Fundamental theorems in global knot theory, I

Global Knot Theory in F

Introduction to Property Theory: The Fundamental Theorems

The market system consists of a price mechanism built upon the foundation of a system of property and contract. In many developing and transition economies, the market system does not function well. In many, if not most, cases the malfunctioning is not simply in the price system (e.g., anti-competitive activities) but in the underlying property system (e.g., contracts not being fulfilled and ex...

Algebraic proofs of some fundamental theorems in algebraic K - theory

We present new proofs of the additivity, resolution and cofinality theorems for the algebraic K-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic K-groups via binary complexes. 2000 Mathematics Subject Classification: 19D99

Tensor subalgebras and First Fundamental Theorems in invariant theory

Abstract. Let V = C and let T := T (V ) ⊗ T (V ∗) be the mixed tensor algebra over V . We characterize those subsets A of T for which there is a subgroup G of the unitary group U(n) such that A = T. They are precisely the nondegenerate contraction-closed graded ∗-subalgebras of T . While the proof makes use of the First Fundamental Theorem for GL(n,C) (in the sense of Weyl), the characterizatio...

Analogues of Some Fundamental Theorems of Summability Theory

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0’s and 1’s which is not A-summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x. In this paper, definitions for “subsequences of a double sequence” and “Pri...