Combinatorial Explanations of Known Harmonic Identities

We seek to discover combinatorial explanations of known identities involving harmonic numbers. Harmonic numbers do not readily lend themselves to combinatorial interpretation, since they are sums of fractions, and combinatorial arguments involve counting whole objects. It turns out that we can transform these harmonic identities into new identities involving Stirling numbers, which are much more apt to combinatorial interpretation. We have proved four of these identities, the first two being special cases of the third

STRATEGIC PLANNING AND PERFORMANCE MEASUREMENT FOR PUBLIC UNIVERSITIES IN SULAWESI, INDONESIA; QUANTITATIVE APPROACH

The purpose of the study is to examine the real process of strategic planning and performance measurement within public universities in Sulawesi, Indonesia. The specific objective is to focus on strategic planning, performance measurement and associate the findings with the objectives of Higher Education Long Term Strategy from Indonesian Directorate General Higher Education. Quantitative methodology approach with an empirical survey was conducted based on questionnaires. The findings revealed that the process of strategic planning in public universities was consistent with the Higher Education Long Term Strategy guidelines. However, public universities faced challenges to their achievement of all targets. The relationships between strategic planning and performance measurement were positively related, however, the organisational performance could be improved if programs in strategic planning could be more fully implemented. This influenced the refinement of the balanced scorecard approach into a performance measurement model for public universities. The study culminated in the development of a performance measurement model