An upper bound on the first S invariant eigenvalue of the Laplacian for S invariant metrics on S is used to find obstructions to the existence of isometric embeddings of such metrics in (R, can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the surface of revolution cannot be isometrically embedded in (R, can). This leads to a generalization of a...

A sharp upper bound on the first S invariant eigenvalue of the Laplacian for S invariant metrics on S is used to find obstructions to the existence of S equivariant isometric embeddings of such metrics in (R, can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in (R, can). This leads to ge...

The characteristic (or intrinsic) scale of a local image pattern is the scale parameter at which the Laplacian provides a local maximum. Nearly every position in an image will exhibit a small number of such characteristic scales. Computing a Gaussian jet at a characteristic scale provides a scale invariant feature vector for tracking, matching, indexing and recognition. However, the computation...

In this paper, we consider three problems, namely, the consensus (synchronization) problem, the model-reference consensus problem, and the regulation of consensus problem, for a network of identical linear time-invariant (LTI) multiinput and multi-output (MIMO) agents. For each problem, we propose a distributed LTI protocol to solve such a problem for a broad class of time-invariant network top...

Let G be a graph with n vertices and m edges. Let λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G, and let μ1, μ2, . . . , μn be the eigenvalues of the Laplacian matrix of G. An earlier much studied quantity E(G) = ∑ni=1 |λi | is the energy of the graph G. We now define and investigate the Laplacian energy as LE(G) = ∑ni=1 |μi − 2m/n|. There is a great deal of analogy between...