On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair coprime integers $(p,q)$ it was found numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ satisfying inequalities $\pi/3< \alpha_1 < \alpha_2 2\pi/3$ such that with faces angle $\alpha \in \left( \pi/3, \right)$ exists unique, up to rigid motion tetrahedron, geodesic type $(p,q...

in this article, we study the artin-rees property in  c(x), in the  rings of fractions of  c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if  z(f)  is an open p-space. a necessary and sufficient condition for the local rings of  c(x)   to be artin-rees rings is that each prime ideal in  c(x)  becomes minimal and it turns out that every local ring ...

In a study of surface branched coverings, one can ask naturally: In how many different ways can a given surface be a branched covering of another given surface? This problem was studied by many authors in Quart. J. Math. Oxford Ser. 2 46 (1995) 485, Math. Scand. 84 (1999) 23, Discrete Math. 156 (1996) 141, Discrete Math. 183 (1998) 193, Discrete Math. (in press), European J. Combin. 22 (2001) 1...

Thanks to the development of a number of eeciency enhancing techniques, state-space exploration based veriication, and in particular model checking, has been quite successful for nite-state systems. This has prompted eeorts to apply a similar approach to systems with innnite state spaces. Doing so amounts to developing algorithms for computing a symbolic representation of the innnite state spac...