A remark on the approximation of plurisubharmonic functions

We show by an example that the Demailly approximation sequence of a plurisubharmonic function, constructed via Bergman kernels, is not a decreasing sequence in general.Comment: 4 pages, to appear in C. R. Math. Acad. Sci. Pari

Canonical bundle formula and degenerating families of volume forms

For log Calabi-Yau fibrations in all base dimensions, we determine the asymptotic behavior of integrals near singular fibers which generalizes numerous previous results in the base dimension $1$. This follows from our main result, a metric version of Kawamata's canonical bundle formula: the $L^2$ metric carries the singularity described by the discriminant divisor and the moduli part line bundle has a singular hermitian metric with vanishing Lelong numbers. This answers a question of Eriksson, Freixas i Montplet and Mourougane. It has immediate applications to $L^2$ extension theorems which was our starting point. We also strengthen the celebrated semipositivity theorems due to Fujita, Kawamata and others for log Calabi-Yau fibrations, giving an entirely new simpler proof which does not use technical results from the theory of variation of Hodge structure. Instead, in the proof of our main result, together with the analysis of plurisubharmonic singularities, we use a special case of the positivity of direct images. The fact that this can replace the use of Hodge theory in the semipositivity theorems answers a question of Berndtsson.Comment: 41 pages. The main Theorems 1.1, 1.2 are the same as the previous version, but in Cor. 1.3, a NON log Calabi-Yau case is removed. Sec. 3 is simplified with (3.11) merged into (3.2). The proof in Sec. 4 is reorganized with (4.8), (4.9) and Lem. 4.12 is adde

Investigating youth perceptions of youth participation in development: a focus on community engagement as a platform for youth/student participation at Rhodes University

The main objective of the study is to investigate youth perceptions of youth participation in development with a focus on the Rhodes Community Engagement programme as a platform for youth participation. The study was inspired by trying to locate the position that youth put themselves in when they regard their own participation in development. It was further motivated by trying to gain perspectives from the youth themselves because most discourses on youth rarely feature their own voices. The study utilized a qualitative methodology with an interpretive paradigm, which used semi-structured in-depth interviews as a method of data collection. The theoretical framework used was the notion of participatory development. The literature consulted was broken up into participation in development which looked at the history of participation and the need for participation, the importance of participation and the limits of participation and the type of participation. It looked at youth participation, the definition of youth as a group in society and the discourses that surround how youth are defined; lastly it looked at community engage in higher education, the role students place in community engagement and the nature of Rhodes Community engagement. The data was discussed and analysed following the above mentioned themes which were participation in development, youth participation and community engagement. From the data collected it was made evident that if youth are given more spaces and chances to actively participate they could challenge prominent discourses that treat them as irresponsible minors and exclude them from decision-making processes that directly affect them and the society within which they live

L2L^2 extension of holomorphic functions for log canonical pairs

In a general $L^2$ extension theorem of Demailly for log canonical pairs, the $L^2$ criterion with respect to a measure called the Ohsawa measure determines when a given holomorphic function can be extended. Despite the analytic nature of the Ohsawa measure, we establish a geometric characterization of this analytic criterion using the theory of log canonical centers from algebraic geometry. Along the way, we characterize when the Ohsawa measure fails to have generically smooth positive density, which answers an essential question arising from Demailly's work.Comment: Part of Ver 1 (Thm. 1.5 and Sec.5) is moved elsewher

PENGARUH LOKASI, PROMOSI, FASILITAS DAN KUALITAS LAYANAN TERHADAP KEPUTUSAN MENGGUNAKAN WARNET PLANET CYBER DI GRESIK

Pada era globalisasi saat ini segala sesuatu berjalan dan berkembang dengan pesat. Dewasa ini kebutuhan telekomunikasi menjadi kebutuhan yang sangat penting di negara-negara maju maupun negara berkembang seperti Indonesia. Pada saat ini pertelekomunikasian di Indonesia dimarakkan oleh hadirnya telepon genggam atau seluler digital GSM (Global System for Mobile communications). Dilihat dari perkembangan telekomunikasi di Indonesia melalui situs i-mobile, kini Indonesia memiliki tak kurang dari 11 operator selular, antara lain Indosat, Telkomsel, XL, Axis, Three, Flexy, Smart dan lainnya. Persaingan antara operatorpun cukup ketat, karena semua operator berusaha dalam meraih pasar dan memperoleh keuntungan dari para pelanggannya. Perumusan masalah dari penelitian ini adalah Apakah Pelayanan, Lokasi dan Fasilitas secara simultan berpengaruh terhadap Kepuasan Konsumen pada Gallery Indosat Mojokerto. Variabel yang digunakan dalam penelitian ini adalah variabel pelayanan, lokasi, fasilitas. Sample dari yang digunakan pada penelitian ini sebanyak 100 orang pengguna atau konsumen layanan Gallery Indosat Mojokerto. Jenis data yang digunakan untuk penelitian ini adalah data primer dengan menyebarkan kuesioner pada 100 orang pengguna atau konsumen layanan Gallery Indosat Mojokerto. Tehnik analisis yang digunakan adalah tehnik analisis regresi linier berganda. Hasil analisis dari penelitian ini adalah variabel pelayanan, lokasi dan fasilitas secara simultan berpengaruh signifikan terhadap kepuasan konsumen di Gallery Indosat. Variabel pelayanan, lokasi dan fasilitas secara parsial berpengaruh signifikan terhadap kepuasan konsumen. Variabel fasilitas mempunyai pengaruh yang dominan dan signifikan terhadap kepuasan konsumen. Keyword : Pelayanan (X1), Lokasi (X2), Fasilitas (X) dan Kepuasan Konsumen (Y