Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Quotients of Koszul Algebras and 2-D-Determined Algebras

Vatne [13] and Green and Marcos [9] have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees.

Semantic priming of familiar songs

We explored the functional organization of semantic memory for music by comparing priming across familiar songs both within modalities (Experiment 1, tune to tune; Experiment 3, category label to lyrics) and across modalities (Experiment 2, category label to tune; Experiment 4, tune to lyrics). Participants judged whether or not the target tune or lyrics were real (akin to lexical decision tasks). We found significant priming, analogous to linguistic associative-priming effects, in reaction times for related primes as compared to unrelated primes, but primarily for within-modality comparisons. Reaction times to tunes (e.g., "Silent Night") were faster following related tunes ("Deck the Hall") than following unrelated tunes ("God Bless America"). However, a category label (e.g., Christmas) did not prime tunes from within that category. Lyrics were primed by a related category label, but not by a related tune. These results support the conceptual organization of music in semantic memory, but with potentially weaker associations across modalities.

Contextual Information and Memory for Unfamiliar Tunes in Older and Younger Adults

We examined age differences in the effectiveness of multiple repetitions and providing associative facts on tune memory. For both tune and fact recognition, three presentations were beneficial. Age was irrelevant in fact recognition, but older adults were less successful than younger in tune recognition. The associative fact did not affect young adults' performance. Among older people, the neutral association harmed performance; the emotional fact mitigated performance back to baseline. Young adults seemed to rely solely on procedural memory, or repetition, to learn tunes. Older adults benefitted by using emotional associative information to counteract memory burdens imposed by neutral associative information.

Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work. (C) 2013 Elsevier B.V. All rights reserved.

Semantic Categorization of Unfamiliar Tunes in Older and Younger Adults

The process of learning the categories of new tunes in older and younger adults was examined for this study. Tunes were presented either one or three times along with a category name to see if multiple repetitions aid in category memory. Additionally, toexamine if an association may help some listeners, especially older ones, to better remember category information, some tunes were presented with a short associative fact; this fact was either neutral or emotional. Participants were tested on song recognition,fact recognition, and category memory. For all tasks, there was a benefit of three presentations. There were no age differences in fact recognition. For both song recognition and categorization, the memory burden of a neutral association was lessened when the association was emotional.