The quantitative determination of columbium based on reduction by amalgamated zin c and reox idation with potassium permanganate has, in general, produced results that lack both accuracy and precision. A study of t he various factors involved indicates that essential conditions requ ire adequate duration of reduction in t he presence of an excess of zinc and a proper concentration of both acid ...

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Let G be a finite group and U ( Z ) ${\mathcal {U}}({\mathbb {Z}}G)$ the unit of integral ring ${\mathbb {Z}}G$ . We prove theorem, namely, characterization when $\mathcal {U}(\mathbb {Z}G)$ satisfies Kazhdan's property T $(\operatorname{T})$ , both in terms simple components semisimple algebra Q $\mathbb {Q}G$ Furthermore, it is shown that for {Z} G)$ this equivalent to weaker FAb $\operatorna...

We introduce the notion of amalgamation geometry manifolds. We show that the limit set of any surface group of amalgamated geometry is locally connected, thus giving a partial answer to a question (conjecture) raised by Cannon and Thurston, special cases of which have been obtained by Cannon and Thurston, Minsky, Klarreich and the author. The notion of amalgamated geometry includes, in a sense,...

We examine the question of when the ∗–homomorphism λ : A ∗D B → Ã ∗ D̃ B̃ of full amalgamated free product C∗–algebras, arising from compatible inclusions of C∗–algebras A ⊆ Ã, B ⊆ B̃ and D ⊆ D̃, is an embedding. Results giving sufficient conditions for λ to be injective, as well of classes of examples where λ fails to be injective, are obtained. As an application, we give necessary and sufficient ...