Universal deformation rings of modules for algebras of dihedral type of polynomial growth

Let k be an algebraically closed field, and let \Lambda\ be an algebra of dihedral type of polynomial growth as classified by Erdmann and Skowro\'{n}ski. We describe all finitely generated \Lambda-modules V whose stable endomorphism rings are isomorphic to k and determine their universal deformation rings R(\Lambda,V). We prove that only three isomorphism types occur for R(\Lambda,V): k, k[[t]]/(t^2) and k[[t]].Comment: 11 pages, 2 figure

Synthesis of an Amide-Based Extended Heterocyclic System Capable of Hydrogen Bonding to Both the Adenine and Uracil in dsRNA for RNA Recognition Using PNA

The majority of information known about RNA is centered around coding RNA for its role in synthesizing proteins from DNA. However, noncoding RNA is also biologically relevant, showing importance in gene expression and catalyzing reactions. Peptide Nucleic Acids, or PNAs, are a promising tool that can be used to study noncoding RNA. PNAs can bind to double-stranded RNA forming a triple helix and are highly selective for specific sequences of dsRNA. A current limitation of PNA as a ligand is that traditional nucleobases only bind with high affinity to single purine residues on the RNA, as triplex formation relies on the two hydrogen bonding sites offered by purines as opposed to only one offered by pyrimidines. More recent developments in our group and others have shown that synthetic nucleobases may be used to increase both affinity and selectivity. We have synthesized a uracil nucleobase modified to bind both the adenine and the uracil of the A-U base pair by adding a benzamide moiety to isoorotic acid. Computations suggest that this will increase the affinity of binding and make PNA relevant for use in dsRNA sequences containing both purine and pyrimidine bases

Word Length Perturbations in Certain Symmetric Presentations of Dihedral Groups

Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities called $\lambda_{1}$ and $\lambda_{2}$ have been defined that allow for a precise measure of how stable a group is under certain types of small perturbations in the generating expressions for the elements of the group. These quantities provide a means to measure differences among all possible paths in a Cayley graph for a group, establish a group theoretic analog for the notion of stability in nonlinear dynamical systems, and play an important role in the application of groups to computational genomics. In this paper, we further expose the fundamental properties of $\lambda_{1}$ and $\lambda_{2}$ by establishing their bounds when the underlying group is a dihedral group. An essential step in our approach is to completely characterize so-called symmetric presentations of the dihedral groups, providing insight into the manner in which $\lambda_{1}$ and $\lambda_{2}$ interact with finite group presentations. This is of interest independent of the study of the quantities $\lambda_{1},\; \lambda_{2}$. Finally, we discuss several conjectures and open questions for future consideration

Possible Psychosocial Benefits of Having a Sibling with a Disability

Possible psychosocial benefits resulting from exposure to siblings with disabilities are investigated in the current study. Previous literature has generally overlooked the possibility of psychosocial benefits by exclusively focusing on the negative effects of having a sibling with disabilities. Contact theory suggests that the increased exposure to individuals with disabilities should increase positive attitude toward those who are struggling with disadvantages. This investigation hypothesized that this tendency would be manifested as elevated empathy and compassion in individuals who have siblings with disabilities, and that these traits would be influenced by certain demographic variables. A survey was distributed, and the responses of 182 college-student participants were evaluated using self-report demographic questions and measures of empathy (the Interpersonal Reactivity Index) and compassion (the Care for Others Scale). In addition, an exploratory qualitative inquiry prompted participants to identify other possible benefits they thought they gained from having a sibling with a disability. Scores on the empathy and compassion scales were quantitatively analyzed for demographic variations, and the qualitative responses were analyzed for content themes. Implications of the results are discussed