In this paper, we study two questions related to the problem of testing whether a function is close to a homomorphism. For two finite groups (not necessarily Abelian), an arbitrary map , and a parameter , say that is -close to a homomorphism if there is some homomorphism such that and differ on at most elements of , and say that is -far otherwise. For a given and , a homomorphism tester should ...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

We use the results on the minimal basis of the centre of an Iwahori-Hecke algebra from our earlier work, as well as some additional results on the minimal basis, to describe the image and kernel of the Brauer homomorphism defined by L. Jones for Iwahori-Hecke algebras of type A.

There exists a PT0L language L0 such that the following holds. A language L is an ET0L language if and only if there exists a mapping T induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that L = T (L0). There exists an infinite collection of EPDT0L languages Dmn ⊆ Σ ⋆ mn (n ≥ m ≥ 1) such that the family EDT0L is characterized in the following way....

A connected reductive algebraic group G is said to be an l-adic algebraic monodromy group for ΓQ if there is a continuous homomorphism Gal(Q/Q)→ G(Ql) with Zariski-dense image. In this paper, we give a classification of connected l-adic algebraic monodromy groups for Gal(Q/Q), in particular producing the first such examples for SLn,Sp2n,Spinn and E sc 6 . To do this, we start with a mod-l repre...

Let L=K1 U .. , U Kp.r;;;S3 be a tame link of Jl~ 1 components with group G=7r1(S3_L). Also, let H=G/G' be the abelianization of G; H is then the (multiplicative) free abelian group generated by the meridians t1, ••• , tp. of L, and its integral group ring ZH consists of polynomials (with integer coefficients) in t 1 ,. .. , tp.' til, ... , t;l. The homomorphism 6: ZH~Z (which has 6(t;)=1 for e...