The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving exa...

In this article, we associate a Hermitian matrix to multidigraph G. We call it the complex Laplacian of G and denote by L​C(G). It is shown that generalization graph. But, unlike graph, may not always be singular. obtain necessary sufficient condition for For G, if L​C(G) singular, say L​C-singular. generalize some properties Fiedler vectors undirected graphs eigenvectors corresponding second s...

The reduction of a large-scale symmetric linear discrete ill-posed problem with multiple right-hand sides to smaller block tridiagonal matrix can easily be carried out by the application small number steps Lanczos method. We show that subdiagonal blocks reduced converge zero fairly rapidly increasing number. This quick convergence indicates there is little advantage in expressing solutions prob...

As whole genome sequences continue to expand in number and complexity, effective methods for comparing and categorizing both genes and species represented within extremely large datasets are required. Methods introduced to date have generally utilized incomplete and likely insufficient subsets of the available data. We have developed an accurate and efficient method for producing robust gene an...

We extend the notion of singular vectors to context Diophantine approximation real numbers with elements a totally number field K. For $$m\ge 1$$ , we establish version Dani’s correspondence in fields and prove that under class ‘friendly measures’ $$K_S^m$$ set has measure zero. Here S is Archimedean valuations K $$K_S$$ product completions $$\sigma (K)$$ \in S$$ . On other hand, show existence...