Institutional structures for student-inclusivity in quality assurance promotion in higher education: The case of one university in Zimbabwe

Researchers have investigated co-curricular and extracurricular activities associated with student learning and personal development but neglected exploring levels of students' involvement. IHLs oftentimes have no structures responsible for quality assurance (QA). Research should focus on specific structures, activities and the frequency of student involvement. Although Zimbabwe Council for Higher Education superintends over QA processes, it remains unclear which/how institutional structures foster student inclusivity in QA processes. Pragmatic research, marked by mixed methods was used to examine university QA structures for inclusivity. Science, Technology, Engineering and Mathematics IHLs were targeted and purposive sampling helped select 15 QA office(rs) and SRC in one STEM university. Primary data from questionnaires and key informant interviews were used. Structures governing IHLs are prescribed by Acts of Parliament and the current frequency of involvement depends on meetings scheduled for IHL structures. This constricts effective involvement. Minimal involvement occurs in prescribed structures although more satisfying involvement is in student-initiated social clubs and organisations. IHL legislative instruments should be amended to reflect diversity in higher education; allow university Councils to tailor-make IHL institutional/infrastructural structures to deliver on their mandates than rely on prescribed one size fits all. Such change will foster more satisfying involvement for student socio-academic success

The finiteness dimension of local cohomology modules and its dual notion

Let \fa be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We explore the behavior of the two notions f_{\fa}(M), the finiteness dimension of M with respect to \fa, and, its dual notion q_{\fa}(M), the Artinianess dimension of M with respect to \fa. When (R,\fm) is local and r:=f_{\fa}(M) is less than f_{\fa}^{\fm}(M), the \fm-finiteness dimension of M relative to \fa, we prove that H^r_{\fa}(M) is not Artinian, and so the filter depth of \fa on M doesn't exceeds f_{\fa}(M). Also, we show that if M has finite dimension and H^i_{\fa}(M) is Artinian for all i>t, where t is a given positive integer, then H^t_{\fa}(M)/\fa H^t_{\fa}(M) is Artinian. It immediately implies that if q:=q_{\fa}(M)>0, then H^q_{\fa}(M) is not finitely generated, and so f_{\fa}(M)\leq q_{\fa}(M).Comment: 14 pages, to appear in Journal of Pure and Applied Algebr

K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products

We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function for p-cores due to Klyachko [17] and Garvan, Kim and Stanton [10]. A number of other infinite products are shown to have nonnegative coefficients. In the process a new generalization of the quintuple product identity is derived.Comment: 15 pages; greatly expanded version of the earlier 8 page paper math.NT/060760

Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems

In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous approaches and some explanations added. To appear in J. Phys.