Time Asymmetry and Chaos in General Relativity

In this work the late-time evolution of Bianchi type $VIII$ models is discussed. These cosmological models exhibit a chaotic behaviour towards the initial singularity and our investigations show that towards the future, far from the initial singularity, these models have a non-chaotic evolution, even in the case of vacuum and without inflation. These space-time solutions turn out to exhibit a particular time asymmetry. On the other hand, investigations of the late-time behaviour of type $VIII$ models by another author have the result that chaos continues for ever in the far future and that these solutions have a time symmetric behaviour: this result was obtained using the approximation methods of Belinski, Khalatnikov and Lifshitz ($BKL$) and we try to find out a possible reason explaining why the different approaches lead to distinct outcomes. It will be shown that, at a heuristic level, the $BKL$ method gives a valid approximation of the late-time evolution of type $VIII$ models, agreeing with the result of our investigations.Comment: Latex, 14 pages, no figures. Submitted to Gen. Rel. Gra

Keefektifan Pengelolaan Laboratorium IPA SMP/MTs di Kabupaten Nagekeo, Propinsi Nusa Tenggara Timur

Penelitian ini bertujuan untuk mengetahui: (1) keefektifan pengelolaan laboratorium IPA SMP/MTs di Kabupaten Nagekeo, dan (2) keefektifan pengelolaan laboratorium yang menghasilkan keefektifan pembelajaran IPA, yang dilihat melalui perencanaan, pengorganisasian, pelaksanaan, pengawasan dan evaluasi pengelolaan laboratorium IPA, dan nilai ujian nasional mata pelajaran IPA tahun 2008. Penelitian ini merupakan penelitian survei terhadap populasi 3 SMP/MTs di Kabupaten Nagekeo. Subjek penelitian terdiri dari: kepala sekolah sebanyak 3 responden, koordinator laboratorium sebanyak 3 responden, guru IPA, laboran sebanyak 5 responden dan peserta didik kelas IX tahun pelajaran 2008/2009 sebanyak 168 responden. Pengumpulan data menggunakan observasi, wawancara, dokumentasi dan angket. Pengujian validitas instrument dilakukan dengan metode korelasi. Analisis data dilakukan dengan menggunakan teknik deskriptif kualitatif. Hasil penelitian menunjukkan bahwa: (1) pengelolaan laboratorium IPA SMP/MTs di Kabupaten Nagekeo adalah cukup efektif, yang didukung oleh perencanaan efektif, pengorganisasian kurang efektif, pelaksanaan cukup efektif, pengawasan dan evaluasi kurang efektif, dan (2) keefektifan pengelolaan laboratorium cenderung menghasilkan pembelajaran IPA yang efektif

Factorization of the Shoenfield-like bounded functional interpretation

We adapt Streicher and Kohlenbach's proof of the factorization S = KD of the Shoenfield translation S in terms of Krivine's negative translation K and the G\"odel functional interpretation D, obtaining a proof of the factorization U = KB of Ferreira's Shoenfield-like bounded functional interpretation U in terms of K and Ferreira and Oliva's bounded functional interpretation B