Every finitely presented group G has a quotient group with solvable word problem – namely the trivial group. We will construct a finitely presented group G such that every non-trivial quotient of G has unsolvable word problem (of degree 0′ in case the quotient is recursively presented) and such that every countable group is embedded in some quotient of G. A presentation of a group is an ordered...

We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the S equivariant cohomology of the original symplectic manifold and the fixed point data. The key idea is the construction of a small resolution of the symplectic quotient.

The paper presents a genetic algorithm for maximizing the Isoperimetric Quotient of poly hedral clusters This algorithm helped extending the de nition of Isoperimetric Quotient to clusters with nonplanar faces Detailed description of the genetic algorithm is followed by the performance analysis Some other observations of genetic algorithm s behavior are also presented Introduction Evolutionary ...

The thesis is devoted to studying normal complex Q-acyclic algebraic surfaces S ′. Let S0 be the smooth locus of such a surface. The following results have been obtained. If S ′ has non-negative Kodaira dimension then it is logarithmic, i.e. its singularities are of quotient type. We classify possible S ′ with non-quotient singularities. S ′ can be nonrational. The completion of the resolution ...

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

Residue Number System (RNS) has computational advantages for large integer arithmetic. It provides the benefits of parallel, carry-free, and high-speed arithmetic in addition, subtraction, and multiplication. However, overflow detection, sign detection, magnitude detection, and division are time-consuming operations in RNS. The most interesting one of the above operations is division, and many ...