The design of automatic layout algorithms for single graphs is a well established field, and some recent studies show how these algorithms affect human understanding. By contrast, layout algorithms for graphs that change over time are relatively immature, and few studies exist to evaluate their effectiveness empirically. This paper presents two new dynamic graph layout algorithms and empirical ...

This paper proposes an automated quadrilateral meshing technique based on the conversion of triangular meshes. Given a triangular mesh and a vector eld representing the desired directionality of quadrilateral elements, our new approach generates a well-shaped and well-aligned quadrilateral mesh. In the approach, the values of three scalar functions are rst calculated for each pair of adjacent t...

The spatial interpolation of property fields in 3D, such as the temperature, salinity, and organic content of ocean water, is an active area of research in the applied geosciences. Conventional interpolation methods have not adequately addressed anisotropy in these data. Thus, in our research we considered two interpolation methods based on a triangular prism volume element, as a triangular pri...

Automatic layout analysis has proven to be extremely important in the process of digitization of large amounts of documents. In this paper we present a mixed approach to layout analysis, introducing a SVM-aided layout segmentation process and a classification process based on local and geometrical features. The final output of the automatic analysis algorithm is a complete and structured annota...

This note employs recurrence techniques to obtain entry-wise optimal inequalities for inverses of triangular matrices whose entries satisfy some monotonicity constraints. The derived bounds are easily computable.

In this paper, the triangular structures of a Hopf algebra A are discussed as a tensor Morita invariant. It is shown by many examples that triangular structures are useful for detecting whether module categories are monoidally equivalent or not. By counting and comparing the numbers of triangular structures, we give simple proofs of some results obtained in [25] without polynomial invariants.

In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, ba...

Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in finite dimensional and infinite dimensional Banach spaces. In addition, we investigate whether approximate spectral mapping conditions (being “close” in some sense) is similarly a su...

In this paper we prove a general theorem on |A; δ|k -summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method. c © 2007 Elsevier Ltd. All rights reserved.

We propose a hyperbolic counterpart of the Schur decomposition, with the emphasis on the preservation of structures related to some given hyperbolic scalar product. We give results regarding the existence of such a decomposition and research the properties of its block triangular factor for various structured matrices.