A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio

Central extension of the reflection equations and an analog of Miki's formula

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.

Assessing Students’ Object-Oriented Programming Skills with Java: The “Department-Employee” Project

Java is arguably today’s most popular and widely used object-oriented programming language. Learning Java is a daunting task for students, and teaching it is a challenging undertaking for instructors. To assess students’ object-oriented programming skills with Java, we developed the “Department-Employee” project. In this article, we review the history of object-oriented programming and provide an overview of object-oriented programming with Java. We also provide the project specification as well as the course background, grading rubric, and score reports. Survey data are presented on students’ backgrounds, as well as students’ perceptions regarding the project. Results from the instructor score reports and student perceptions show that the “Department-Employee” project was effective in assessing students’ object-oriented programming skills with Java

Teaching Introductory Programming from A to Z: Twenty-Six Tips from the Trenches

A solid foundation in computer programming is critical for students to succeed in advanced computing courses, but teaching such an introductory course is challenging. Therefore, it is important to develop better approaches in order to improve teaching effectiveness and enhance student learning. In this paper, we present 26 tips for teaching introductory programming drawn from the experiences of four well-qualified college professors. It is our hope that our peers can pick up some tips from this paper, apply them in their own classroom, improve their teaching effectiveness, and ultimately enhance student learning

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTA