Isometric multipliers and isometric isomorphisms of $l\sb{1}(S)$

Isometric Isomorphisms of Measure Algebras

On Isometric and Minimal Isometric Embeddings

In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call quasi-κ-curved metrics. Quasi-κ-curved metrics generalize the metrics of space forms. We construct explicit examples and prove results about existence and rigidity. Introduction Definition: Let (M, g̃) be a Riemannian manifold. We will say g̃ is a quasi-κcurved metric if there ...

Labeling Isometric and Almost Isometric n-Point Configurations in R

Consider two n-point configurations X and Y in R with the same distance distribution and distinct distances. We begin with proposing an algorithm that tries to find a bijection ψ : X → Y such that X and Y are congruent under ψ, or determines that no such bijection exists. Next, we discuss extending this algorithm to the case where X and Y have small multiplicities of recurring distances, then t...

Isometric Decompositions

The study of decompositions of sets in U, n ^ 1, into disjoint, mutually isometric subsets has a long and distinguished history. In 1928 J. von Neumann [2] proved that an interval in U (with or without endpoints) is decomposable into Ko disjoint sets which are mutually isometric under translations. In 1951 W. Gustin [1] proved that no such decomposition into n, 2 ^ n < No, sets is possible. A b...

Isometric Projection

Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. The most popular manifold learning algorithms include Locally Linear Embedding, ISOMAP, and Laplacian Eigenmap. However, these algorithms are no...