Differential geometry is used to investigate the structure of neural-network-based control systems. The key aspect is relative order-an invariant property of dynamic systems. Finite relative order allows the specification of a minimal architecture for a recurrent network. Any system with finite rela
On group inverses and the sharp order
β Scribed by Sujit Kumar Mitra
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 879 KB
- Volume
- 92
- Category
- Article
- ISSN
- 0024-3795
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In this note we revisit the sharp partial order introduced by Mitra [S.K. Mitra, On group inverses and the sharp order, Linear Algebra Appl. 92 (1987) 17-37]. We recall some already known facts from certain matrix decompositions and derive new statements, relating our discussion to recent results in
## Abstract We consider graphs __G = (V,E)__ with order Ο = |__V__|, size __e__ = |__E__|, and stability number Ξ²~0~. We collect or determine upper and lower bounds on each of these parameters expressed as functions of the two others. We prove that all these bounds are sharp. Β© __1993 by John Wiley
We use a bijection from the set of words onto the set of multisets of primitive circular words, to find a construction of the inverse of a word having the properties required by Foata and Han. Moreover, we show the link of this construction with the parabolic structure of the symmetric group, seen a