established breast cancer cell lines[16].Decreased ING1expression has been found in many other forms of solid and blood tumors[17–26].Similarly,the expression of ING2,ING3 and ING4is reduced in human melanoma[27–29].All ING family proteins have been shown to cooperate with p53to induce apoptosis and cellular senescence[12,13,30–33], and accordingly the notion that the ING family proteins act as class II tumor suppressors has emerged.In addition, suppression of ING proteins has been shown to increase cell migration and to relieve contact inhibition[10,34,35].In addition,many studies using different model systems have implicated the ING family proteins in promotion of apoptosis[30,31,36,37],DNA damage repair[38–40], control of cellular aging[41],negative regulation of cell proliferation[1,42],chromatin remodeling[43,44],hor-mone responses[45,46]and regulation of tumor growth via NF-j B[47]and hypoxia inducible factor pathways[48, 49].Several types of tumors have been found to have either altered ING protein subcellular localization,ING muta-tions,or deletions[28,50–53].Various studies have suggested that most of the ING proteins are required for proper p53function[14,15],although more recent mouse model experiments indicate otherwise[54].ING family proteins in chromatin remodeling and gene transcriptionThe ING proteins have been found in chromatin remodel-ing complexes[55],indicating that ING proteins may act in the nucleus to regulate transcription[56,57].The chro-matin structure is very dynamic and is affected by multiple modiﬁcations of chromatin-associated proteins,including, but not limited to,histones and remodeling cofactors within particular chromatin regions.Indeed,chromosomal DNA and its associated proteins undergo dramatic alterations in structure during normal cellular processes such as DNA synthesis,transcription and repair[58,59].Conversely,it is known that DNA damage leads to changes in gene expression[60–62],and it is now clear that mechanisms that affect directly upon higher-order chromatin structure regulate cellular metabolic processes such as transcription, DNA replication and DNA repair.Chromatin structure is increasingly being attributed to modiﬁcation of the basic histones,the subunits of nucleo-somes.Histones are positively charged,low molecular weight DNA scaffolding proteins that are subject to numerous posttranslational modiﬁcations including acety-lation,methylation,phosphorylation,SUMOylation and ubiquitination[63,64].These modiﬁcations play diverse roles in modulating chromatin structure and have been linked to the regulation of gene transcription[65].Histone acetylation neutralizes the charge of basic(positively charged)lysine residues within histone proteins.Conse-quently,there is destabilization of the binding of histones to the negatively charged DNA so that other enzymes/ protein complexes are capable of unwinding the chromatin, accessing the DNA at selective sites and transcribing target genes.In other words,the dynamic modiﬁcation of histones through the enzymatic actions of histone acetyltransferase (HAT)and histone deacetylase(HDAC)protein complexes modiﬁes nucleosome structure,altering the degree of DNA relaxation and subsequently modifying the accessibility of regions of DNA to transcription factors[66].Not surprisingly,HAT and HDAC protein complex activity must be tightly regulated in order to maintain the appropriate level of histone acetylation in a given cellular environment.In fact,deacetylation of histone residues by HDAC can tighten a DNA strand because of the electric charge change of the histone tails;positively charged his-tone tails,which have high afﬁnity for negatively charged DNA,can be neutralized by acetylation,causing DNA relaxation.Several HAT/HDAC coactivators and core-pressors have been identiﬁed.The ING family proteins are involved in chromatin remodeling,and bind to and affect the activity of both HAT and HDAC protein complexes.In fact,ING1induces histone acetylation,promotes DNA repair and interacts with proliferating cell nuclear antigen (PCNA)[39,67].ING2is also implicated in the initial DNA damage sensing and chromatin remodeling in the nucleotide excision repair(NER)process[38,68],and recently a new function of ING2in the control of DNA replication has been found[69].The functional domains of ING family proteinsING proteins are a well-conserved family which are present throughout eukaryotic proteomes[70].Phylogenetic anal-yses have identiﬁed new ING family members in diverse organisms,including rats,frogs,ﬁsh,mosquitoes,fruitﬂies, worms,fungi and plants[70].All ING genes with the exception of ING3are found near the ends of chromosomes, and the function and expression of ING5could be affected by telomere erosion[70].ING1has four protein isoforms with identical C-terminus parts containing a conserved PHD ﬁnger motif[14].p33ING2shares60%identity with p33ING1b and encodes a33-kDa protein[11].Compared to ING1b,ING2contains an extra and unique leucine zipper domain which is thought to mediate hydrophobic protein–protein interactions[56].p29ING4and p28ING5are highly homologous with72.8%identity[13].Various studies have suggested that ING family proteins exert their biological functions through their associations46 A.-H.Aguissa-Toure´et al.with speciﬁc molecular partners(Table1).These associa-tions are possible through various structural and functional domains present in proteins.Thus,they allow the assembly and regulate the subnuclear localization of distinct com-plexes consisting of different combinations of proteins and interactors.In fact,the ING family members share a highly conserved PHD at their C-termini,a conserved central region containing the nuclear localization signal(NLS)and a variable N-terminal region.Thus,within ING proteins there are a number of distinct domains including PCNA-interacting protein(PIP)box,partial bromodomain(PBD), leucine zipper-like(LZL)domain,novel conserved region/ lamin interaction domain(NCR/LID),NLS,PHD,and polybasic region(PBR)(Fig.1).The N-terminus of ING family proteinsThe N-termini of ING proteins are more variable and mediate the majority of reported protein–protein interac-tions and functions as a protein-binding domain that targets distinct nuclear components and chromatin-remodeling complexes[14].It contains a LZL domain and a NCR[71]. Also,a functionally deﬁned domain,called SAID (SAP30-interacting domain)has been reported for ING1b at the N-terminus[44].This domain,which was deﬁned as the region of ING1b that directly interacts with SAP30(the sin3-associated protein30),is also suspected to be present on ING2,since both of these proteins directly interact with SAP30[44,72].This interaction is thought to bridge ING1 and ING2to SAP30-containing HDAC1/2complexes.ING1also has in its N-terminus a PIP box through which it binds PCNA in a DNA damage-inducible manner [67].Since PCNA is an essential factor for DNA replica-tion and repair,ING1may act to couple these processes to chromatin remodeling.The interaction of this domain is speciﬁcally induced upon UV damage[67]and has been hypothesized to switch PCNA activity away from DNA replication towards DNA repair.Among ING members,the PIP box is unique to ING1b.Bioinformatics analysis has revealed a second domain present only in ING1b and called PBD(partial bromodomain because of its sequence homology to bromodomains).The PBD binds SAP30of mSin3A-HDAC1which might target HDAC,and possibly HAT activity for some ING proteins[44].The LZL domain is found in the N-terminus of all ING proteins,except ING1.This domain consists of four toﬁve conserved leucine or isoleucine residues spanning every seven amino acids(forming a hydrophobic patch near the N-terminus)with a similar leucine distribution for ING3to ING5[15,70].However,little is known about the function of LZL and it been has reported that the LZL domain of Table1Protein or complex reported to bind to ING family protein domainProtein Domain Protein/complex involved ReferenceING1PHD ARF[119]PHD Brg1,BAF47/53/60/155/170/250[44]PHD DMAP-1[120]N/A GADD45[40]PHD H3K4me2/3[103,105,121]PHD HDAC1[122]N/A HMT activity[123]N/A hSir2[124]NLS Karyopherin a,b[78]LID Lamin A[74]PHD mSin3,HDAC1/2,SAP30,RbAp46/48[44,125] N/A p15(PAF)[126]N/A p42,p35[125]N/A p53[127]PHD p300[122]PIP PCNA[67]N/A RBP1[125]N/A SIRT1[128]N/A TRRAP,PCAF,CBP[122]N/A14-3-3[129]ING2PHD H3K4me2/3[103,105] N/A BAF47/53a/155/170[55]N/A HMT activity[123]PHD mSin3A,HDAC1/2,RbAp46/48[55]PHD p300,p300/p53[32,73]PHD PtdIns5P[33]PHD SNON[130]NCR PCNA[69]N/A RBP1/RBP1-like[55]N/A SAP30,SAP130,SDS3,BRMS1/BRMS1-like[131]N/A SIRT1[128]ING3N/A AcK5-H4,AcK8-H4,AcK12-H4[55]N/A DMAP1,RUVBL1/2,MRG15,hEaf6,BAF53a[55]N/A GAS41[55]PHD H3K4me2/3[103,105]PHD TIP60,p400,TRRAP,Brd8,EPC1/2[55]ING4N/A AcK5-H4,AcK8-H4,AcK12-H4[55]N/A G3BP2a[10,35]PHD H3K4me1/2/3[103,105]PHD HBO1[55]N/A hEaf6[55]N/A HPH-2[48]N/A JADE1/2/3[55]NCR Liprin alpha1[10,35]N/A NF-j B p65[47,132]PHD p53[13,77]PHD p300[13]ING proteins:structure to function47ING2is required for the induction of apoptosis and NER [73].Truncated ING2mutants lacking the LZL domain do not display elevated apoptosis following UV exposure [73],suggesting that this domain is required for ING2-mediated apoptosis.RNAi-mediated knockdown of ING2has also been found to abrogate the NER capacity of melanoma cells [38].Interestingly,the NER ability of ING2has been found to require the LZL domain [73].In 2005,He et al.[70]proposed that this region is responsible for homo-and hetero-oligomerization between the members of the family.The NCR is found in all ING proteins [70].It was identiﬁed by sequence analyses and constitutes the second most highly conserved domain in the ING family proteins.The NCR domain is now known as LID.This N-terminal region of ING1has been found to interact directly with lamin A [74].The NCR/LID domain is found only in ING proteins,through which they bind to and colocalize with lamin A [74],suggesting that the association with nuclear lamina is a common feature of this family.The NCR/LID domain has been speculated to be another region of ING proteins to which HAT and HDAC complexes,includingthe SAP30protein,bind by its KIQI or KVQL sequence[15].The central nuclear localization signalAll ING family proteins contain an NLS with an additional NLS for ING4and ING5.Recently,many studies have been conducted for ING1to understand the role of NLS [37,75],and have shown that NLS deletion results in cytoplasmic accumulation of the protein.The nuclear localization of ING proteins appear critical for their func-tions,as is evident by the observation of loss of nuclear ING1staining in a number of cancers [76],and that deleting the entire NLS of ING4results in a protein that can no longer bind to p53in cotransfection experiments [77].Also,the NLS of ING1contains two copies of a putative nucleolar translocation signal which interacts with the proteins karyopherin-a and -b for nuclear import [78].The nucleolar translocation of ING1after exposure to UV light appears to be required for ING-associated apoptosis [37].The C-terminus plant homeodomainAmong ING family proteins,the greatest homology occurs within the PHD motif [70].This highly conserved motif is found throughout eukaryotic proteomes,predominantly on chromatin-associated proteins [79].Structurally,the PHD motif is close to RING (Really Interesting New Gene)and LIM (Lin-11/Isl-1/Mec-3)domains,which contain a zinc-binding domains that ligate two zinc ions [80].The PHD motif which has been associated with SUMOylation is found in more than 400eukaryotic proteins and has recently emerged as a chromatin recognition motif thatTable 1continuedProtein Domain Protein/complex involved Reference ING5N/A AcK5-H4,AcK8-H4,AcK12-H4,AcK14-H4[55]N/A BRPF1/2/3[55]PHD H3K4me1/2/3[103,105,133]PHD HBO1[55]N/A JADE1/2/3[55]N/A MCM2/4/6[55]PHD MOZ/MORF [55]PHD p53[13]PHDp300[13]N/A not available48A.-H.Aguissa-Toure´et al.reads the methylation state of histones.The PHD motif comprises approximately60amino acids with a C4HC3 signature and belongs to the treble class of zinc-binding domains,containing two zinc ions bound in a cross-braced topology[81–83].Zinc coordination by PHDﬁngers is achieved via ligation of zinc atoms to alternating pairs of residues from the consensus Cys4-His-Cys3sequence dis-tribution:zinc one is bound by Cys1,Cys2,His and Cys6, whereas zinc two is bound by Cys3,Cys4,Cys7and Cys8 [82,84–86].Beyond the conservation of zinc-coordinating residues,approximately150distinct PHD-bearing proteins have been predicted to occur in humans[81].PHDﬁngers display substantial diversity in their sequences,particularly between Cys6and Cys7,suggesting that the biological activity of PHDﬁngers might similarly be diverse[85].There is much evidence that PHDﬁngers mediate important physiological functions[81].Mutations within the PHDﬁngers of numerous proteins have been implicated in tumorigenesis,as well as the pathogenesis of immuno-deﬁciency syndromes,autoimmune syndromes,and several other genetic disorders[82,87–89].Many of these muta-tions occur at zinc-coordinating residues,indicating that zinc ligation and hence integrity of the PHDﬁnger fold are critical for the function of PHDﬁnger-containing proteins.A second class of disease-linked PHDﬁnger mutations do not disrupt zinc coordination but rather are located between the sixth and seventh zinc-coordinating residues,a segment which,based on known PHDﬁnger structures and struc-tural modeling,is thought to be at or near the surface of the domain.Some have postulated that this surface forms a molecular interaction interface and that mutations within this region might disrupt this activity and in doing so manifest the disease phenotype[85,90].In fact,substitu-tion of the basic residues between the sixth and seventh zinc-coordinating residues into alanines disrupts binding of the PHDﬁngers of ING1,ING2,ATP-dependent chroma-tin remodeling factor,and recombination activating gene2 (RAG2)to phosphatidylinositol phosphates(PtdInsPs) [89].Further,such mutations render ING2and RAG2lar-gely inactive[33,89].The PHD motif closely resembles a canonical RING domain but lacks the RING E2ubiquitin ligase activity[83].Insight into the biological function of PHDﬁngers comes in part from studies of the structurally related FYVE and RINGﬁnger modules[82–84,86,91, 92].The FYVEﬁnger is a well-characterized PtdInsP-binding module,and RINGﬁngers function as components of E3ubiquitin ligase enzymes[93,94].Both of these functions have been reported for PHDﬁngers from dif-ferent proteins[33,95–98],though recent analyses argue that putative PHDﬁngers with E3-ubiquitin ligase activity are more likely to be RINGﬁnger variants rather than true PHDﬁngers[99,100].The phosphoinositide signaling pathways regulate a diverse array of cellular processes including actin poly-merization,cell migration,and vesicular trafﬁcking.These phosphoinositide-dependent processes are modulated by the tightly regulated synthesis and metabolism of mono-and polyphosphorylated phosphoinosotide species at dis-crete subcellular sites[101].A nuclear phosphoinositide signaling was reported in2003by Gozani et al.[33]who identiﬁed a physiologically important interaction between PtdIns5P and ING2mediated by the ING2PHD motif. In addition,PHDﬁngers have also been reported to be involved in other protein–protein interactions[91,102]and to interact with nucleosomes by a direct link to methylated histones(Table2),speciﬁcally H3K4me2and H3K4me3 [103,104],supporting a functional role for the PHD motif.In fact,the PHD motif,which is the most conserved region within the ING family showing sequence homology greater than78%,has been found in all human ING pro-teins to preferentially bind di-and trimethylated H3K4and repress gene transcription[103,105,106].Mutations in the PHD motif of p33ING1b and a region found to interact with SAP30(Sin3A Associated Protein30),a component of Sin3A corepressor complexes[107],abrogate the enhancement of p33ING1b in DNA repair in host cell reactivation assays and radioimmunoassays[50,108]. Furthermore,the p33ING1b variant is not recruited to UV-induced DNA lesions,but enhances NER in XPC-proﬁcient cells possibly due to its ability to bind XPA[39]. Since XPC/hHR23B acts as theﬁrst step of the NER pathway by recognizing helix-distorting DNA lesions and XPA acts to stabilize the resulting open DNA structure [109],p33ING1b may play an essential role in the early steps of the NER pathway,possibly by facilitating access of the NER machinery to chromatin.Additionally,two p33ING1b PHD mutations(R102L and N260S)were detected in20%of46tested melanomas [50],and either of these alterations proved to be as detri-mental as deletion of the entire PHD motif for the enhancement of NER mediated by p33ING1b in host-cell-reactivation assays and radioimmunoassays.Furthermore, those patients bearing an ING1codon102or260mutation had a reduced5-year survival rate(50vs.82%)[50].These ﬁndings highlight the importance of the PHD motif in ING1function and tumor suppression,as loss of NER activity would likely facilitate tumorigenesis by increasing genomic instability.In agreement with this proposal,other reports have indicated the presence of ING1mutations in the coding region for the PHD motif or the NLS in mela-noma,head and neck squamous cell carcinoma,esophageal squamous cell carcinoma,breast cancer,pancreatic cancer, and in colon cancer[14],supporting a role for ING PHD motif in epigenetic regulation of gene expression.ING proteins:structure to function49The polybasic regionING1and ING2,which are evolutionarily and functionally close[55,70,110],contain a short region called the PBR in their C-terminus part,adjacent to the PHD motif.Although the biological functions of this region are not well under-stood,it has been reported that PtdIns5P bind to the PHD motif of ING2[33,111].Later,it was found that PtdIns3P and PtdIns4P can bind to the PBR[112].These authors showed that when exchanged between different PHD motif,the PBR is a strong determinant of the binding speciﬁcity of PtdInsPs[112].Theseﬁndings establish the PBR as a phosphoinositide-binding module and suggest that the PHD domains function downstream of phospho-inositide signaling triggered by the interaction between PBRs and phosphoinositides.ConclusionNumerous studies have been done to elucidate the func-tional mechanisms of ING family proteins.To date,two mechanisms have been clearly identiﬁed in ING family proteins that regulate the major biological processes.These are the interaction of the ING PHD domain with methyl-ated histone tails[103,105,113,114],and the binding of ING(ING1-2)proteins to bioactive signaling phospholip-ids[33,112,115]to function as nuclear PtdIns receptors [101,116,117].PtdIns have an important role in mediating a variety of biological processes,including the response to stress,and because they regulate essential cellular func-tions,PtdIns metabolism is tightly regulated at the subcellular level[118].Therefore,it is possible that the ING proteins transduce stress signals by binding phos-pholipids,targeting to chromatin,and reading the local histone code,which subsequently contributes to epigenetic regulation.However,these mechanisms cannot by them-selves explain all the events in which ING proteins are involved.This is reinforced by the existence within this family of various functional domains,ﬁrst among the proteins,then among the isoforms of some proteins.Thus, for a better understanding of the precise function of each domain,it would be necessary to pursue a motif–function relationship study for each member and each isoform of ING family proteins.A systematic functional analysis of different domains to understand their inactivation mecha-nism and the role in tumor suppression should help to deﬁne the functional differences between members of the ING family proteins.Acknowledgments This work was supported by the Canadian Institutes of Health Research(MOP-84559and MOP-93810)and the Canadian Dermatology Foundation to G.Li.R.P.C.W.is a recipient of a Terry Fox Foundation Research Studentship from Canadian Cancer Society Research Institute.References1.Garkavtsev I,Kazarov A,Gudkov A,Riabowol 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Organizational Leadership（CBYD）Final Paper李晓祥20116811412In China, there is an ancient saying: To see or do something once is better than to hear about it a hundred times. It means that if people only know about the theory were not enough. The practice is also important, especially in leadership. Theory must not be divorced from practice. We need to understand the purpose of Leadership: Theory and Practice. In every organization, if a leader can make the theory work useful in daily work, the organization make changes to improve further. So in this book, we learned some new theories. And we need to learn how to use them and how to make them work in practice. Our purpose of learn is to be a good leader, isn’t it?So, the question is how to be a good leader? In the trait theory, it is an approach to the study of human personality. If you want to be a good leader, you should have some traits when you born. Maybe in nowadays many people can to be a leader depends on learn and study, but I still think a good leader should have some trait that can help them when you born. There are big five personality factors, neuroticism, extraversion, openness, agreeableness and conscientiousness (Goldberg, 1990). For example, Confucius is considered the greatest people of the ancient China. Even today, Confucius's edification of "Being insatiable in learning" is still regarded as a motto by most people. His traits were influence people, etiquette and benevolent. These embody respects for emperors, putting people first, government by man and fair regulations. It had a profound effect on China and seriously changed many people’s life, people begin to respect him until now.In another theory, Path–goal theory in the book, teach us how to achieve organizational goals depends on motivate follower’s work. The theory states that a leader's behavior is contingent to the satisfaction, motivation and performance of her or his subordinate, and the leader engages in behaviors that complement subordinates abilities and compensate for deficiencies (Wikipedia, 2013). There are four different leadership behaviors in path-goal theory, every leader need to choose a leadership style to response different follower characteristics and task characteristics. For the leadership behavior there are directive, supportive, participative and achievement oriented. For example, in the restaurant, the cook’s job is cooking for customers, he find boring because his task is repetitive, unchallenging and mundane. We need to choose the supportive to help him, to respect him with kindly encouragement, and Innovation new menu to train him. Make him fell the leader is care for him and trust him. And in some big organizations, followers will not reflect the same characteristics; leaders need to choose the best leadership style to deal with different problem of followers. It can help organization achieve the goals easily.Transformational leadership theory is my efforts, in the old Transactional Leadership, followers and leaders have exchange all the time, in this process, leaders use the reward of resources exchange the obedience for followers. But the transformational leadership style where the leader is charged with identifying the needed change, creating an environment that good for improve enhance the motivation and morale. Leader is example to inspire followers and raise their interest in the project, understanding the strengths and weaknesses of followers, allowing theleader and followers work on tasks together that can enhance their performance. Such as Martin Luther King was known for using persuasive appeals based on reason and Nonviolent Communication. “Darkness cannot drive out darkness; only light can do that. Hate cannot drive out hate; only love can do that.” (INeedMotivation, 2010). He lead the civil rights movement and united the whole black people of America, crate a Nonviolent environment and make people knows they fight for themselves, people loved him and trust him. Although he was murdered, the new Civil Rights Act was achieved succeed. Forty years ago, when Mr. Martin Luther King fell down, his words “I have a dream” spread across the world. The human race has benefited from a number of individuals who promoted peace and service to others.In the end, after this term’s study, there is a new understand of leadership in my brain. There are many ways to be a good leader, but the most important thing is you need to learn choose the best leadership style to deal with problem depends on different conditions. Times are changing all the time, every leader should continuous to learn. And I believe that increasingly the young students hardworking treasure the opportunities to be improved, to learn and to grow, rather than simply being led. I love this world, I want to be a good leader.References1.Goldberg, L.R. (1990). An alternative ”description of personality”: The big-fivefactor structure. Journal of personality and social psychology, 59, 1216-1229.2.Wikipedia. (2013). Path-Goal Theory.From: /wiki/Path%E2%80%93goal_theory3.INeedMotivation. 20 Great Quotes From Martin Luther King Jr.From:/blog/2008/05/20-great-quotes-from-martin-luther -king-jr/。

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