交换环上线性群中含根子群的极大子群

本文验证了交换环上线性群中三种含根子群的子群的极大性,并讨论了交换环上线性群中含根子群的极大子群的可能类型。

基于CL加密的改进分布式解密系统

近些年,无线医疗传感器网络(Wireless Medicine Sensor Networks,WMSNs)得到了广泛的应用。WMSNs提高了患者护理质量,但同时也存在许多安全隐患。为了保护患者数据的隐私安全,Yi等人提出了一个基于Paillier密码系统的分布式ElGamal密码系统。然而,Rao分析了他们的方案并展示了一种可行的攻击,该攻击允许攻击者获取密钥。因此,是否可以将具有加法同态性质的密码系统修改为安全的分布式解密系统,以实现更简单的分布式密钥生成和更高效的分布式解密仍然是一个挑战。针对上述挑战,该文提出了一种基于Castagnos和Laguillaumie(CL)加密的改进分布式解密系统,并对未知阶群G上的离散对数关系给出了有效的零知识证明。与其他分布式解密系统相比,基于CL加密的改进分布式系统具有良好的性能、更可靠的设置、更高的安全级别。

Biodiversity of arbuscular mycorrhizal colonization and spore population in different agroforestry trees and crop species growing in Dinajpur,Bangladesh

Biodiversity of arbuscular mycorrhizal colonization and spore population was investigated in different agroforestry trees and crop species collected from different locations of Dinajpur district of Bangladesh. Roots and rhizosphere soils of Albizia procera Benth., Capsicum frutescens L, Curcuma domestica Vahl., Dalbergia sissoo Roxb. and Swietenia macrophylla King. from Dashmail; C. domestica, D. sissoo, Eucalyptus camaldulensis Dehnn., Gmelina arborea （Roxb） DC and Oryza sativa L. from Kantaji and C. domestica, D. sissoo, Litchi chinensis Sonn. and O. sativa from Ramsagar were collected. Roots and soils were assessed following standard methods. The range of AM colonization was recorded 36%-79% from Dashmail. The highest AM colonization was recorded in C. frutescens （79%） and the lowest was in C. domestica （36%）. The range of colonization was recorded as 33%-70% from Kantaji. The highest AM colonization was recorded in G. arborea （70%） and the lowest was in O. sativa （33%）. The range of AM colonization was recorded as 35%-70% from Ramsagar. The highest AM colonization was recorded in D. sissoo （70%） and the lowest was in O. sativa （35%）. Arbuscular mycorrhizal spore population varied from 54 to 140/100g dry soil in the soils from Dashmail. The highest was in the soils of D. sissoo （140） and the lowest was in C. domestica （54）. The spore population varied from 63 to 221 in Kantaji. The highest was in G. arborea （221） and the lowest was in O. sativa （63）. The range population in Ramsagar varied from 69 to 160. The highest was recorded in D. sissoo （160） and the lowest was in L. chinensis （69）. No significant relationship of soil pH and soil OM with AM colonization and with spore population was observed. Simpson＇s index of diversity （Ds） and Shannon＇s index of diversity- （Hs） were highest in the soil of D. sissoo from Kantaji and the lowest in the soils of O. sativa from Ramsagar. Biodiversity of AM colonization, spore population and the distribution of AM fungi in the rhizosphere soils of different agroforestry plants indicated the occurrence of AM fungi, mycotrophic nature of the trees and crop species, contribution and necessity of AM fungi and the AM dependence of the agroforestry plants growing in Dinajpur district of Bangladesh.

Quantum Weyl symmetric polynomials and the center of quantum group U_q(sl_4)

Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.

A NEW TYPE OF PRONORMAT SUBGROUPS IN CHEVALLEY GROUPS

Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.