Cosmological solutions of braneworlds with warped and compact dimensions

We study cosmological aspects of braneworld models with a warped dimension and an arbitrary number of compact dimensions. With a stabilized radion, a number of different cosmological bulk solutions are found in a general case. Both one and two brane models are considered. The Friedmann equation is calculated in each case. Particular attention is paid to six dimensional models where we find that the usual Friedmann equation can typically be recovered without fine-tuning.Comment: 11 page

BOOK REVIEW OF THE NOTEBOOK WRITTEN BY NICHOLAS SPARKS

Final Project ini berjudul “Book Review of The Notebook written by Nicholas Sparks”. Final project ini bertujuan untuk mereview dan membahas kelemahan serta kelebihan dari novel The Notebook. Permasalahan yang dibahas dalam novel ini adalah tentang pejuangan cinta dari kedua tokoh utama untuk dapat bersatu kembali walaupun mereka sudah terpisah jarak dan waktu. Dalam mengerjakan final project ini, penulis memperoleh data data dengan melakukan studi kepustakaan di perpustakaan serta melalui berbagai referensi melalui website, termasuk website resmi dari sang penulis. Dari hasil penganalisaan, dapat dismpulkan bahwa perjuangan kedua tokoh utama untuk mendapatkan cinta mereka kembali memanglah tidak mudah, karena harus melalui berbagai macam rintangan dan halangan, bahkan di penghujung cerita, tokoh utama pria juga sempat akan kehilangan pujaan hatinya, walau akhirnya mereka bisa kembali bersatu. Final project ini dibagi menjadi 4 bagian dimana pada Bab I dibahas pendahuluan yang terdiri dari latar belakang penulisan, tujuan dari penulisan final project ini serta tercantum biografi dari penulis novel. Pada Bab II dituliskan ringkasan dari novel yang akan dibahas. Sedangkan pada Bab III, terdapat review keseluruhan yang membahas kelebihan dan kekurangan dari novel The Notebook serta terdapat pula pembahasan mengenai motif yang dipakai dalam novel tersebut. Akhir dari analisis final project ini terangkum pada kesimpulan yang terdapat pada Bab IV di akhir bagian final project ini

An overview of the quantization for mixed distributions

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixed distributions are an exciting new area for optimal quantization. In this paper, we have determined the optimal sets of $n$-means, the $n$th quantization error, and the quantization dimensions of different mixed distributions. Besides, we have discussed whether the quantization coefficients for the mixed distributions exist. The results in this paper will give a motivation and insight into more general problems in quantization of mixed distributions.Comment: arXiv admin note: text overlap with arXiv:1701.0416

Nonhomogeneous distributions and optimal quantizers for Sierpi\'nski carpets

The purpose of quantization of a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonhomogeneous probability measure $P$ on $\mathbb R^2$ which has support the Sierpi\'nski carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered . For this probability measure, the optimal sets of $n$-means and the $n$th quantization errors are investigated for all $n\geq 2$.Comment: arXiv admin note: text overlap with arXiv:1603.0073