Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure

Analisis Komparasi Pembentukan Gap Sensitivitas sebagai Instrumen Manajemen Risiko (Studi pada Bank Umum Konvensional dan Bank Umum Syari`ah)

Penelitian ini merupakan penelitian kuantitatif dengan studi komparatif yang bertujuan untuk mengetahui posisi gap yang terbentuk pada Bank Umum Konvensional dan Bank Umum Syari`ah serta membadingkan dampaknya terhadap Perubahan suku bunga sehingga dapat ditentukan gap terbaik. Posisi gap terbentuk oleh struktur gap dengan metode gap sensitivitas, Analisis korelasi dan volatilitas digunakan untuk mengetahui sejauhmana variabel-variabel suku bunga mempengaruhi suku bunga benchmark (SBI dan SWBI) serta Uji F statistik untuk menguji hipotesis. Data yang digunakan adalah data sekunder berupa laporan keuangan Bank Umum Konvensional dan Bank Umum Syariah tahun 2004-2008 serta suku bunga domestic periode Januari 2004-Desember 2008. Hasil penelitian menujukkan bahwa Gap terbaik pada BUK terbentuk oleh Bank Mayapada, untuk BUS pada Bank Syari`ah Mandiri, sementara secara keseluruhan pembentukan gap terbaik adalah Bank Syari`ah Mandiri. Sehingga dapat disimpulkan bahwa bank syariah memiliki pembentukan posisi gap yang lebih baik dari pada bank konvensional selama periode 2004-2008.JEL Classification : E5, G2

Aplikasi Model Optimasi Untuk Meningkatkan Efisiensi Pengangkutan Sampah Di Kota Cilegon

Most cities in developing countries face inefficiency problem of waste collection service run by government. The purpose of this study is to estimate the efficiency of waste collection service and the capital cost requirement in 2019 to cover 100% waste collection service in Cilegon City. The efficiency is calculated by comparing the current costs with the optimization costs by the model of vehicle routing problem. The result shows that the obtained inefficiency reaches 37,48% which largely comes from the labor component. To cover all of resident in Cilegon City, the city needs to increase their budget allocation as much as IDR 33,884 billion in 2019

On independent sets in purely atomic probability spaces with geometric distribution.

We are interested in constructing concrete independent events in purely atomic probability spaces with geometric distribution. Among other facts we prove that there are uncountable many sequences of independent events