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

Lenition and Language Contact in Peru

Lenition is defined as any type of articulatory consonantal weakening which can result in voicing, spirantization, or elision. Synchronically and diachronically, lenition has had a consistent and considerable influence on the development of Spanish as well as on its variation. For example, historically, intervocalic /p t k/ were lenited and voiced in Spanish and the other Western Romance languages Contemporarily, varying levels of lenition have been documented in wide array of Spanish varieties, some of which have been shown to correlate with different sociolinguistic factors. While the degree of lenition for different consonantal segments varies, the general consensus is that lenition is present and active in most, if not all, monolingual varieties of Spanish. In varieties of Latin American Spanish in contact with indigenous languages, variation that differs from what has been observed in monolingual varieties of Spanish has been reported (see Davidson 2019, Lope Blanch 1987 Michnowicz 2009, 2011, among others). The current study examines how contact with Quechua in southern Peru slows down or impedes several lenitive processes in the Andean Spanish of the region. Specifically, 23 sociolinguistic interviews gathered in a community in southern Peru were analyzed. The results of mixed-effects linear regressions indicate that contact with Quechua, specifically Cusco Quechua, is correlated with lesser degrees of spirantization of intervocalic /d/, as well as with minimal intervocalic sibilant voicing. We hypothesize that Quechuan phonology as well as L2 learning of Spanish has resulted in the lessening of the role of certain processes of lenition, some of which are otherwise rather common in Spanish. Likewise, the current study emphasizes the importance of specifying what variety of Quechua contact linguistics researchers work with as different varieties of Quechua have differing consonantal phonologies