Primary spaces, Mackey’s obstruction, and the generalized barycentric decomposition

Generalized barycentric coordinates

Barycentric extension of generalized matching.

In most studies of choice under concurrent schedules of reinforcement, two physically identical operanda are provided. In the "real world," however, more than two choice alternatives are often available and biases are common. This paper describes a method for studying choices among an indefinite number of alternatives when large biases are present. Twenty rats were rewarded for choosing among f...

Constrained and generalized barycentric Davenport constants

Let G be a finite abelian group. The constrained barycentric Davenport constant BD(G) with s ≥ 2, is the smallest positive integer d such that every sequence with d terms in G contains a k-barycentric subsequence with 2 ≤ k ≤ s. The generalized barycentric Davenport constant BDs(G), s ≥ 1, is the least positive integer d such that in every sequence with d terms there exist s disjoint barycentri...

Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition

We construct interpolation operators for functions taking values in a symmetric space—a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition—a generalization of the well-known factorizat...

On the Decomposition of Hilbert Spaces

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...