We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms φ and ψ such that certain remnant words from φ are longer than the images of generators under ψ. Our first result is a remnant inequality condition which implies that two words u and v are not doubly-twisted conjugate. Further we show that if ψ is given and φ, u, and v are chosen at...

The most powerful method for the study of finite geometries with regular or quasiregular automorphism groups G is to translate their definition into an equation over the integral group ring Z[G] and to investigate this equation by applying complex representations of G. For the definitions and the basic facts, see Section 2. If G is abelian, this approach boils down to proving or disproving the ...

We consider group-valued cocycles over a partially hyperbolic diffeomorphism which is accessible volume-preserving and center bunched. We study cocycles with values in the group of invertible continuous linear operators on a Banach space. We describe properties of holonomies for fiber bunched cocycles and establish their Hölder regularity. We also study cohomology of cocycles and its connection...

New hybrid conjugate gradient algorithms are proposed and analyzed. In these hybrid algorithms the famous parameter k β is computed as a convex combination of the Polak-Ribière-Polyak and Dai-Yuan conjugate gradient algorithms. In one hybrid algorithm the parameter in convex combination is computed in such a way that the conjugacy condition is satisfied, independent of the line search. In the o...

A celebrated theorem by Herman and Yoccoz asserts that if the rotation number α of a C∞-diffeomorphism of the circle f satisfies a Diophantine condition, then f is C∞-conjugated to a rotation. In this paper, we establish explicit relationships between the Ck norms of this conjugacy and the Diophantine condition on α. To obtain these estimates, we follow a suitably modified version of Yoccoz’s p...

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series and spherical conjugacy growth series, as well as on regularity of the geodesic conjugacy language and spherical conjugacy language. In particular, we show t...

We show that the Wirtinger presentation of a prime alternating link group satisfies a generalized small cancellation condition. This gives a simplification of Weinbaum’s solution to the word and conjugacy problems for these groups, which extends to finite sums of alternating links.

We construct boundary states representing D-strings in AdS3. These wrap twisted conjugacy classes of SL(2, IR), and the boundary states are therefore based on continuous representations only. We check Cardy’s condition and find a consistent open string spectrum. The open string spectrum on all the D-branes is the same.

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...