Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations

Fluorine gas is produced industrially by electrolysing hydrogen fluoride in a potassium acid fluoride electrolyte. Fluorine is produced at the carbon anode, while hydrogen is produced at the mild-steel cathode. The fluorine produced has a wide range of uses, most notably in the nuclear industry

Abstract: Online learning initia-tives over the past decade have become increasingly comprehen-sive in their selection of courses and sophisticated in their presen-tation, culminating in the recent announcement of a number of consortium and startup activities that promise to make a university education on the internet, free of charge, a real possibility. At this pivotal moment it is appropriate to explore the potential for obtaining comprehensive bioinformatics training with currently existing free video resources. This article pre-sents such a bioinformatics curric-ulum in the form of a virtual course catalog, together with editorial commentary, and an assessment of strengths, weaknesses, and likely future directions for open online learning in this field. Online Learning Comes of Age Online academic ‘‘courseware’ ’ at the university level has now been available to the public for a decade, the earliest concerted effort having originated in 2002 with the Massachusetts Institute of Technology (MIT) and their OpenCour-seWare initiative

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collection of DNA sequences thought to contain TF binding sites. The computational task is to identify the TF binding site amongst these DNA sequences. Early approaches used simple models such as exact DNA motif sequences. These have largely been supplanted by position weight matrices (PWMs, alternatively

legacy queries and updates under schema and integrity constraints evolution. The PRISM/PRISM++ approach consists in providing the users with a set of SQL-based Schema Modification Opera-tors (SMOs), which describe how the tables in the old schema are modified into those in the new schema. In order to sup

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This is a preliminary version of a Chapter on Algebraic Algorithms in the up-