A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for eac...A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for each e=uv∈E(T), assigns each edge e a different label. In this paper, we constructively proved that more classes of trees are felicitous. In the end, we gave a conjecture that every lobster tree is felicitous.展开更多
Let P be an inner point of a convex N-gon ΓN ： A1A2… ANA1（N ≥ 3）, and let di,k denote the distance from the point Ai＋k to the line PAi（i = 1,2,…,N, Ai = Aj〈=〉 i ≡ j（modN））, which is called the k-Brocard...Let P be an inner point of a convex N-gon ΓN ： A1A2… ANA1（N ≥ 3）, and let di,k denote the distance from the point Ai＋k to the line PAi（i = 1,2,…,N, Ai = Aj〈=〉 i ≡ j（modN））, which is called the k-Brocard distance for P of ΓN. We have proved the following double-inequality： If P ∈ ΓN, k = N↑∩i=1∠Ai-kAiAi＋k（1 ≤ k 〈 N/2,i =1,2,…,N）, and r ≤ lnN-ln（N-1）/ln2＋2[lnN-ln（N-1）], then （1/N N↑∑↑i=1di^r, k）^1/r≤1/N coskπ/N N↑∑↑i=1｜AiAi＋k｜≤sin2kπ/2sinπ/N（1/N N↑∑↑i=1｜AiAi＋1｜^2.展开更多
Public Key Encryption with Keyword Search （PEKS）, an indispensable part of searchable encryption, is stock-in- trade for both protecting data and providing operability of encrypted data. So far most of PEKS schemes ...Public Key Encryption with Keyword Search （PEKS）, an indispensable part of searchable encryption, is stock-in- trade for both protecting data and providing operability of encrypted data. So far most of PEKS schemes have been established on Identity-Based Cryptography （IBC） with key escrow problem inherently. Such problem severely restricts the promotion of IBC-based Public Key Infrastructure including PEKS component. Hence, Certificateless Public Key Cryptography （CLPKC） is efficient to remove such problem. CLPKC is introduced into PEKS, and a general model of Certificateless PEKS （CLPEKS） is formalized. In addition, a practical CLPEKS scheme is constructed with security and efficiency analyses. The proposal is secure channel free, and semantically secure against adaptive chosen keyword attack and keyword guessing attack. To illustrate the superiority, massive experiments are conducted on Enron Email dataset which is famous in information retrieval field. Compared with existed constructions, CLPEKS improves the efficiency in theory and removes the key escrow problem.展开更多
In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
A new structure with the special property that instantaneous state and catas-trophes is imposed to ordinary birth-death processes is considered. Kendall's conjecture forthe processes is proved to be right.
文摘A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for each e=uv∈E(T), assigns each edge e a different label. In this paper, we constructively proved that more classes of trees are felicitous. In the end, we gave a conjecture that every lobster tree is felicitous.
文摘Let P be an inner point of a convex N-gon ΓN ： A1A2… ANA1（N ≥ 3）, and let di,k denote the distance from the point Ai＋k to the line PAi（i = 1,2,…,N, Ai = Aj〈=〉 i ≡ j（modN））, which is called the k-Brocard distance for P of ΓN. We have proved the following double-inequality： If P ∈ ΓN, k = N↑∩i=1∠Ai-kAiAi＋k（1 ≤ k 〈 N/2,i =1,2,…,N）, and r ≤ lnN-ln（N-1）/ln2＋2[lnN-ln（N-1）], then （1/N N↑∑↑i=1di^r, k）^1/r≤1/N coskπ/N N↑∑↑i=1｜AiAi＋k｜≤sin2kπ/2sinπ/N（1/N N↑∑↑i=1｜AiAi＋1｜^2.
基金This research was supported by the National Science Foundation of China for Funding Projects （61173089,61472298） and National Statistical Science Program of China（2013LZ46）.
文摘Public Key Encryption with Keyword Search （PEKS）, an indispensable part of searchable encryption, is stock-in- trade for both protecting data and providing operability of encrypted data. So far most of PEKS schemes have been established on Identity-Based Cryptography （IBC） with key escrow problem inherently. Such problem severely restricts the promotion of IBC-based Public Key Infrastructure including PEKS component. Hence, Certificateless Public Key Cryptography （CLPKC） is efficient to remove such problem. CLPKC is introduced into PEKS, and a general model of Certificateless PEKS （CLPEKS） is formalized. In addition, a practical CLPEKS scheme is constructed with security and efficiency analyses. The proposal is secure channel free, and semantically secure against adaptive chosen keyword attack and keyword guessing attack. To illustrate the superiority, massive experiments are conducted on Enron Email dataset which is famous in information retrieval field. Compared with existed constructions, CLPEKS improves the efficiency in theory and removes the key escrow problem.
文摘In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
基金Supported by the Guangxi Science Foundation(0339071)
文摘A new structure with the special property that instantaneous state and catas-trophes is imposed to ordinary birth-death processes is considered. Kendall's conjecture forthe processes is proved to be right.
