高等教育

多项式插值公式的全新证明研究目的: 通过特定代数多项式上的中国剩余定理的建立及应用，进行拉格朗日多项式插值公式的全新证明，项目的创新点和特色有别于一般待定系数法的证明，通过建立特定多项式上的中国剩余定理，求出特定解，进行拉格朗日多项式插值公式的全新证明；关键问题：寻找特殊多项式上的中国剩余定理的表现形式。

一种全新动态口令构造方法基于口令的认证可以看成是密码学中的单向身份认证协议。

由于其成本低，操作性强，用户界面好，简单易行，速度快等优点，成为目前较为广泛的认证方法。

[47]Haller N.The S/KEY one-time password system [R].New Jersey:BellcoreCo,1995.[48] Lamport L. Password authentication with insecure communication [J].Comm ACM,1981,24(11):770-772.[49]Hwang TY. Password Authentication Using Publickey Encryption. International Carnahanconterence on security Technology, 1983:141-144[50]Laih CS, Harn L and Hwang D. Password Authentication Using Quadratic Residues. International Symposium,1988:1484-1489[51]Chang CC and Lian HT. Sharing a polynomial for password authentication.电脑学刊，1990:11-17[52]Harn L, Hung P,Laih C S. Password authentication using public-key cryptosystems. Computer Math.App.,1989,18(12):1001-1017.[53]Harn L.A public-key based dynamic password scheme. personnel communication.Ron Rivest和Adi Shamir以及Leonard Adleman于1978年提出RSA的公钥密码体制至今仍被公认为是一个安全性能良好的密码体制[26]。

[26]陈鲁生，沈世镒, 现代密码学[M], 北京：科学出版社, 2002, pp.71-72.On normal and fantastic filters of BL-algebrasThe origin of BL-algebras is in Mathematical Logic.Hajek introduced BL-algebras as algebraicstructures for his Basic Logic in order to investigate many-valued logic by algebraic means.[3,9]. They play the role of Lindenbaum algebras from classical propositional calculus. The main example of a BL-algebra is the interval [0,1] endowed with the structure induced by a continuous t-norm. MV-algebras, Godel algebras and Product algebras are the most known classes of BL-algebras[4].In studying of algebras, filters theory plays an important role. From logical point of view, various filters correspond to various sets of provable formulae [11]. In [4,5,8], the notions of prime filter, Boolean filter, implicative filters, normal filters, fantastic filters and positive implicative filters in BL-algebras were proposed, and theproperties of the filters were investigated. In [2], several different filters of residuated lattices and triangle algebras were defined and their mutual dependencies and connectionswere examined. In [6,1,12], filters of pseudo MV-algebras, pseudo BL-algebras, pseudo effect algebras and pseudo hoops were further studied. We found that filters are a useful tool to obtain results of BL-algebras.we present some basic definitions and results onfilters and BL-algebras, then we introduce the some kinds offilters in BL-algebras.In[8],Saeid and Motamed proposed two open problems that "Under what suitable condition a normal filter becomes afantastic filter? " and "(Extension property for a normal filter)Under what suitable condition extension property for normal filterholds? " in BL-algebras. by studying the equivalent condition of fantastic filter, we reveal the relation betweenfantastic filter and normal filter of BL-algebras and we solve theopen problems.[1] L.C. Ciungu, Algebras on subintervals of pseudo-hoops, Fuzzy Sets and Systems 160(2009) 1099-1113.[2]B.V. Gasse, G. Deschrijver, C. Cornelis, E.E. Kerre, Filters of residuated lattices and triangle algebras, Information Sciences (2010) (online).[3]P. H\'ajek, Metamathematics of fuzzy logic,Kluwer, Dordrecht(1998)[4]刘练珍,李开泰, Fuzzy filters of BL-algebras, Information Sciences 173 (2005) 141–154.[5]刘练珍,李开泰, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets and Systems 152 (2005) 333–348.[6]J. Mertanen, E. Turunen, States on semi-divisible generalized residuated lattices reduce to states on $MV$-algebras, Fuzzy Sets and Systems 159(2008) 3051-3064.[7]J. Rachu\aa nek, D. \v{S}alounov\'a, Classes of filters in generalizationsof commutative fuzzy structures, Acta Univ. Palacki. Olomuc., Fac.rer. nat., Mathematica 48 (2009) 93-107.[8]A.B. Saeid, S. Motamed, Normal Filters in BL-Algebras, 世界应用科学期刊7 (2009) 70-76.[9]E. Turunen, Mathematics Behind Fuzzy Logic, 自然出版社, 海德堡(1999)[10]张小红,模糊逻辑及其代数分析，科学出版社，北京(2008)[11]张小红, W.H. Li, On pseudo-$BL$ algebras and $BCC$-algebras, Soft Comput 10(2006) 941-952.[12]张小红, 樊雪双, Pseudo-$BL$ algebras and pseudo-effect algebras, Fuzzy sets and systems 159(1)(2008) 95-106.。