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"Didalam skripsi ini dibahas sebuah simulasi penyandian siklis dengan menggabungkan teknik BCH (Bose Chaudhuri Hocquenghem) dan teknik RS (Reed-Solomon). Panjang kata sandi yang dipergunakan untuk masing-masing teknik adalah 7 bit dan panjang informasi yang dipergunakan adalah 3 bit.Penggabungan ini didasarkan pada kemampuan masing-masing teknik dalam mengkoreksi kesalahan dimana teknik BCH dapat mengkoreksi kesalahan sebanyak 1 bit secara acak (random) sedangkan teknik RS dapat mengkoreksi kesalahan sebanyak 2 bit simbol secara acak. Penggabungan ini dilakukan secara serial (concatenated) dan diharapkan dapat meningkatkan kemampuannya dalam mengkoreksi kesalahan pada informasi yang diterima.Simulasi penyandian siklis ini diaplikasikan dengan menggunakan sistem komunikasi antar komputer melalui kabel xtalk RS232. Dan dalam perancangan perangkat lunaknya menggunakan bahasa pemograman MATLAB versi 7.0.1 (R14). Setelah diujicoba software ini maka penggabungan kedua teknik RS (7, 3) dan teknik BCH (7, 3) maka akan dihasilkan panjang kata sandi 49 bit yang dibagi kedalam 7 byte simbol dengan masing-masing simbol terdiri dari 7 bit dan panjang informasi 9 bit. Sedangkan untuk kemampuan dalam mengkoreksi kesalahan adalah 14 bit kesalahan berurutan (2 byte simbol) ditambah dengan 1 bit kesalahan acak pada 5 byte simbol lainnya.

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This final project developed error correcting simulation generated by combination of RS (Reed Solomon) method and BCH (Bose Chaudhuri Hocquenghem) method. 7 bit Code length used for each method and 3 bit information length for each method. The combination was done based on the different capability of each method to perform the error correction. The BCH method able to corrects 1 bit errors in random distribution while RS method able to corrects 2 bit error in symbol randomly. This combination constructed serially (concatenated) and was expected to improve its capability to correct errors on received information.

This cyclic code simulation was implemented by using the communication system between two computers through xtalk RS232 cable. The software was designed and built using programming language MATLAB ver. 7.0.1 (R14). The software tests had been carried out and it turned out that the combination of the two methods, RS (7, 3) and BCH (7, 3), the resulted in 49 bit code length consists of 7 byte symbols where every symbol consists of 7 bit and the length of 9 bit information. Error correction capability of the software is 14 bit burst error (2 byte symbol) and 1 bit random error on other 5 byte symbol."

"Penelitian kali ini mencoba memodelkan materi gelap yang menggumpal menjadi objek mampat yang disebut bintang gelap dengan mempertimbangkan efek temperatur. Partikel berjenis fermion, boson dan parafermion digunakan untuk memodelkan partikel gelap. Penentuan suhu bintang dilakukan dengan 2 metode yaitu: i) menganggap suhu bin- tang seragam dan ii) temperatur berubah-ubah bergantung tekanan dengan menganggap entropinya tetap. Didapati bahwa pada temeratur tidak nol, jenis partikel sangat mem- pengaruhi sifat-sifat dari bintang gelap. Pada kasus fermion, efek temperatur dan en- tropi membuat persamaan keadaannya lebih lunak dan didapatkan bintang yang memiliki massa dan radius lebih besar. Pada kasus boson, efek temperatur dan entropi tidak terlalu signifikan. Sedangkan pada kasus parafermion didapat persamaan keadaan tidak stabil dan perlu telaah lebih lanjut.

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In this work we model dark matter that clumps into a compact object called a dark stars, the effects of temperature is considered. We use Fermi-Dirac, Bose-Einstein and Parafermion statistics to model dark matter particles. To determine the temperature of the star 2 methods are used, i) Assume the temperature is uniform throughout the star and ii) the temperature varies depending on pressure by assuming that the entropy is constant. It was found that in the case of finite temeratures, the type of particle statisticss greatly affects the properties of dark stars. In the case of fermions, the effects temperature and entropy make the equation of state(EoS) softer and have larger mass and radius. In the case of bosons, the effect of temperature and entropy is not too significant. Whereas in the case of parafermion, the results obtained unstable equations of state and need further study."

"Kami telah membahas fungsi partisi dari kondensasi Bose-Einstein di dalam perangkap parabola yang dinyatakan oleh persamaan Gross-Pitaevskii satu dimensi. Fungsi partisi itu sendiri dirumuskan hanya dengan meninjau semua tingkat-tingkat energi dari osilator kuantum makroskopik yang mirip seperti di dalam mekanika statistika. Solusi-solusi dari tingkat-tingkat energi untuk kasus ini dapat diturunkan dengan mengikuti metode yang menggunakan teori perturbasi bebas waktu. Pada kasus ini, persamaan Gross-Pitaevskii satu dimensi dapat diperlakukan sebagai osilator kuantum makroskopik dengan menerapkan kondisi bahwa faktor nonlinearnya sangat kecil. Selain itu, perumusan analitik untuk energi tingkat dasar dapat diperoleh dengan menggunakan metode tersebut. Namun demikian, tingkat-tingkat eksitasinya tidak diberikan secara eksplisit. Saat ini, kami melanjutkan pekerjaan sebelumnya untuk menurunkan tingkat-tingkat keadaan lainnya supaya dapat merumuskan fungsi partisi. Akan tetapi, kami tidak mendapatkan bentuk analitik dari fungsi partisi karena integral dari suku-suku nonlinear tidak dapat membentuk hubungan rekursif. Akibatnya, tidak hanya fungsi partisi tetapi juga energi bebas Helmholtz dan entropi harus dikaji ulang untuk memeriksa sifat konvergennya.

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We have discussed the partition function of the Bose-Einstein condensation in parabolic trap associated to the one-dimensional Gross-Pitaevskii equation. The partition function itself is constructed by considering all the energy levels of the macroscopic quantum oscillator which is similar to statistical mechanics. The solutions of the energy levels for this case can be derived by pursuing the method that applies the time-independent perturbation theory. In this case, the one-dimensional Gross Pitaevskii equation can be treated as the one-dimensional macroscopic quantum oscillator on condition that the nonlinearity is very small. Moreover, the analytical expression for the ground state energy can be obtained by applying the method. However, the higher level states were not explicitly provided. In this research we followed up on the former work to derive explicitly the other states in order to formulate the partition function. However, we did not find the closed form of the partition function since the results of nonlinear term integral could not form the recursion relation. As a consequence, not only should the partition function but also the Helmholtz free energy and entropy should be reevaluated to check their convergences. "

"We consider the correction of ground state energy of one-dimensional Gross-Pitaevskii equation by adding a gain-loss term as a time-dependent external potential. The interesting purpose of this term is that it can be used to explain the experimental results especially in the nonlinear fiber optics regarding the pulse propagation and collapse-revival of the condensate in the Bose-Einstein condensation. In the Bose-Einstein condensation itself, the function can represent thatcondensate can interact with the normal atomic cloud. Some analytical solutions have been obtained by choosing anansatz solution of the wave function and its solution can be dark or bright soliton. Since the Gross-Pitaevskii equation can be treated as a macroscopic quantum oscillator, we can use time-dependent perturbation theory as in ordinaryquantum mechanics to find the ground state energy correction if we assume other terms to be very small. In addition, time-dependent potential allows a transition from one energy level to others. In this case, we expand the solution of nonstationary one-dimensional wave function as a linear superposition of harmonic oscillator normalized eigen functions. To get the recursive formulas, we suggest an option to formulate the coefficients after inserting the initial condition which must be satisfied such as in quantum mechanics. "