The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Thought-Action Fusion and Neutralization Behavior

This study presents a new inventory to assess thought-action fusion (TAF). 160 college students ages 18 to 22 (M = 19.17, SD = 1.11) completed the new Modified Thought Action Scale (MTAFS). Results indicated high internal consistency in the MTAFS (Cronbach’s α = .95). A principal component analysis suggested a three factor solution of TAF-Moral (TAFM), TAFLikelihood (TAFL), and TAF-Harm avoidance-Positive (TAFHP) all with eigenvalues above 1, and factor loadings above .4. A second study examined the association between TAF, obsessivecompulsive and anxiety tendencies after the activation of TAF-like thought processes in a nonclinical sample (n=76). Subjects were randomly assigned to one of three treatment groups intended to provoke TAFL-self, TAFL-other, and TAF moral thought processes. Stepwise regression analyses revealed: 1) the Obsessive-Compulsive Inventory subscales Neutralizing and Ordering significantly predicted instructed neutralization behavior (INB) in non-clinical participants; 2) TAF-Likelihood contributed significant unique variance in INB. These findings suggest that the provocation of neutralization behavior may be mediated by specific subsets of TAF and obsessive-compulsive tendencies.