Calculations of generalized Kervaire's invariant

Generalized shift invariant systems

A countable collection X of functions in L2(IR ) is said to be a Bessel system if the associated analysis operator T ∗ X : L2(IR ) → `2(X) : f 7→ (〈f, x〉)x∈X is well-defined and bounded. A Bessel system is a fundamental frame if T ∗ X is injective and its range is closed. This paper considers the above two properties for a generalized shift-invariant system X. By definition, such a system has t...

Generalized Invariant Imbedding Relation.

Generalized Invexity and Generalized Invariant Monotonicity

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results...

Generalized Baer-Invariant of a Pair of Groups and Marginal Extension

In this paper, we give connection between the order of the generalized Baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. Moreover, we give a necessary and sufficient condition in which the generalized Baer-invariant of a pair of groups can be embedded into the generalized Baer-invariant of pair of its factor groups.

Generalized Baer-Invariant of a Pair of Groups and the Direct Limit

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...