A case study of middle school students\u27 development and application of three-dimensional geometry language in hands-on and computer learning environments

http://www.worldcat.org/oclc/3401834

On a counterexample to a conjecture by Blackadar

Blackadar conjectured that if we have a split short-exact sequence 0 -> I -> A -> A/I -> 0 where I is semiprojective and A/I is isomorphic to the complex numbers, then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I is split. We will show how to modify their examples to find a non-semiprojective C*-algebra B with a semiprojective ideal J such that B/J is the complex numbers and the quotient map does not split.Comment: 6 page

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less

The ordered K-theory of a full extension

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if and only if the extension is stenotic and K-lexicographic. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9 is not correct as stated. See arXiv:1505.05951 for more details. Since Theorem 4.9 is an application to the main results of the paper, the main results of this paper are not affected by the error. Version III comments: Some typos and errors corrected. Some references adde

Amplified graph C*-algebras

We provide a complete invariant for graph C*-algebras which are amplified in the sense that whenever there is an edge between two vertices, there are infinitely many. The invariant used is the standard primitive ideal space adorned with a map into {−1, 0, 1, 2,...}, and we prove that the classification result is strong in the sense that isomorphisms at the level of the invariant always lift. We extend the classification result to cover more graphs, and give a range result for the invariant (in the vein of Effros–Handelman–Shen) which is further used to prove that extensions of graph C*-algebras associated to amplified graphs are again graph C*-algebras of amplified graphs

Adolescent Relationship Quality: Is There an Intergenerational Link?

Objective:This study examines intergenerational continuities in relationship instability, general relationship quality, and intimate partner violence (IPV) between mothers and adolescents. Background:A growing body of literature has observed similarities in relationship quality between parents and their adult offspring. Less attention has focused on whether intergenerational continuities are present in adolescent relationships. Method:Using age 3, 5, 9, and 15 data from the Fragile Families and Child Wellbeing birth cohort study (N=3,162), the authors examined associations between maternal reports of relationship instability, general quality, and IPV in early and middle childhood and similar adolescent reports at age 15. Variations based on timing and persistence of exposures were considered. Results:In general, exposures to low-quality maternal relationships were associated with higher risk of forming adolescent partnerships and lower relationship quality. Intergenerational links in quality were predominantly construct-specific, consistent with observational learning processes. Adolescents exposed to maternal relationships of poor general quality in middle childhood were less likely to report high-quality relationships themselves, and those exposed to any maternal physical IPV victimization during childhood were more likely to perpetrate IPV in their own relationships. Exposure to maternal relationship instability in both early and middle childhood was associated with more adolescent romantic partners. Conclusion:The study illuminates additional pathways through which healthy and unhealthy relationships are reproduced across generations