in this work we consider conjugacy of elements and parabolic subgroups‎ ‎in details‎, ‎in a new class of artin groups‎, ‎introduced in an earlier work‎, ‎which may contain arbitrary parabolic subgroups‎. ‎in particular‎, ‎we find‎ ‎algorithmically minimal representatives of elements in a conjugacy class‎ ‎and also an algorithm to pass from one minimal representative to the others‎.

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

We present techniques which may be used to perform computations of very high accuracy using only straightforward oating point arithmetic operations of limited precision, and we prove the validity of these techniques under very general hypotheses satissed by most implementations of oating point arithmetic. To illustrate the application of these techniques, we present an algorithm which computes ...

At NTCIR-4, new retrieval effectiveness metrics called Q-measure and R-measure were proposed for evaluation based on multigrade relevance. This paper shows that Q-measure inherits both the reliability of noninterpolated Average Precision and the multigrade relevance capability of Average Weighted Precision through a theoretical analysis, and then verify the above claim through experiments by ac...

Smart cards have opened up possibilities for many exciting applications. However, one problem with conventional smart cards is that they only have very limited computational power. As a result, it takes too long for a smart card to perform a single RSA signature operation in real time applications. Server-aided RSA signature computation protocols offer feasible solutions for this problem. The b...

An approach to extract watersheds and watercourses, as well as their corresponding valleys and hills, from images with subpixel precision is proposed. The critical points of the terrain are essential as the starting points for the construction of these separatrices. They are extracted efficiently with subpixel precision using an approach based on derivatives of Gaussian filters. The separatrice...