The synthesis and conformational analysis of amino acid-tetrahydroanthranilic acid hybrids

The optimization of a palladium-catalyzed amidation reaction providing a new class of amino acid-tetrahydroanthranilic acid derivatives has been achieved. The scope of the reaction and preliminary conformational analysis of the resulting series of molecules is discussed.     

Infinitesimal CR automorphisms of rigid hypersurfaces in C2

In this paper, we describe the space of infinitesimal CR automorphisms of a rigid, real analytic, real hypersurface in C². We use these results to obtain a geometric characterization of the homogeneous hypersurfaces. Here, a hypersurface is called homogeneous if it is equivalent to one given by an equation of the formIm(w) =p wherep is a homogeneous polynomial inz and \(\bar z\) . This gives an answer in dimension 2 to a problem posed by Linda Rothschild. We give another answer, in terms of a normal form for the defining function, in our paper “A normal form for rigid hypersurfaces in C².”     

Conflicting Beliefs: A Story of a Chemistry Teacher's Struggle with Change

One teacher's struggle to develop and implement a curriculum focused on student understanding of chemistry is explored in this case study of a high school chemistry teacher. Conflicting beliefs about her roles as a teacher in the classroom and her professional responsibilities are addressed. Three primary conflicts that emerged from data collected over a two year period include, (a) conflicts between state curriculum mandates and individual student understanding; (b) conflicts between theoretical and applicable chemistry content knowledge, and (c) conflicts between the students' goals and the teachers' goals for the course. The impact of the research process on the teacher's change process included reconceptualization of constraints and development of confidence in her professional judgment. The case study provides insights into contextual problems teachers face as they attempt to change practices.     

The Abel Lemma and the -Gosper Algorithm

Chu has recently shown that the Abel lemma on summation by parts reveals the telescoping nature of Bailey's bilateral summation formula. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the -Gosper algorithm. It is demonstrated that Abel pairs can be derived from Gosper pairs. This approach applies to many classical summation formulas.

     

On some continued fraction expansions of the Rogers–Ramanujan type

By guessing the relative quantities and proving the recursive relation, we present some continued fraction expansions of the Rogers–Ramanujan type. Meanwhile, we also give some J-fraction expansions for the q-tangent and q-cotangent functions.     

Embeddings of open manifolds

Let be the simplicial group of homeomorphisms of . The following theorems are proved.

Theorem A. Let be a topological manifold of dim 5 with a finite number of tame ends , . Let be the simplicial group of end preserving homeomorphisms of . Let be a periodic neighborhood of each end in , and let be manifold approximate fibrations. Then there exists a map such that the homotopy fiber of is equivalent to , the simplicial group of homeomorphisms of which have compact support.

Theorem B. Let be a compact topological manifold of dim 5, with connected boundary , and denote the interior of by . Let be the restriction map and let be the homotopy fiber of over . Then is isomorphic to for , where is the concordance space of .

Theorem C. Let be a manifold approximate fibration with dim 5. Then there exist maps and for , such that , where is a compact and connected manifold and is the infinite cyclic cover of .

     

Perfect Simulation for a Stationary Silo with Absorbing Walls

The objective of this work is to generate random samples of the unique stationary distribution associated to the stochastic model for grain storage in a finite bidimensional silo. The support of this measure is an unbounded and continuous state space and therefore a truncation was necessary to apply the CFTP perfect simulation scheme. The performance of the algorithm was measured by comparing the sample moments to the theoretical ones.     

Collaborative Teams in a University Statistics Course: A Case Study of How Differing Value Structures Inhibit Change

In a rapidly changing world, individuals need the intellectual agility, problem‐solving skills, and increased interdependence that are not developed in a traditional classroom. Despite years of reform efforts, little change in practice has been observed. This is a case study of the efforts of a statistics professor who used collaborative learning to prepare his students for the challenges of the 21^st century. The nature of the statistics course, the intentions of the professor, and the interactions and feedback of his students are analyzed in terms of their underlying value structures ( Beck & Cowan, 1996 ). Conflicting expectations and experiences, particularly with assessment, resulted in dissatisfaction and frustrations for the professor and the students.