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Showing 1 to 6 of 6 for “"Border basis"”.
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Border Basis Schemes
The basic idea of border basis theory is to describe a zero-dimensional ring P/I by an order ideal of terms whose residue classes form a K-vector space basis of P/I. The O-border basis scheme is a scheme that parametrizes all zero-dimensional ideals that have an O-border basis. In general, the …
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Generalizations and Applications of Border Bases
This doctoral thesis is devoted to generalize border bases to the module setting and to apply them in various ways. First, we generalize the theory of border bases to finitely generated modules over a polynomial ring. We characterize these generalized border bases and show that we can compute them. …
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The role of the South African regulatory authorities in combating money laundering and terrorist financing perpetrated through alternative remittance systems
… can be sent both on a domestic and on a cross-border basis. The methods used to remit money or value can be used for both legitimate and illegal purposes. The question posed by this research is whether the Money Service Businesses that operate in South Africa and provide crossborder remittance …
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Computation of Approximate Border Bases and Applications
… associated with the computation of approximate border bases, a generalisation of border bases, in the context of the oil and gas industry. The concept of approximate border bases was introduced by D. Heldt, M. Kreuzer, S. Pokutta and H. Poulisse in "Approximate computation of zero-dimensional …
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Algebraic and Logic Solving Methods for Cryptanalysis
… SAT solving and techniques that are related to border bases and Gröbner bases. In particular, we describe in detail the Border Basis Algorithm and discuss its specialized version for Boolean polynomials called the Boolean Border Basis Algorithm. In the second part of the thesis, we deal with …
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New Techniques for Polynomial System Solving
… elements. Instead of using traditional Gröbner basis techniques we focus on highly developed methods from several other areas like linear algebra, discrete optimization, numerical analysis and number theory. We study some techniques from combinatorial optimization to transform a polynomial …