LetR be a finitely generated commutative algebra over an algebraically closed field k and let A = R[t;σ, δ] be the Ore extension with respect to an automorphism σ and a σ-derivation δ. We view A as the coordinate ring of an affine non-commutative space X. The inclusion R → A gives an affine map ξ : X → SpecR, and X is a non-commutative analogue of A 1 ×SpecR. We define the fiber Xp of ξ over a ...

The subresultants play a fundamental role in elimination theory and computer algebra. Recently they have been extended to Ore polynomials. They are de ̄ned by an expression in the coe±cients of Ore polynomials. In this paper, we provide another expression for them. This expression is written in terms of the \solutions" of Ore polynomials (in \generic" case). It is a generalization of our previou...

Silica sand is widely used in the transformation industry. For instance, it is used in the making of glass, silicates, paints, glass-ceramics and ceramics. Traditionally, glass and ceramic materials have been manufactured using high-purity silica and minerals taken from ore on the surface of the earth. However, during recent decades, the manufacture of household and industrial products has incr...

A traceability system simplifies investigation of causes of product failures and is therefore vital for many industries. Traceability systems are extensively used in manufacturing industries, but creating traceability in continuous processes implies great challenges. The aim of this paper is to illustrate how traceability can be achieved in the distribution chain for iron ore pellets. Radio fre...

We determined the composition of ~30-m.y.-old solutions extracted from fluid inclusions in one of the world's largest and richest silver ore deposits at Fresnillo, Mexico. Silver concentrations average 14 ppm and have a maximum of 27 ppm. The highest silver, lead and zinc concentrations correlate with salinity, consistent with transport by chloro-complexes and confirming the importance of brine...

Abstra t. Here, we have designed and implemented algorithms for string mat hing with gaps for musi al melodi re ognition on polyphoni musi using bit-wise operations. Musi analysts are often on erned with nding o urren es of patterns (motifs), or repetitions of the same pattern, possibly with variations, in a s ore. An important example of exibility required in s ore sear hing arises from the na...

The dominant working structure of an underground mine is a set of interconnected tunnels which provides access to ore zones and haulage of ore from the designated ore zones to the mill. This set of interconnected tunnels forms a network. We describe a mathematical network model and the modelling features of our two software tools for designing underground mine layouts that minimise associated c...

Abstra t. This paper proposes an e ient algorithm to solve the problem of string mat hing with mismat hes. For a text of length n and a pattern of length m over an alphabet , the problem is known to be solved in O(j jn logm) time by omputing a s ore by the fast Fourier transformation (FFT). Atallah et al. introdu ed a randomized algorithm in whi h the time omplexity an be de reased by the trade...

Abstra t. This paper proposes an e ient algorithm to solve the problem of string mat hing with mismat hes. For a text of length n and a pattern of length m over an alphabet , the problem is known to be solved in O(j jn logm) time by omputing a s ore by the fast Fourier transformation (FFT). Atallah et al. introdu ed a randomized algorithm in whi h the time omplexity an be de reased by the trade...

Comminution tests are an important element in the proper design of ore beneficiation plants. In the past, test work has been conducted for particular representative reference samples. Within geometallurgy the entire ore body is explored in order to further identify the variation within the resource and to establish spatial geometallurgical domains that show the differential response to mineral ...