On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed.     

Divisibility in the K0‐Group of the Algebra of Operators on a Banach Space

Let Figiel's reflexive Banach space which is not isomorphic to its Cartesian square. We show that the K ₀group of the algebra of continuous, linear operators on contain a subgroup isomorphic to the group c ₀₀( ) of sequences rational numbers with z _n=0 eventually.     

On the Koszul Modules of Exterior Algebras

We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.     

On the Countable Tightness of Product Spaces

In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following conditions are equivalent： （1） b = ω1; （2） t（Sω×Sω1） 〉 ω; （3） For any pair （X, Y）, which are k-spaces with a point-countable k-network consisting of cosmic subspaces, t（X×Y）≤ω if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the k-space property of products of spaces with certain k-networks could be deduced from the above theorem.     

Asymptotic Morphisms and Elliptic Operators over C*‐Algebras

This paper provides an Etheoretic proof of an exact form, due to E. Troitsky, of the Mischenko–Fomenko Index Theorem for elliptic pseudodifferential operators over a unital C^*algebra. The main ingredients in the proof are the use of asymptotic morphisms of Connes and Higson, vector bundle modification, a Baum–Douglastype group, and a K Kargument of Kasparov.     

Relatively Free Algebras with the Identity x 3 = 0 #

A basis for a relatively free associative algebra with the identity x ³ = 0 over a field of an arbitrary characteristic is found. As an application, a minimal generating system for the 3 × 3 matrix invariant algebra is determined.     

On the Deformation of Lie–Yamaguti Algebras

The deformation theory of Lie–Yamaguti algebras is developed by choosing a suitable cohomology. The relationship between the deformation and the obstruction of Lie–Yamaguti algebras is obtained.     

On the Characteristic of Proper Lattice Implication Algebras

ＯｎｔｈｅＣｈａｒａｃｔｅｒｉｓｔｉｃｏｆＰｒｏｐｅｒＬａｔｔｉｃｅＩｍｐｌｉｃａｔｉｏｎＡｌｇｅｂｒａｓ￥ＸｕＹａｎｇ；ＱｉｎＫｅｙｕｎ（ＳｏｕｔｈｗｅｓｔＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ）（ＨｅｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔ...     

On the Self-adjointness of the Product Operators of Two ruth-Order Differential Operators on [0, ＋∞）

In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, ∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.     

On the 0-dimensional cusps of the Kähler moduli of a K3 surface

Let S be a complex algebraic K3 surface. It is proved that the 0-dimensional cusps of the Kähler moduli of S are in one-to-one correspondence with the twisted Fourier-Mukai partners of S. As a result, a counting formula for the 0-dimensional cusps of the Kähler moduli is obtained. Applications to rational maps between K3 surfaces are given. When the Picard number of S is 1, the bijective correspondence is calculated explicitly by using the Fricke modular curve.     

On the P-Torsion Subgrup of Homotopy Group

ＯｎｔｈｅＰ－ＴｏｒｓｉｏｎＳｕｂｇｒｏｕｐｏｆＨｏｍｏｔｏｐｙＧｒｏｕｐＳｈｅｎＸｉｎｙａｏ（沈信耀）（Ｉｎｓｔ．ｏｆＭａｔｈ．ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ，１０００８０，Ｃｈｉｎａ）ＲｅｃｅｉｖｅｄＮｏｖｅｍｂｅｒ２６．１９９３Ｏ...     

On the Stability of Deformations of Cuntz–Toeplitz Algebras

Ukrainian Mathematical Journal - We study C*-algebras $$ {\mathcal{O}}_{n+m}^{\hat{q}} $$ generated by isometries $$ {\left\{{S}_i\right\}}_{i=1}^n\bigcup {\left\{{t}_j\right\}}_{j=1}^m, $$ where...     

On the Universal Unfoldings of C~∞ Map Germs Under Some Subgroups of A and K

ＯｎｔｈｅＵｎｉｖｅｒｓａｌＵｎｆｏｌｄｉｎｇｓｏｆＣ￣∞ＭａｐＧｅｒｍｓＵｎｄｅｒＳｏｍｅＳｕｂｇｒｏｕｐｓｏｆＡａｎｄＫＸｉｏｎｇＪｉａｎｆｅｉ（熊剑飞）（ＩｎｓｔｉｔｕｔｅｏｆＡＰＰｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＱｉｎｇｄａｏＵｎｉｖｅｒｓｉ...     

On the Characterization of the Full p-Defective Finite Group

A finite group G is called a full p-defective group if every p-block of G isof the highest defect.In this paper, we shall mainly study the full p-defectivefinite groups and characterize them.     

RESEARCH ANNOUNCEMENTS──On the Maps of Deleted Product

ＬｅｔＭａｎｄＮｂｅｓｉｍｐｌｙｃｏｎｎｅｃｔｅｄｃｌｏｓｅｄｍａｎｉｆｏｌｄｓ，ｆ：Ｍ→Ｎｂｅａｈｏｍｏｔｏｐｙｅｑｕｉｖａｌｅｎｃｅ．Ｗｅｄｅｆｉｎｅｄａｎｉｓｏｍｏｒｐｈｉｓｍｏｆｃｏｈｏｍｏｌｏｇｙｓｙｓｔｅｍｆ：Ｈ（Ｎ（ｋ）；Ｇ）→Ｈ...     

On the Group of ρ-endotrivial κG-modules

In this paper, we define a group T_ρ(G) of p-endotrivial κG-modules and a generalized Dade group D_ρ(G) for a finite group G. We prove that T_ρ(G)? T_ρ(H)whenever the subgroup H contains a normalizer of a Sylow p-subgroup of G, in this case, K(G)? K(H). We also prove that the group D_ρ(G) can be embedded into T_ρ(G) as a subgroup.