A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of no...

Schoof's algorithm is used to nd a secure elliptic curve for cryptosystems, as it can compute the number of rational points on a randomly selected elliptic curve de ned over a nite eld. By realizing e cient combination of several improvements, such as Atkin-Elkies's method, the isogeny cycles method, and trial search by match-and-sort techniques, we can count the number of rational points on an...

The formalisation of defeasible reasoning in automated systems is becoming increasingly important. Description Logics (DLs) are nowadays the main logical formalism in the field of formal ontologies. Our focus in this paper is to devise a practical implementation for prior work that formalises a version of Rational Closure (an important type of defeasible reasoning) for DLs. We show that the con...

What is the relation between morality and partiality? Can the kind of partiality that matters to us be accommodated within moral thought, or are morality and partiality rival sources of normative considerations? These are questions that moral philosophy has struggled with in recent decades.1 They may not have much intuitive resonance, because the term ‘partiality’ is not used much in everyday d...