The Jordan canonical form parametrises similarity classes in the nilpotent cone Nn, consisting of n× n nilpotent complex matrices, by partitions of n. Achar and Henderson (2008) extended this and other well-known results about Nn to the case of the enhanced nilpotent cone C ×Nn. 1. Jordan canonical form The Jordan canonical form (JCF), introduced in 1870 [10], is one of the most useful tools in...

In this paper, we derive a canonical representation for the first order hyperbolic equation systems with their coefficient matrices satisfying the Clifford algebra Cl(1, 3), and then demonstrate some of its applications. This canonical formalism can naturally give a unified description for the fundamental fields in physics. PACS numbers: 11.10.-z, 11.10.Cd, 12.10.-g

Glossary Canonical realization: A state-space realization that has specific properties that makes it unique. Characteristic polynomial: The scalar denominator of a transfer function. Column-reduced: A polynomial matrix with non-singular column leading coefficient matrix. Coprime: See relatively prime. Denominator polynomial: The polynomial appearing in the denominator of a rational transfer fun...

We derive the complete (curvature) terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the o(α′ ) corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3-brane with trivial normal bundle, considerations ...

We prove that the canonical Thurston obstruction for a sub-hyperbolic semi-rational branched covering exists if the branched covering is not CLH-equivalent to a rational map.

in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

We investigate the structure of a variety new Moishezon twistor spaces, by utilizing pluri-half-anti-canonical map from spaces. Each these spaces is bimeromorphic to double covering scroll planes over rational normal curve, and branch divisor cover cut quartic hypersurface. In particular, has pencil Del Pezzo surfaces degree two. Correspondingly, have with big anti-canonical class. The base loc...