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In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ*-algebras for the following Cauchy-Jensen additive mapping: The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300. This is applied to investigate isometric isomorphisms between proper CQ*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we study exhaustions, referred to as ρ–restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as ρ–restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δ ρ , canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of ρ–restricted Patterson measure, and show that these measures are non–atomic, δ ρ –harmonic, δ ρ –subconformal on special sets and δ ρ –conformal on very special sets. Furthermore, we obtain the results that each ρ–restriction of our Kleinian group is of δ ρ –divergence type and that the Hausdorff dimension of the ρ–restricted limit set is equal to δ ρ . [ABSTRACT FROM AUTHOR]

Let $${\fancyscript G}$$ be a generalized Kac–Moody algebra with an integral Borcherds–Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac–Moody algebra $$ wU^{d}_{q} {\left( {\fancyscript G} \right)} $$ , which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra $$ wU^{d}_{q} {\left( {\fancyscript G} \right)} $$ and weak A-forms of $$ wU^{d}_{q} {\left( {\fancyscript G} \right)} $$ . [ABSTRACT FROM AUTHOR]

A Cayley graph Γ = Cay( G, S) of a group G with respect to S is called a circulant digraph of order p k if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc–transitive circulant (di)graphs of order p2 and the classification of all such graphs. It is proved that any connected arc–transitive circulant digraph of order p2 is, up to a graph isomorphism, either $$ K_{{p^{2} }} $$, G( p2, r), or G( p, r)[ pK1], where r | p − 1. [ABSTRACT FROM AUTHOR]

In this paper the following theorem is proved: Every group L3( q) for q = 3(2 m–1)( m ≥ 2) is characterized by its set of element orders. [ABSTRACT FROM AUTHOR]

In this paper, we present some modules over the rank–three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined. [ABSTRACT FROM AUTHOR]

We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified. [ABSTRACT FROM AUTHOR]

For positive integers N, N, ..., N, let L = ℤ + A and Λ = Nℤ × ... × Nℤ + gT be two rational periodic sets, where A ⊂ (1/ N)ℤ × ... × (1/ N)ℤ and gT ⊂ ℤ are finite sets with ( A−A)∩ℤ = {0} and (gT−gT)∩( Nℤ×...× Nℤ) = {0}. In this note, we shall determine conditions under which the tiling set L has universal spectrum Л. We first obtain a criterion of universal spectra. This criterion combined with the properties of compatible pair yields many necessary and sufficient conditions for Л to be a universal spectrum for L. We then show that, under some mild additional conditions, the conjecture of Lagarias and Szabó is true. The results here extend the corresponding results of Lagarias, Szabó and Wang. [ABSTRACT FROM AUTHOR]

Let ( X, $${\mathfrak{S}}$$ ( X), $${\mathfrak{m}})$$ be a probability space with σ-algebra , $${\mathfrak{S}}$$ ( X) and probability measure $${\mathfrak{m}}.$$ The set V in $${\mathfrak{S}}$$ is called P-admissible, provided that for any positive integer n and positive-measure set V n ∈ $${\mathfrak{S}}$$ contained in V , there exists a Z n ∈ $${\mathfrak{S}}$$ such that Z n ⊂ V n and 0 < $${\mathfrak{m}}$$ ( Z n ) < 1/ n. Let T be an ergodic automorphism of ( X, $${\mathfrak{S}})$$ preserving $${\mathfrak{m}},$$ and A belong to the space of linear measurable symplectic cocycles $${\fancyscript G}$$ IC ( X, SL(2,ℝ)) := { A : X → SL(2,ℝ)| log ∥ A ±1( x)∥ ∈ $${\Bbb L}$$ 1( X, $${\mathfrak{m}}).$$ We prove that for any P–admissible set V and ε > 0, there exists a B ∈ $${\fancyscript G}$$ IC ( X, SL(2,ℝ)) such that max{∥ A( x) − B( x)∥, ∥ A −1( x) − B −1( x)∥} < ε for all x ∈ V, A( x) = B( x) for all x ∈ X \ V, and B has the simple Lyapunov spectrum over the system ( X, $${\mathfrak{m}},$$ T). [ABSTRACT FROM AUTHOR]