分配格和素域生成的半环簇

Let V be the variety generated by two-element distributive lattice B2 and k prime fields Fp1,...,Fpk. That is to say that V = HSP{B2, Fp1,...,Fpk}. It is proved that the variety V is finitely based. Also, the two-element distributive lattice B2 and prime fields Fp1,..., Fpk are, up to isomorphism, the only subdirectly irreducible semirings in V. Some known results are extended and enriched.     

特征标次数图是一种连通图的单群

对有限单群G,假设其不可约特征标次数图Δ(G)连通,且图顶点集ρ(G)=π_1∪π_2∪{p},其中|π_1|,|π_2|≥1,π_1∩π_2=θ,且π_1与π_2中顶点不相邻.证明了Δ(G)满足上面的假设的有限单群G只有4种:M_(11),J_1,PSL_3(4)或²B_2(q2B_2(q²),其中q2),其中q²一1是Mersenne素数.     

广义Carmichael数

设n是一个合数,Z_n表示模n的剩余类环,r(x)∈Z_n[x]是一个首一的k(>0)次不可约多项式。本文引入n是k阶摸r(x)的Carmichael数的定义,全体这样的数记为集C_(k,r)(x),由此给出k阶Carmichael数集:C_k={∪C_(k,r)(x)|r(x)过全体Z_n上的首一k次不可约多项式}。显然C_1表示通常的Carmichael数集。作者得到了n∈C_(k,r(x))的一个充要条件,进而得到n∈C_k的一个充要条件及n∈C_2的一个更易计算的充要条件,还证明了C_1(?)C_2以及|C_2|=∞。     

Strongly Irreducible Submodules of Modules

Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.     

Symmetrized Wavefunctions in a Quantum N-Body System

A general method for symmetrizing the generalized radial functions in a quantum N-body system to belong to the irreducible representation of the proper point symmetry group of the system is presented, based on irreducible bases in the point group space.     

关于拓扑对策中的I2(κ)(∈)I(κ)问题

证明了如果空间类K为D-空间类或闭遗传不可约空间类,则I（K）包含K.这一结果对于K为D空间类和闭遗传不可约空间类,肯定地回答了I（K）是否包含I^2（K）问题.     

THE (U K)-ORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＴｂｅａｌｉｎｅａｒ，ｂｏｕｎｄｅｄｏｐｅｒａｔｏｒａｃｔｉｎｇｏｎａｃｏｍｐｌｅｘ，ｓｅｐａｒａｂｌｅ，ｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌＨｉｂｅｒｔｓｐａｃｅＨ．Ｗｅｃａｌ（Ｕ＋Ｋ）（Ｔ）＝｛ＲＴＲ－１，Ｒ...     

What Makes a Theory Testable, or Is Intelligent Design Less Scientific Than String Theory?

I compare the theory of intelligent design to string theory to see on what basis, if any, only the former can be justifiably excluded as being scientific.We shall see that the classic criterion of testability or falsifiability is sometimes not so straightforward, and that there are other criteria to help us make such a distinction.     

局部双a对角占优矩阵及应用

利用局部双d对角占优矩阵，给出了非奇H矩阵的充分条件和等价表征，改进了文[1]主要结果。     

On tridiagonal conjugate-normal matrices

Conjugate-normal matrices play the same role in the theory of unitary congruences as conventional normal matrices do with respect to unitary similarities. Naturally, the properties of both matrix classes are fairly similar up to the distinction between the congruence and similarity. However, in certain respects, conjugate-normal matrices differ substantially from normal ones. Our goal in this paper is to indicate one of such distinctions. It is shown that none of the familiar characterizations of normal matrices having the irreducible tridiagonal form has a natural counterpart in the case of conjugate-normal matrices.