Is it necessary to sign prenuptial agreement
为确保信息安全英语作文
为确保信息安全英语作文下载温馨提示:该文档是我店铺精心编制而成，希望大家下载以后，能够帮助大家解决实际的问题。
文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by theeditor. I hope that after you download them,they can help yousolve practical problems. The document can be customized andmodified after downloading,please adjust and use it according toactual needs, thank you!In addition, our shop provides you with various types ofpractical materials,such as educational essays, diaryappreciation,sentence excerpts,ancient poems,classic articles,topic composition,work summary,word parsing,copyexcerpts,other materials and so on,want to know different data formats andwriting methods,please pay attention!In today's digital age, ensuring information security has become more crucial than ever before. With the increasing reliance on technology and the internet, individuals and organizations are constantly at risk of cyber threats and attacks. Therefore, it is essential to take proactive measures to safeguard sensitive information and protect ourselves from potential harm.One effective way to ensure information security is by implementing strong passwords. Passwords serve as the first line of defense against unauthorized access to our personal accounts and data. It is important to create passwords that are unique, complex, and difficult to guess. Avoid using common phrases or personal information that can be easily deduced. Regularly updating passwords and using two-factor authentication can further enhance security.Another important aspect of information security is staying vigilant against phishing scams. Phishing is afraudulent practice where cybercriminals attempt to deceive individuals into revealing sensitive information, such as passwords or credit card details. These scams often come in the form of deceptive emails or websites that mimic legitimate sources. Therefore, it is crucial to be cautious when clicking on links or providing personal information online. Verifying the authenticity of the source and regularly updating antivirus software can help prevent falling victim to these scams.Furthermore, it is essential to keep software and devices up to date. Software updates often include security patches and bug fixes that address vulnerabilities in the system. Ignoring these updates can leave devices and networks susceptible to attacks. Additionally, regularly backing up important data is crucial in case of any unforeseen circumstances, such as a system crash or ransomware attack. By having a backup, one can avoid losing critical information and minimize the impact of such incidents.In today's interconnected world, it is also importantto be cautious about the information we share online. Social media platforms and online forums have become breeding grounds for cybercriminals to gather personal information. Therefore, it is essential to be mindful of the information we post online and adjust privacy settings accordingly. Limiting the amount of personal information shared and being cautious about accepting friend requests or connecting with unknown individuals can help protect our privacy and reduce the risk of identity theft.In conclusion, ensuring information security is of paramount importance in today's digital era. By implementing strong passwords, staying vigilant against phishing scams, keeping software up to date, and being cautious about the information we share online, we can minimize the risk of cyber threats and protect ourselves from potential harm. It is crucial to remain proactive and informed about the latest security measures to stay one step ahead of cybercriminals.。
token为空,请重新请求 英文的正确说法
token为空,请重新请求英文的正确说法The access token provided is invalid or empty. Please make a new request.When we make requests to APIs or authorization servers, we often need to include access tokens in our requests. These tokens serve as a unique identifier that grants us permission to access certain resources or perform specific actions.However, sometimes we may encounter situations where the access token we provide is invalid or empty. This could be due to various reasons, such as the token has expired, it was revoked, or it was not generated correctly.When we receive an error message indicating that the access token is empty or invalid, we need to take appropriate actions to rectify the issue. The following steps could be considered:1. Verify the token entry: Ensure that the access token has been properly entered in the request. Double-check for any typos, missing characters, or whitespace issues that might cause the token to be invalid. Correct any mistakes if found.2. Generate a new token: If the token has expired or has been revoked, we need to generate a new access token. This typically involves authenticating ourselves with the API or authorization server and requesting a new token. Follow the established protocol or documentation provided by the service provider to generate a valid token.3. Check token validity: Before making a request, check the validity of the token. Some API or authentication servers might provide a mechanism to verify the validity of the token beforehand. This could involve making a separate API call or using a specific endpoint provided by the service. Implement this step to ensure that the token is still valid and can be used for authentication.4. Handle token expiration: If the access token has an expiration time, we need to handle the situation when the token expires. In such cases, we need to generate a new token before making subsequent requests. It is common to include an expiration timer along with the token response, enabling us to proactively refresh the token before it becomes invalid.5. Secure token transmission: Ensure that the access token is transmitted securely over the network. Using secure protocols like HTTPS and encrypting the token during transmission can help prevent interception or tampering by malicious entities.6. Re-authenticate if necessary: In some cases, an empty or invalid access token might indicate that the user needs to re-authenticate themselves. This could be due to a change in permissions or unusual activity. If we receive such an error, prompt the user to re-enter their credentials and obtain a new access token.Remember to handle error cases gracefully in your application. Display clear and meaningful error messages to the user, specifying that the access token is invalid or empty, and provide appropriateinstructions on how to resolve the issue. Additionally, consider implementing robust error handling and logging mechanisms on the server-side to capture and investigate any token-related errors.In conclusion, when encountering an empty or invalid access token, it is necessary to address the issue promptly to ensure continued access to resources and services provided by API or authorization servers. By following the steps mentioned above, we can resolve the problem and successfully authenticate ourselves for subsequent requests.。
上海婚姻登记流程
上海婚姻登记流程1.想要在上海进行婚姻登记，首先需要去当地的民政局了解相关流程。
To register for marriage in Shanghai, you first need to go to the local civil affairs bureau to inquire about the relevant procedures.2.在民政局办理婚姻登记需要准备一系列的文件和证件。
You need to prepare a series of documents andcertificates for marriage registration at the civil affairs bureau.3.需要提供身份证、户口本、单身证明等材料。
You need to provide materials such as ID card, household registration booklet, and certificate of single status.4.提供的文件需要经过公证处认证。
The provided documents need to be notarized by the notary office.5.外国人办理婚姻登记需要提供有效护照和签证。
Foreigners need to provide valid passport and visa for marriage registration.6.如果有子女，需要提供子女的相关证明文件。
If there are children, relevant documents related to the children need to be provided.7.所有文件和证件均需原件和复印件。
All documents and certificates need to have the original and a photocopy.8.在民政局递交完所有材料后，将安排具体的登记时间。
请你重视这个问题英语作文
请你重视这个问题英语作文Title: The Significance of Prioritizing an Issue。
Addressing a critical issue requires not only acknowledgment but also sincere consideration and action. The importance of prioritizing an issue cannot be overstated, as it directly impacts individuals, communities, and even societies at large. In this essay, we will delve into the significance of giving due attention to pressing matters and the implications of neglecting them.First and foremost, prioritizing an issue demonstratesa commitment to addressing challenges and fosteringpositive change. When a problem is identified and placed at the forefront of attention, it signifies a willingness to confront obstacles head-on rather than turning a blind eye. This proactive approach is essential for effective problem-solving and ensuring that issues do not escalate into crises.Furthermore, prioritizing an issue allows for the allocation of resources and efforts towards finding viable solutions. By acknowledging the urgency and importance of a particular matter, decision-makers can mobilize support, both financial and logistical, to tackle the problem effectively. Whether it involves implementing policies, conducting research, or providing assistance,prioritization ensures that the necessary steps are taken to mitigate the issue's impact.Moreover, prioritizing an issue fosters awareness and dialogue within society. When an issue is brought to the forefront of public discourse, it prompts discussions, debates, and engagement from various stakeholders. This exchange of ideas and perspectives is crucial for fostering understanding, empathy, and collaboration in addressing complex challenges. Through open dialogue, individuals can share insights, propose solutions, and advocate for change, thereby catalyzing progress towards resolution.On the other hand, neglecting to prioritize an issue can have detrimental consequences that reverberatethroughout society. Ignoring pressing matters not only perpetuates existing problems but also allows them to worsen over time. Issues such as poverty, inequality, and environmental degradation require sustained attention and action to prevent them from spiraling out of control.Failure to address these issues promptly can lead to far-reaching social, economic, and environmental impacts that affect the well-being of current and future generations.Furthermore, neglecting to prioritize an issue undermines trust in institutions and erodes social cohesion. When people perceive that their concerns are being ignoredor marginalized, it breeds disillusionment, resentment, and distrust towards those in positions of power. This lack of confidence in the ability of institutions to address pressing issues can fuel social unrest, polarization, and instability, posing significant challenges to governanceand democracy.In conclusion, the significance of prioritizing anissue cannot be overstated. By giving due attention to pressing matters, societies can demonstrate theircommitment to addressing challenges, allocating resources effectively, fostering awareness and dialogue, and ultimately, promoting positive change. Conversely, neglecting to prioritize an issue can have far-reaching consequences that undermine social progress and cohesion. Therefore, it is imperative that individuals, communities, and institutions recognize the importance of addressing pressing issues and take proactive steps to confront them head-on.。
PAPER Special Section on Discrete Mathematics and Its Applications An Optimal Certificate D
PAPER Special Section on Discrete Mathematics and Its ApplicationsAn Optimal Certificate Dispersal Algorithm for MobileAd Hoc Networks∗Hua ZHENG†a),Student Member,Shingo OMURA†b),Member,Jiro UCHIDA†c),Student Member,and Koichi W ADA††d),MemberSUMMARY In this paper,we focus on the problem thatin an ad hoc network,how to send a message securely betweentwo users using the certificate dispersal system.In this system,special data called certificate is issued between two users andthese issued certificates are stored among the network.Ourfinal purpose on this certificate dispersal problem is to construct cer-tificate graphs with lower dispersability cost which indicates theaverage number of certificates stored in each node in an ad hocnetwork.As ourfirst step,when a certificate graph is given,weconstruct two efficient certificate dispersal algorithms for stronglyconnected graphs and directed graphs in this paper.We canshow that for a strongly connected graph G=(V,E)and a di-rected graph H=(V ,E ),new upper bounds on dispersability cost on the average number of certificates stored in one nodeare O(D G+|E|/|V|)and O(p G d max+|E |/|V |)respectively, where D G is the diameter of G,d max is the maximum diameterof strongly connected components of H and p G is the numberof strongly connected components of H.Furthermore,we givesome new lower bounds for the problem and we also show that our algorithms are optimal for several graph classes.key words:certificate dispersability,certificate dispersal algo-rithm,mobile ad hoc network,optimal algorithm1.IntroductionThe recent history of the Internet and of computer net-works has shown that if security of a given network architecture is not properly designed from the very be-ginning,then the security breaches will be exploited by malicious users.Security in mobile ad hoc networks is particularly difficult to achieve,notably because of the vulnerability of the links,the limited physical pro-tection of each node,the sporadic nature of connectiv-ity,the dynamically changing topology,the absence of a certification authority,and the lack of a centralizedManuscript received August20,2004.Manuscript revised November5,2004.Final manuscript received January11,2005.†The authors are with the Department of Computer Science and Engineering,Graduate School of Engineer-ing,Nagoya Institute of Technology,Nagoya-shi,466-8555 Japan.††The author is with the Nagoya Institute of Technology,Nagoya-shi,466-8555Japan.a)E-mail:roxanne@phaser.elcom.nitech.ac.jpb)E-mail:shingo@phaser.elcom.nitech.ac.jpc)E-mail:jiro@phaser.elcom.nitech.ac.jpd)E-mail:wada@nitech.ac.jp∗This paper was presented at the3rd International Sym-posium on Parallel and Distributed Computing in associa-tion with HeteroPar’04(ISPDC/HeteroPar2004)monitoring or management point.As such,our approach is developed mainly for “open”networks,in which users can join and leave the network without any centralized control.Therefore,it is necessary to establish distributed and secure authen-tication systems in mobile ad hoc networks.There is much research on secure authentication systems,such as in[4]it provided a system in which,if two nodes meet,they can communicate securely with high proba-bility,and in[10]it guaranteed the probability1.The main problem of any public-key based secu-rity system is to make each user’s public key available to others in such a way that its authenticity is verifiable. In mobile ad hoc networks,this problem becomes even more difficult to solve because of the absence of cen-tralized services and possible network partitions.More precisely,two users willing to authenticate each other are likely to have access only to a subset of nodes of the network(possibly those in their geographic neigh-borhoods).One of the best known approaches to the public-key management problem is based on public-key certificates[5].A public-key certificate is a data struc-ture in which a public key is bound to an identity(and possibly to some other attributes)by the digital sig-nature of the issuer of the certificate.All certificates issued by nodes in a network can be represented by a directed graph,called certificate graph.Each node in a certificate graph represents a mobile user in the net-work,and each directed edge in the certificate graph represents a certificate.A certificate graph indicates a relationship of mutual trust during the mobile users, not a physical model of an ad hoc network;so if there exists an edge from user u to v in a certificate graph, then it means that u knows v’s public key and there exists a certificate from u to v,it does not mean v is in the u’s communication area.The certificate can be used by any node in the network that knows the public key of one node to further acquire the public key of the other node.The issued certificates are necessary to be dispersed among nodes in the network such that if a node u approaches another node v and wishes to se-curely send messages to v,then u can obtain the public key of v using certificates stored either in u or v in the certificate graph.Several papers have investigated the use of certifi-cates to provide security in traditional networks and inad hoc ones.Architectures for issuing,storing,discov-ery,and validating certificates in traditional networks are presented in [1],[2],[6],[7],[9],[11].In [4],the authors investigated how to disperse cer-tificates in a certificate graph in a mobile ad hoc net-work under the following two conditions:first,each node stores the same number of certificates.Second,with high probability,if two nodes meet then they have enough certificates for each of them to compute the public key of the other.In [10],it is proved that a lower bound on the num-ber of certificates to be stored in a node is √n −1which satisfies the following conditions:first,each certificate is stored in the same number of nodes.And secondly,the same number of the certificates is stored in each node,where n is the number of nodes in the system.In [3],another condition,that every certificate must be stored in some node,is considered,and the dis-persability cost of a certificate graph G ,denoted c.G ,is defined as the minimum average number of certificates stored in one node.Under this condition,a dispersal algorithm called Full Tree algorithm and an improved version of Full Tree algorithm called Half Tree algo-rithm are presented.The upper bound c.G ≤n −1,and the lower bound c.G ≥e/n are also proved,where n is the number of nodes and e is the number of edges in a certificate graph G .The authors have shown in [3]that c.G =n −1=e/n for a complete certificate graph,c.G =n −1for a ring graph,c.G =(n −1)/n for a hour-glass graph,and c.G =2(n −1)/n for a star graph.Our work is based on two conditions considered in [3].First,different nodes may store different number of certificates,but the average number of certificates stored in one node is minimized.Secondly,it is guar-anteed (i.e.with probability 1)that if two nodes meet then they have enough certificates for each of them to compute the public key of the other.In this paper,we construct two efficient certificate dispersal algorithms.Our algorithms are proposed for computing how many certificates have to be stored in each node,where these certificates are needed for se-cure communication in mobile ad hoc networks.Our algorithms do not run in a changing ad hoc network,and it is performed before the nodes are distributed in an ad hoc network,and after running a certificate dispersal algorithms,the certificates of the graph are dispersed to each node.We show that for a strongly connected graph G =(V,E )and a directed graph H =(V ,E ),the upper bounds on the dispersability cost are 2D G +|E |/|V |and 2p G d max +p G −1+|E |/|V |re-spectively.Our results in detail are summarized in Ta-ble 1.For a given graph,an algorithm whose complex-ity of the cost is asymptotically equal to the complex-ity of the lower bound of the dispersability cost of the graph,is called an optimal algorithm.We prove that our algorithms are optimal for several graph classes,such as Hypercubes,Meshes,complete k -ary trees andde-Bruijn graphs.Table 1Our results.Graph DispersabilityStrongly Connected O (D G +|E |/|V |)Upper BoundBi-directional O (R G +|E |/|V |)Directed O (p G d max +|E |/|V |)Hypercubes,Meshs,Ω(R G +|E |/|V |)Lower BoundComplete k -ary trees,de-Bruijn graphs Ω(D G +|E |/|V |)D G :Diameter of a strongly connected graph G .R G :Radius of a bi-directional graph G .p G :the number of strongly connected components of a graph G .d max :the maximum diameter of strongly connected components of a graph G .2.Preliminaries 2.1DefinitionsIn this subsection,we define some terms used in this paper.In a directed graph G ,a sequence of edges (v 0,v 1),(v 1,v 2),···,(v k −1,v k )where v 0,v 1,···,v k are distinct is called a path from v 0to v k ,denoted by p (v 0,v k ).We call v 0and v k end nodes.If there exist a path from v 0to v k ,then we say v 0and v k are reachable.Define E (p (v 0,v k ))as the set of edges on the path p (v 0,v k ),which means E (p (v 0,v k ))={(v 0,v 1),(v 1,v 2),···,(v k −1,v k )}.The length of a path p (u,v )is the number of edges in it,denoted by |p (u,v )|.A path from u to v is the shortest one iffits length is not larger than the length of any other paths from u to v in the graph.A distance from u to v is the length of a shortest path from u to v ,denoted by d (u,v ).And the maximum distance between any two nodes in G is defined as a diameter of the graph,denoted by D G .A directed graph,in which there exists at least one path from u to v for any two distinct nodes u and v ,is said to be strongly connected.A strongly con-nected component C of a directed graph G =(V,E )is a subgraph C =(V ,E )(V ⊂V and E ⊂E )which sat-isfies that no node of G can be added to C such that it is strongly connected.A directed graph can be parti-tioned into strongly connected components.Note that this partition is unique.A directed graph is bi-directional if there is an edge from node u to node v then there exists an edge from v to u .For any node v in graph G ,we define the eccen-tricity of v as the length of a longest shortest path from the node v to any other nodes.In a bi-directional graph G ,for any node v ,the minimum value of eccentricity of v is defined as the radius of the graph,denoted by R G .Free tree T is a connected undirected graph with-out cycle.A rooted tree is a free tree in which one ofZHENG et al.:AN OPTIMAL CERTIFICATE DISPERSAL ALGORITHM FOR MOBILE AD HOC NETWORKS3the nodes is distinguished from the others.The distin-guished node is called the root of the tree.If the last edge on the path from the root of a tree T to a node x is(y,x),then y is the parent of x,and x is a child of y. The root is the only node in T with no parent.A node with no children is an external node or leaf.A nonleaf node is an internal node.The number of children of a node x in a tree is called the degree of x.The largest depth of any node in T is the height of T,denoted by H(T).For a directed graph G,incoming tree T rooted at node v on G is a subgraph of G,whose nodes set are all nodes reachable to v and there is a unique path from any other node to v on T.A shortest incoming tree rooted at v is an incoming tree in which the path from any other node to v corresponds to a shortest path in G.For a directed graph G,outgoing tree T rooted at node v on G is a graph,whose nodes set are all nodes reachable from v and there is a unique path from v to any other nodes on T.A shortest outgoing tree rooted at v is an outgoing tree in which the path from v to any other node corresponds to a shortest path in G.Given a graph G=(V,E)and a source node v, breadth-first search is one of the algorithms for search-ing a graph that systematically explores the edges of G to discover every node that is reachable from v.It produces a breadth-first tree with root v that contains all such reachable nodes.For any node u reachable from v,the path in the breadth-first tree from v to u corresponds to a shortest path from v to u in G.2.2Certificate Dispersal Problem[3]For simplicity,we assume that each honest user owns a single mobile node.We consider a mobile ad hoc network,where each node u has a private key pri.u and a public key ers themselves create their public and private keys.In this network,in order for a node u to send a message m to v securely,u needs to know pub.v to encrypt the message by it,denoted by pub.v m .If a node u knows the public key pub.v of another node v in the network,then node u can issue a certifi-cate from u to v that identifies pub.v.The certificate can be used by any node in the network that knows pub.u to further acquire pub.v.A certificate from node u to node v is of the fol-lowing form:pri.u u,v,pub.v .The certificate is en-crypted using pri.u,and it contains three items:(i) The identity of the certificate issuer u,(ii)the identity of the certificate subject v,and(iii)the public key of the certificate subject pub.v.Any node who knows pub.u can use it to decrypt the certificate from u to v for obtaining pub.v.When a node u wants to obtain the public key of another node v,u acquires a sequence of cer-tificates pri.u u,v0,pub.v0 ,pri.v0 v0,v1,pub.v1 ,..., pri.v i v i,v,pub.v which stored in either u or v.u can get the public key of v during these phases.1.Thefirst certificate pri.u u,v0,pub.v0 of the se-quence can be directly verified by u,by using a public key that u holds and trusts,so u can get pub.v0.2.Each of remaining certificates pri.v j v j,v j+1,pub.v j+1 can be verified using the public key pub.v j contained in the previous certificate pri.v j−1 v j−1,v j,pub.v j of the sequence.3.The last certificate contains the public key pub.vof the target node v.All certificates issued by the nodes in a network can be represented by a directed graph,called a certificate graph,denoted by G=(V,E).Each node in the certifi-cate graph represents a mobile user in the network.A directed edge from node u to v in the certificate graph represents a certificate from u to v.Note that a cer-tificate graph is a directed graph that does not have self-loops and multiple edges between two nodes.The issued certificates are necessary to be dis-persed among nodes in the network such that if a node u approaches another node v and wishes to securely send messages to v,then u can obtain the public key of v using certificates stored either in u or v provided that there is a directed path,called certificate path,from u to v in the certificate graph.Note that if there exists a path from v0to v k,then,v0can get the public key of v k.For simplicity,we call certificate path as path in this paper.A certificate dispersal algorithm F is an algorithm that takes a certificate graph G as an input and outputs a subset of the certificates,which is stored in each node v in G,denoted F.(G,v),such that the following two certificate dispersal conditions hold;1)Connectivity:For any reachable pair of nodes u and v in G,the certificates on a path which connects u and v in G are in the set F.(G,u)∪F.(G,v).2)Completeness:For every certificate in G,there exists a node v inG such that this certificate is in F.(G,v).Let G be a certificate graph,and F be a certificate dispersal algorithm.The cost of F to disperse the cer-tificates in G,denoted by c.(F,G),is defined as follows:c.(F,G)=1nv∈V|F.(G,v)|,(1) where n is the number of nodes in G,and|F.(G,v)| denotes the number of certificates in the set F.(G,v) assigned by F to the node v.Note that c.(F,G)is the average number of certificates assigned by F to a node.The dispersability cost of a certificate graph G, denoted by c.G,is defined as follows:c.G=minF{c.(F,G)}.(2)4IEICE TRANS.FUNDAMENTALS,VOL.E88–A,NO.5MAY20053.New Upper BoundsIn this section,we introduce a procedure Pivotfirst. Using Pivot procedure,we construct CPivot algorithm for strongly connected certificate graphs and GPivot algorithm for arbitrary directed graphs later.New upper bounds O(D G+|E|/|V|)for a strongly connected graph G=(V,E)and O(p G d max+|E |/|V |) for a directed graph H=(V ,E )are proved in this section,where D G is the diameter of graph G,d max is the maximum diameter of strongly connected compo-nents of H and p G is the number of strongly connected components of H.In section4,CPivot algorithm will be proved to be an optimal algorithm for Hypercubes, Meshes,complete k-ary trees and de-Bruijn graphs.3.1PivotProcedure Pivot takes a strongly connected certificate graph as an input.We sketch an outline of Pivot.Select one node as a pivot node pvt arbitrarily. And then,for every node x(x=pvt),all of the certifi-cates on two shortest paths in both directions between x and pvt are stored in x.Pivot is formulated as follows:Procedure Pivot(G=(V,E))1.Select an arbitrary node as a pivot node pvt2.For every node v in V−{pvt}2.1Compute the shortest path from v to pvt,p(v,pvt)and the shortest path from pvt tov,p(pvt,v)2.2Store E(p(v,pvt))∪E(p(pvt,v))to v Lemma1:Pivot satisfies connectivity,and its com-putation time is O(|E|).Proof:Let G be a strongly connected graph.Since G is strongly connected,for every node v(=pvt)in G, there exist paths p(v,pvt)and p(pvt,v).In Pivot,we store all the certificates on p(v,pvt)and p(pvt,v)to v. That means,for every distinct pair of nodes u and v, there exists a path from u to v via pvt in G,and the certificates on the path are in the sets of the certificates stored in u and v.We prove the computation time next.For com-puting two shortest paths p(v,pvt)and p(pvt,v),in-coming and outgoing breadth-first trees rooted at pivot node pvt are needed.These trees can be constructed in time of O(|V|+|E|)and two shortest paths p(v,pvt) and p(pvt,v)for each node v can be computed simul-taneously with constructing these breadth-first trees. The main loop is repeated O(|V|)times.There is no more need to compute the paths in step2.1,because the incoming and outgoing breadth-first trees rooted at pvt and shortest paths are computed in advance.Stor-ing operation consumes constant time.Therefore one iteration of the main loop can be computed in con-stant time.Since G is strongly connected,we have |E|≥|V|.So the total computation time of Pivot is O((|V|+|E|)+|V|)=O(|E|).✷3.2Certificate Dispersal Algorithm CPivotIn order to construct a certificate dispersal algorithm, we make a slight change to the Pivot.From Lemma1, we know that Pivot satisfies connectivity.For satisfying the second condition,completeness,we store all unused certificates to the pivot node after running Pivot proce-dure.Through this addition,Pivot can be changed to a certificate dispersal algorithm,which satisfying both of two conditions,connectivity and completeness.We call this algorithm as CPivot.Lemma2:CPivot is a certificate dispersal algorithm. Proof:When constructing CPivot algorithm,after run-ning Pivot procedure,we store all remaining certificates to pivot node.That means all the certificates are stored in some nodes,which satisfies completeness.And Pivot procedure satisfies connectivity from Lemma1.We know that CPivot satisfies both of two conditions.✷Theorem1:For any strongly connected certificate graph G,c.(CP ivot,G)≤2D G+|E|/|V|.Proof:CPivot consists of two phases,Pivot procedure and the additional storing operation.In Pivot proce-dure,it is clear that even if which node is selected as pivot node pvt,for any v,|E(p(v,pvt))∪E(p(pvt,v))|≤2D G.Therefore,at the end of Pivot procedure,the to-tal number of certificates stored in all of the nodes is at most2|V|D G.In the time of starting the additional storing operation,at most|E|certificates are remained. So,the cost of CPivot is2D G+|E|/|V|.✷3.3Pivot SelectionHow to select a pivot node pvt in Pivot procedure,de-termines the cost of the CPivot.We can choose a spe-cial node as pivot node pvt to decrease the cost.In this subsection,for strongly connected graphs and bi-directional graphs,we introduce two efficient methods to select pivot node pvt,respectively.For a strongly connected graph,for each node x, compute incoming breadth-first tree T in rooted at x and outgoing breadth-first tree T out rooted at x.Select node x with the minimum value ofy∈V(T out)d(x,y)+z∈V(T in)d(z,x)as pivot node pvt.Lemma3:Pivot selection for strongly connected graphs is computed in O(|V|·|E|)time.Proof:For any node,incoming and outgoing breadth-first trees rooted at the node is computed in O(|V|+ |E|).For G is strongly connected,we have|E|≥|V|. So the total computation time is O((|V|+|E|)·|V|)=ZHENG et al.:AN OPTIMAL CERTIFICATE DISPERSAL ALGORITHM FOR MOBILE AD HOC NETWORKS5O (|V |·|E |).✷For a bi-directional graph,for each node x ,com-pute outgoing breadth-first tree T out rooted at x .Select node x with the minimum value ofy ∈V (T out )d (x,y )as pivot node pvt .Lemma 4:Pivot selection for bi-directional and strongly connected graphs is computed in O (|V |·|E |)time.Proof:Outgoing breadth-first tree for any node is com-puted in O (|V |+|E |)time.For G is bi-directional and strongly connected,we have |E |≥|V |.So the total computation time is O ((|V |+|E |)·|V |)=O (|V |·|E |).✷Theorem 2:For any bi-directional certificate graph G ,c.(CP ivot,G )≤2R G +|E |/|V |.Proof:For a node u whose eccentricity is equal to R G , v ∈V (T out )d (u,v )≤|V |R G holds.In Pivot se-lection ,we select a special node x with the mini-mum value of v ∈V (T out )d (x,v )as pivot node pvt .So, v ∈V (T out )d (x,v )≤|V |R G .Therefore,at the end of Pivot procedure,the total number of certifi-cates stored in all of the nodes is v ∈V |E (p (v,pvt ))∪E (p (pvt,v ))|≤ v ∈V (T out )2d (pvt,v )≤2|V |R G .In the time of starting the additional storing operation,at most |E |certificates are remained.So,the cost of CPivot is 2R G +|E |/|V |.✷3.4Certificate Dispersal Algorithm GPivotIn this subsection,a certificate dispersal algorithm GPivot ,which takes an arbitrary directed graph as an input,is presented.Algorithm GPivot formulated is as follows.Algorithm GPivot (G =(V,E ))1.Partition G into strongly connected components C i =(V i ,E i ),i =1,2,···,p G .Let pvt i be a pivot node of C i .2.For each C i do Pivot (C i )3.Construct a graph H s.t.V (H )={C 1,C 2,···,C p G }and E (H )={(C i ,C j )|(v,w )∈E,v ∈V (C i )and w ∈V (C j )}.Note that H contains no cycles (H is a directed acyclic graph).4.For each node C i ∈V (H )4.1Compute a shortest outgoing tree T i rooted atC i on H4.2For each node v ∈V (C i )4.2.1For each edge (C j ,C k )∈E (T i )Store the certificates on the shortest path p (pvt j ,pvt k )in G into v5.Store all unused certificates to an arbitrary node An example of GPivot is shown in Fig.1.A di-rected graph G (Fig.1(a))is given as an input of GPivot .We partition G into four strongly connected compo-nents C 1,C 2,C 3and C 4.For any reachable nodes pair,following certificates are stored in.As an example,we(a)an input graphG(b)T 1on H(c)certificates stored in nodes 1and 9Fig.1An example of GPivot .(a):an input graph G and pivotnode of each strongly connected component.(b):induced graph H and a shortest outgoing tree rooted at C 1.(c):the certificates on the path p (1,9)by concatenating p (1,3),p (3,4),p (4,7)and p (7,9).focus on the nodes 1and 9in different components.In step 2,through Pivot procedure,the certificates (1,2),(2,3)and (3,1)are stored in node 1,and the certificates (9,7)and (7,9)are stored in node 9.And the induced graph H from G is shown in Fig.1(b).A shortest outgoing tree T 1rooted at C 1on H is shown in Fig.1(b),in which the edges of T 1are denoted by solid lines.A path from pvt 1in C 1to pvt 4in C 4,which is constructed in step 4is shown in Fig.1(c).The cer-tificates (3,1),(1,2),(2,4)and (4,7)on the path p (3,7)are stored in node 1.After running of GPivot (G ),the certificates (1,2),(2,4),(4,7)and (7,9)are stored in nodes 1and 9,which satisfies connectivity.Lemma 5:For any directed graph G ,GPivot is a cer-tificate dispersal algorithm,and its computation time is O (p G ·(|V |+|E |)).Proof:To prove that GPivot is a certificate dispersal algorithm,we show connectivity first.For any reach-able pair u and v in G ,we consider two different cases,whether u and v are in the same strongly connected component,or not.In the case where u and v are in the same component C i ,since C i is strongly con-nected,there must exist a path from u to v .After running Pivot (C i ),all of the certificates on p (u,pvt i )6IEICE TRANS.FUNDAMENTALS,VOL.E88–A,NO.5MAY 2005and p (pvt i ,v )are stored in u and v respectively,which satisfies connectivity.In the other case where reach-able pair u and v are in different strongly connected components,assume that u ∈C i ,v ∈C j (i =j ).The certificates on p (u,pvt i )are stored in u and the cer-tificates on p (pvt j ,v )are stored in v in step 2.And in step 4.1,we construct a shortest outgoing tree T i rooted at C i .Since u and v are reachable,there must exist a path from C i to C j in T i .Furthermore,in step 4.2certificates on the shortest path from pvt i to pvt j are stored in u .We know that for any reachable pair u and v ,there exists a path p (u,v )which concatenat-ing p (u,pvt i ),p (pvt i ,pvt j )and p (pvt j ,v ),and all of the certificates on p (u,v )are stored in u and v ,this satisfies connectivity.We show completeness second.In step 5,we store all remained certificates in an arbitrary node.That means all of the certificates are stored in some nodes,which satisfies completeness.Therefore,GPivot is a certificate dispersal algorithm.For the proof of computation time,we consider the time needed for each step.In step 1,G can be parti-tioned into strongly connected components by Tarjan’s algorithm [8]in O (|V |+|E |)time.It takes O (|V |+|E |)time for Pivot procedure in step 2,and O (|E |)time is needed for constructing graph H in step 3.In step 4.1,we need O (p G +|E (H )|)time for computing shortest outgoing tree for each component,and in step 4.2,for constructing the shortest paths between two reachable pivot nodes,we need to construct shortest outgoing tree rooted at each pivot node,which needs O (|V |+|E |)time.Therefore,we can finish the computation in step 4in time of O (p G ·(p G +|E (H )|+|V |+|E |))=O (p G ·(|V |+|E |)).In step 5,at most |E |certificates are remained,that means we need at most O (|E |)time for step 5.Hence,the total computation time for GPivot is O (p G ·(|V |+|E |)).✷Theorem 3:For any directed graph G =(V,E ),c.(GPivot ,G )≤2p G d max +p G −1+|E |/|V |,where p G is the number of strongly connected components of G and d max is the maximum diameter of strongly con-nected components of G .Proof:Let C 1,C 2,···,and C p G be strongly connected components,d i be diameter of C i and d max =max {d 1,d 2,···,d p G }.We consider the number of cer-tificates stored in each step.In step 2,for each node v in C i ,at most 2d i certificates are stored in v by Pivot pro-cedure.In step 4,since T i is a tree and |V (H )|=p G ,there are at most p G −1edges in T i .For any edge (C i ,C j )in T i ,d (pvt i ,pvt j )is at most 2d max +1.There-fore,|GPivot .(G,v )|satisfies an inequality below:|GP ivot.(G,v )|=2d i + (C j ,C k )∈E (T i )E (p (pvt j ,pvt k ))≤2d max +(C j ,C k )∈E (T i )(2d max +1)≤2d max +(p G −1)(2d max +1)≤2p G d max +p G −1(3)This inequality holds for any node v in G .In step 5,at most |E |certificates are remained.Therefore,the costof GPivot is 2p G d max +p G −1+|E |/|V |.✷4.Lower Bounds for Special Graph ClassesIn this section,we introduce some general methods toderive a lower bound of the certificate dispersability cost for a given certificate graph.For some special graph classes,such as n -dimensional Hypercube,n -dimensional Meshs,complete k -ary trees and de-Bruijn graphs,the lower bounds of the dispersability cost are proved.And in the same time,our CPivot algorithm is shown to be optimal algorithms for these graph classes.Lemma 6:Let G =(V,E )be a directed graph,V 1and V 2be subsets of V such that V 1∩V 2=∅,and f :V 1→V 2be an injective function.For any nodes pair u and v ,let P u,v and P v,u be the set of paths from u to v and from v to u .Let d (u,v )=min p (u,v )∈P u,v ,p (v,u )∈P v,u |E (p (u,v ))∪E (p (v,u ))|.Thenc.G ≥max |E ||V |,1|V |u ∈V 1d (u,f (u )).(4)Proof:For satisfying the completeness condition,at least |E |certificates have to be stored.This means the average number of certificates stored in each node is not less than |E |/|V |.On the other hand,since f is an injection from V 1to V 2,for any two dis-tinct nodes u and v in V 1,f (u )and f (v )are dis-tinct.We assume that for some certificate dispersal algorithm F ,there exists a node u (∈V 1),such that |F.(G,u )∪F.(G,f (u ))|<d (u,f (u )).We derive a con-tradiction in three cases.Case 1:u and f (u )are reach-able with each other.Since connectivity is satisfied,there exist two paths p (u,f (u )),denoted by p 1,and p (f (u ),u ),denoted by p 2,such that E (p 1)⊆(F.(G,u )∪F.(G.f (u )))and E (p 2)⊆(F.(G,u )∪F.(G.f (u ))).So |E (p 1)∪E (p 2)|≤|F.(G,u )∪F.(G.f (u ))|.And from the definition of d (u,f (u )),d (u,f (u ))≤|E (p 1)∪E (p 2)|.Therefore d (u,f (u ))≤|F.(G,u )∪F.(G,f (u ))|.Con-tradiction occurs.Case 2:u is reachable to f (u ),and f (u )is unreachable to u .Since connectivity is satisfied,there exists a path p (u,f (u )),denoted by p 1,such that E (p 1)⊆(F.(G,u )∪F.(G.f (u ))).So |E (p 1)|≤|F.(G,u )∪F.(G.f (u ))|.And from the defi-nition of d (u,f (u )),d (u,f (u ))≤|E (p 1)|.Contradic-tion occurs.Case 3:f (u )is reachable to u ,and u is unreachable to f (u ).The proof is similar as Case 2.It is clear that this lemma holds when u and f (u )are unreachable with each other.✷Corollary 1:Let G =(V,E )be a bi-directional and strongly connected graph,V 1and V 2be subsets of V such that V 1∩V 2=∅.Let f :V 1→V 2be an injective。
新视野大学英语读写教程3 UNIT9 课文翻译
婚前协议一位即将结婚的男子希望能够确保即使婚姻失败，他仍可以把他珍爱的冰淇淋藏品好好储存在冰柜里。
一名女子坚持要求明确婚后由谁来遛狗。
一名男子要求，如果他未来的新娘婚后体重增加15磅以上，他有权离婚。
以上这些都是婚前协议中一些比较荒唐的条款。
但是不要弄错了，大多数婚前协议涉及到的都是钱──以及一旦离婚该怎样分配财产。
而且，离婚及其带来的钱财纠纷，在美国是很常见的事。
婚前协议──简称prenup──就是用来处理这些问题的。
婚前协议由即将结婚的男女双方的律师共同协定，然后由双方在牧师宣布他们结为夫妻之前签署。
自20世纪80年代初以来，婚前协议在美国被越来越多的人接受，因为当时越来越多的州开始通过关于离婚财产分配的法律。
这些法律要么是基于“共有财产”（平均分配），要么是基于“合理分配”（法官认为怎样“公平”就怎样分）。
名人的婚前协议总是新闻头条：杰奎琳·肯尼迪·奥纳西斯的律师在亚里士多德·奥纳西斯死后拿出两人的婚前协议对簿公堂，据说她后来在庭外和解中得到了2,600万美元。
但婚前协议也适用于那些不甚有名却很富有的人。
“这是因为离婚会带来巨大的经济后果，而再婚又如此常见，”一位家庭法律师说。
典型的想签订婚前协议的人是那些积累了大量财富、曾吃过苦头的男性，他们想减少日后的麻烦。
“他们想自己安排解决，而不想让法庭裁决，”美国婚姻法律师协会纽约分会的会长说。
保护前一次婚姻的孩子是签署婚前契约的一个重要原因。
“有人可能有价值10亿美元的财产，而他又不想让第二个配偶分得5亿美元。
他可能想多留一点给自己的孩子，”一名律师说。
为了将财产传到自己的儿孙手中，六七十岁的退休丧偶老人在找老伴时，订立婚前协议也很常见。
另一种要求签订婚前协议的情况大多是，未来的丈夫或妻子已经或即将继承巨额遗产或家庭产业，而未来伴侣却家产不多或一贫如洗。
但是，即使双方签订了这样的协议，如果不遵循正确的指导方针，还是不可能在法院实施它。
签名确认的重要性英语作文
Signature confirmation is a critical aspect of various transactions and agreements, ensuring that all parties involved have given their consent and are aware of the terms and conditions.Here are some reasons why signature confirmation is essential:1.Legal Validity:A signature serves as a legal proof that the person has read,understood, and agreed to the terms of a document.Without a signature,a document may not hold up in a court of law.2.Authentication:Signatures help authenticate the identity of the person signing the document.It is a way to verify that the person who claims to have signed the document is indeed the same person.3.Record Keeping:Signatures provide a permanent record of who agreed to the terms ofa document.This is useful for future reference and can help in resolving disputes.4.Prevention of Fraud:By requiring a signature,organizations can reduce the risk of fraud.A forged or unauthorized signature can be detected and investigated.5.Finalization of Agreements:A signature acts as a seal of approval on an agreement, indicating that the negotiation phase is complete and both parties are ready to proceed with the terms as stated.6.Protection of Rights:Signatures ensure that the rights of all parties involved are protected.It is a way to make sure that no one can claim they were not aware of the terms they agreed to.7.Economic Transactions:In business and financial transactions,signatures are used to authorize payments,transfers,and other economic activities.They are a necessary step in the process to ensure that the transaction is legitimate and authorized.8.Electronic Signatures:With the advent of digital technology,electronic signatures have become common.They offer the same legal standing as traditional signatures and are often more convenient and secure.9.Nonrepudiation:Signatures provide a means of nonrepudiation,meaning that once a document is signed,the signer cannot later deny having signed it or claim that they did not agree to its contents.10.Cultural Significance:In many cultures,the act of signing a document is a significant and formal event,symbolizing commitment and seriousness about the agreement.In conclusion,signature confirmation is a fundamental part of ensuring that agreements are binding,legitimate,and respected by all parties involved.It is a simple yet powerful tool that helps maintain trust and integrity in various aspects of life,from personal contracts to international business deals.。
公证的意义英语作文
公证的意义英语作文Title: The Significance of Notarization。
Notarization serves as a crucial pillar in the legaland administrative framework of societies worldwide. Its significance transcends mere authentication; it embodies trust, legality, and protection. In this essay, we delveinto the multifaceted importance of notarization.Firstly, notarization confers authenticity to legal documents. By affixing the seal and signature of a notary public, documents gain credibility and validity. This authentication is instrumental in various legal proceedings, such as contracts, deeds, and affidavits. The notary'sstamp serves as an impartial witness, attesting to the genuineness of the signatures and the veracity of the content.Moreover, notarization facilitates transparency and accountability in transactions. Parties involved incontractual agreements rely on notarized documents to ensure mutual understanding and adherence to terms. It mitigates the risk of fraud or misrepresentation, as the notary verifies the identities of the signatories and ensures their willingness to enter into the agreement. This fosters a conducive environment for business transactions and reinforces the rule of law.Furthermore, notarization plays a pivotal role in protecting the rights and interests of individuals. For instance, in the realm of property transactions, notarized deeds provide legal proof of ownership and prevent disputes over property rights. Similarly, in estate planning, wills and powers of attorney undergo notarization to safeguard the wishes of the testator and prevent undue influence or coercion.In addition to its legal implications, notarization serves as a deterrent against fraudulent activities. The stringent procedures followed by notaries, including identity verification and document scrutiny, act asbarriers to unauthorized alterations or forgeries. Thisfosters public confidence in the integrity of official documents and institutions, thereby bolstering the credibility of the legal system.Furthermore, notarization transcends national borders, facilitating the recognition of documents across jurisdictions. Apostille certificates, issued under the Hague Convention, validate the authenticity of documentsfor use in foreign countries. This simplifies international transactions, expedites legal processes, and promotes global cooperation.Beyond its immediate legal ramifications, notarization contributes to societal cohesion and stability. By upholding the sanctity of contracts and agreements, it fosters trust among individuals, businesses, and institutions. This trust forms the bedrock of a functioning society, underpinning economic activities, interpersonal relationships, and the overall rule of law.In conclusion, notarization embodies the essence of legality, trust, and protection within a legal framework.Its significance extends beyond the mere authentication of documents, encompassing transparency, accountability, andthe safeguarding of individual rights. In an increasingly interconnected world, notarization serves as a linchpin for legal certainty, facilitating transactions, mitigating risks, and upholding the principles of justice and fairness.。