Not all simplicial polytopes are weakly vertex-decomposable

In 1980 Provan and Billera defined the notion of weak $k$-decomposability for pure simplicial complexes. They showed the diameter of a weakly $k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial function of the number of $k$-faces in $\Delta$ and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non-weakly 0-decomposable simplicial polytopes

Localizable invariants of combinatorial manifolds and Euler characteristic

It is shown that if a real value PL-invariant of closed combinatorial manifolds admits a local formula that depends only on the f-vector of the link of each vertex, then the invariant must be a constant times the Euler characteristic.Comment: 14 pages, 5 figures. Some arguments are improved and one picture is adde

Conserving Hawaiian Natural Resources: A Geography Field Trip Experience

For several years San Diego State University\u27s Geography Department has offered a three-unit field course to the island of Kauai, Hawaii. The course surveys the nature and extent of mineral, soil, water, grassland, forest, wildlife, and marine resources on the island, as well as Kauai\u27s conservation management practices. Aside from studying island ecosystems, what is strikingly different about this trip is its strong reliance upon local talent for the actual field teaching and its alliance with an on-campus association for the non-academic portion of the field experience

TVET Capacity Development in Afghanistan: Introducing Self-Reliant Internship in In-Service Technical Teacher Training at the Technical Teacher Training Institute (TTTI)

This paper describes the approach applied to the introduction of self-reliant internship into the in-service TVET (Technical Vocational Education and Training) teacher training at the Technical Teacher Training Institute (TTTI) in Afghanistan. As data show in 2014, Afghan TVET teachers neither meet the legal requirements set by the government (Bachelor degree) nor have contacts to or work experiences in private or public sector companies. They have no knowledge of the working requirements they are preparing their students for. Consequently, in-service teacher training at the TTTI has to provide it\u27s learners with knowledge and skills in accordance with the market requirements. Thus, at the TTTI Capacity Building is focusing among others on the multifaceted interdependent relationship between teacher-student-company in order to empower teachers to be able to contribute to the employability of their students. In this respect TTTI\u27s in-service teacher training foresees the teacher\u27s participation in a private or public sector self-reliant internship to benefit from the expertise of companies\u27 work force and employers and actualize their understanding for the world of work. Afghan TVET teachers completing successful the TTTI in-service training are able to train many cohorts of students for the labor market or self-employment with the gained competences. Two subsequent cohorts of TTTI trainees - government employed TVET teachers undergoing in-service teacher training - have been participating for their first time in self-reliant internship in 2013 and 2014. According to the findings, recommendations are given for using the approach of introducing internship in in-service training for TVET teacher capacity building

Archaeobotanical evidence for pearl millet (Pennisetum glaucum) in sub-Saharan West Africa

The remains of pearl millet (Pennisetum glaucum) dating to 3460±200 and 2960±370 BP have been recovered at the archaeological site of Birimi, northern Ghana, associated with the Kintampo cultural complex. This finding represents the earliest known occurrence of pearl millet in sub-Saharan Africa. Results indicate that Kintampo peoples developed effective subsistence adaptations to savannas as well as tropical forest habitat