Article

# Value functions and associated graded rings for semisimple algebras

Transactions of the American Mathematical Society (Impact Factor: 1.02). 02/2009; 362(02):687-726. DOI: 10.1090/S0002-9947-09-04681-9

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**ABSTRACT:**An approach is presented for dynamic analysis of tensegrity structures in the small displacement regime. Such analyses are characterized by cables switching between taut and slack states. The approach is based on casting the computation in each time increment as a complementarity problem. Numerical examples are presented to illustrate the approach. Despite the nonsmooth nature of cables switching between taut and slack states, the computed solutions exhibit remarkable long-term energy balance. Furthermore, by exploiting some features of the tensegrity model, significant computational efficiency can be gained in the solution of the complementarity problem in each time increment. Due to the use of linearized kinematics, the method is not applicable as is to tensegrity structures with internal mechanisms or where the geometric stiffness is significant compared to the material stiffness. The method however plays a role in a more general nonlinear kinematics formulation.Computers & Structures - COMPUT STRUCT. 01/2011; 89(23):2471-2483. - [Show abstract] [Hide abstract]

**ABSTRACT:**For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that Ki(A, ℤ/m) = Ki(R, ℤ/m) for any m relatively prime to the rank and i ≥ 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semilocal rings, and K-theory of graded central simple algebras indexed by a totally ordered abelian group.Communications in Algebra 03/2010; 38(3):919-926. · 0.36 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Let E be a graded central division algebra (GCDA) over a grade field R. Let S be an unramified graded field extension of R. We describe the grading on the underlying GCDA E' of which is analogous to the valuation on a tame division algebra over Henselian valued field.Communications of the Korean Mathematical Society 01/2014; 29(1).

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