X : f (x) = g(x)} is a compact subset of X\∂X. In case of codimension 0, the Nielsen number is the lower estimate of the number of points in this set. We suggest a generalization of the classical Nielsen theory for the coincidence and as well as the preimage problems in order to provide a framework for some recent Wecken type results for codimension 1. The Nielsen equivalence on the set of coin...

the purpose of this study was to evaluate the web pages of islamic world science citation center (isc), the islamic countries sci using nielsen`s heuristic principles and was performed during september 2012. among nielsen`s 10 usability heuristic principles, five were covered. five professional evaluators were asked to evaluate the database using nielsen`s five criteria. the total average of se...

Let G be a group given by the presentation 〈a1, . . . , ak , b1, . . . bk | ai = ui(b̄), bi = vi(ā) for 1 ≤ i ≤ k〉, where k ≥ 2 and where the ui ∈ F (b1, . . . , bk) and wi ∈ F (a1, . . . , ak) are random words. Generically such a group is a small cancellation group and it is clear that (a1, . . . , ak) and (b1, . . . , bk) are generating n-tuples for G. We prove for generic choices of u1, . . ....

We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW -complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and L2-torsion of mapping tori. We examine its behaviour under fibrations.

We review the quantum instability of the Savvidy-Nielsen-Olesen (SNO) vacuum of the one-loop effective action of SU(2) QCD, and point out a critical defect in the calculation of the functional determinant of the gluon loop in the SNO effective action. We prove that the gauge invariance, in particular the color reflection invariance, exclude the unstable tachyonic modes from the gluon loop integ...

Grushko’s theorem [Mat. Sb. 8 (1940) 169–182] says that any generating tuple (g1, . . . , gm) of a free product H ∗K is Nielsen-equivalent to a tuple (h1, . . . , hl, kl+1, . . . , km) with hi ∈ H and ki ∈ K for all i. The hi and ki are clearly not unique. In this paper we address the extent of this non-uniqueness.

We study the topological space of left-orderings of the braid group, and its subspace of Nielsen-Thurston orderings. Our main result is that no Nielsen-Thurston ordering is isolated in the space of braid orderings. In the course of the proof, we classify the convex subgroups and calculate the Conradian soul for any Nielsen-Thurston ordering of Bn. We also prove that for a large class of Nielsen...