C*-algebras of separated graphs

The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in terms of their ideal theory and K-theory, mainly in the case of partitions by finite sets. The groups $K_0(C^*(E,C))$ and $K_1(C^*(E,C))$ are completely described via a map built from an adjacency matrix associated to $(E,C)$. One application determines the K-theory of the C*-algebras $U^{\text{nc}}_{m,n}$, confirming a conjecture of McClanahan. A reduced C*-algebra \Cstred(E,C) is also introduced and studied. A key tool in its construction is the existence of canonical faithful conditional expectations from the C*-algebra of any row-finite graph to the C*-subalgebra generated by its vertices. Differences between \Cstred(E,C) and $C^*(E,C)$, such as simplicity versus non-simplicity, are exhibited in various examples, related to some algebras studied by McClanahan.Comment: 29 pages. Revised version, to appear in J. Functional Analysi

Restrained Shrinkage of Fly Ash Based Geopolymer Concrete and Analysis of Long Term Shrinkage Prediction Models

The research presented in this manuscript describes the procedure to quantify the restrained shrinkage of geopolymer concrete (GPC) using ring specimen. Massive concrete structures are susceptible to shrinkage and thermal cracking. This cracking can increase the concrete permeability and decrease the strength and design life. This test is comprised of evaluating geopolymer concrete of six different mix designs including different activator solution to fly ash ratio and subjected to both restrained and free shrinkage. Test results obtained from this experimental setup was plotted along with the available empirical equation to observe the shrinkage strain of GPC and a model was suggested to predict the shrinkage strain of GPC. It was found from this study that along with activator solution to fly ash ratio the final compressive strength of GPC plays an important role on shrinkage strai

The almost isomorphism relation for simple regular rings

A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K.C . O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective modules over a simple regular ring