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"ABSTRACTPenulis mempelajari sifat-sifat bintang gelap menggunakan model interaksi diri, model pertukaran meson vektor dan model kondensat Bose-Einstein. Bintang gelap merupakan kumpulan dari materi gelap boson. Materi gelap boson berada dalam keadaan dasar. Sifat-sifat dari bintang gelap yang dipelajari oleh penulis yaitu massa dan jari-jari bintang, deformasi pasang-surut, momen inersia dan hubungan I-Love-Q. Dengan diketahui sifat-sifat tersebut, penulis dapat mengetahui interaksi yang terjadi pada materi gelap boson. Massa materi gelap boson ditetapkan yaitu 300 MeV dan 400 MeV. Nilai konstanta kopling pada model interaksi diri, nilai massa interaksi pada model pertukaran meson vektor dan nilai panjang hamburan pada model kondensat Bose-Einstein diambil dari hasil simulasi numerik materi gelap dingin dan tidak bertumbukan CCDM yang memenuhi persamaan 0.1 ?cm?^2/g le; ?/m_b le;1 ?cm?^2/g.

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ABSTRACTWe study properties of dark stars on self interaction model, exchange vector meson model and Bose Einstein condensate model. Dark stars are compact objects formed from bosonic dark matter. Bosonic dark matter is in ground state. The properties of the dark stars studied by us are the mass and radius of stars, tidal deformation, inertia moment, and I Love Q relation. By knowing these properties, we can see the interactions that occur in bosonic dark matter. Bosonic dark matter mass is set at 300 MeV and 400 MeV. Coupling constant on self interaction model, interaction mass on exchange vector meson model, and scattering length on Bose Einstein condensate model determined by the result of numerical simulations CCDM which requires 0.1 ?cm?^2/g le; ?/m_b le;1 ?cm?^2/g. "

"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. "

"Interferometry, the most precise measurement technique known today, exploits the wave-like nature of the atoms or photons in the interferometer. As expected from the laws of quantum mechanics, the granular, particle-like features of the individually independent atoms or photons are responsible for the precision limit, the shot noise limit. However this “classical” bound is not fundamental and it is the aim of quantum metrology to overcome it by employing entanglement among the particles. This work reports on the realization of spin-squeezed states suitable for atom interferometry. Spin squeezing was generated on the basis of motional and spin degrees of freedom, whereby the latter allowed the implementation of a full interferometer with quantum-enhanced precision."

"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. "

"Malaria merupakan penyakit menular yang disebabkan oleh parasit Plasmodium dan ditularkan melalui gigitan nyamuk Anopheles betina. Dalam penelitian ini dibahas model matematis SIR (susceptible, infected, recovered)-SI untuk penyakit malaria dengan pengobatan (u2) dan fumigasi (u1) sebagai kontrol vektor nyamuk. Penelitian ini bertujuan mengkonstruksi model matematika penyebaran malaria, melakukan analisis kestabilan titik keseimbangan, analisis sensitivitas basic reproduction number (R0) serta melakukan kajian numerik untuk menentukan efektivitas u1 dan u2. Berdasarkan kajia analitik, terdapat dua jenis titik keseimbangan, yaitu titik keseimbangan bebas penyakit dan titik keseimbangan endemik. Terdapat dua titik keseimbangan endemik saat R0 < 1 dan satu titik keseimbangan endemik saat R0 > 1. Dengan analisis bifurkasi diketahui terjadi bifurkasi mundur yang mengimplikasikan kemungkinan terjadi endemik saat R0 < 1. Dilakukan simulasi numerik untuk mendukung intepretasi model.

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Malaria is an infectious disease caused by parasite Plasmodium and transmitted through female Anopheles mosquito bites. In this study we discussed mathematical model of SIR(susceptible, infected, recovered)-SI for malaria with treatment (u2) and fumigation (u1) as intermediary vector control. This study aims to construct mathematical model of malaria disease, analyze stability of equilibrium points, analyze sensitivity of basic reproduction number (R0), and perform numerical studies to determine the effectiveness of u1 and u2. Based on analytical study, there are two types of equilibrium points in this model, they are disease-free-equilibrium (DFE) and endemic-equilibrium (EE). There are two endemic equilibrium points when R0 < 1 and one endemic equilibrium when R0 > 1. Based on bifurcation analysis there is known to be a backward bifurcation that implies possibility of endemic occurrence when R0 < 1. Numerical simulations are performed to support the interpretation of the model."

"ABSTRAKPengaturan arus kompensasi pada tapis aktif sistem tiga fasa empat lengan dengan menggunakan teknik modulasi vektor ruang dilakukan dengan mengatur vektor tegangan dan vektor tegangan referensi. Dalam modulasi vektor ruang maka model vektor tegangan berbentuk silinder tegak telah dikembangkan oleh Zhang dan beberapa peneliti lain.Peninjauan ulang model matrik pemetaan Akagi teori pq-pqr dengan metode rotasi sudut Euler menghasilkan vektor ruang tiga dimensi berbentuk silinder miring sehingga analisis parameter modulasi mengikuti analisis bentuk asimetri. Model vektor tegangan asimetri pada modulasi vektor ruang bersifat unik dalam menentukan vektor tegangan referensi, waktu pensaklaran dan duty cycle. Penentuan parameter modulasi seperti vektor tegangan referensi, duty cycle dan waktu pensaklaran dari model vektor tegangan asimetri menghasilkan harga yang sedikit berbeda dengan model silinder tegak.Modulator membangkitkan sinyal kendali pensaklaran tapis aktif sistem tiga fasa empat lengan bekerja berdasarkan modulasi vektor ruang asimetri dengan kombinasi kendali PI proportional integral dengan luaran berupa arus kompensasi mempunyai amplitudo sama dan polaritas berlawanan dengan arus beban.

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ABSTRACTCurrent compensation controller on three phase four leg system active using space vector modulation technique is done by setting the voltage vector and the reference voltage vector. In vector space modulation, the upright cylindrically vector voltage model has been developed by Zhang and several other researchers.A review mapping matrix model of Akagi the pq pqr theory with Euler angular rotation method result a three dimensional the skewed cylindrical vector so that the analysis of modulation parameters follows asymmetrical form analysis. The asymmetrical voltage vector model in vector space modulation is unique in determining the reference voltage vector, switching time and duty cycle. Determination of modulation parameters such as reference voltage vectors, duty cycle and switching time of the asymmetrical voltage vector model result a slightly different price with the upright cylindrically model.The modulator generates a switching control signal switching the three phase four leg system active filter on of the asymmetrical space vector modulation with a combination of PI proportional integral control with the output of the current compensation having the same amplitude and the opposite polarity of the load current. The modulator generates a switch modulation signal switching system active three phase four leg based on the asymmetrical voltage vector model with the output of the compensation current has the same amplitude and polarity opposite the load current."

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"Telah dipelajari dan dikembangkan sebuah model sederhana untuk reaksi fotoproduksi η pada nukleon yaitu model isobar dengan menggunakan formalisme amplitudo transversal pada kerangka pusat massa. Fotoproduksi dianalisis pada energi foton Lab. antara 0.8-1.2 GeV. Reaksi fotoproduksinya adalah γ N → η N. Amplitudo yang ditinjau melibatkan kanal-s, kanal-t dan kanal-u pada suku Born dan resonan. Perhitungan observable yang ditinjau adalah penampang lintang differensial, penampang lintang total, dan polarisasi foton. Hasil penelitian ini menunjukkan seberapa besar kontribusi dari amplitudo transisi pada kanal-s, kanal-t dan kanal-u dari suku Born dan resonan pada proses perhitungan data observable.

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A simple model for h photoproduction have been studied and developed in this research named isobaric model using transversal amplitudes formalism in the center of mass system. Photoproduction is analyzed in foton Lab. energy 0.8-1.2 GeV. The considered reaction is γN → ηN. Amplitudes consist of s channel, t channel and u channel in Born term and resonance term. Observable that we consider are differential cross section, total cross section and photon polarization. The result of this research is to show how large the contribution of transition amplitudes in channel-s, t-channel and channel-u from Born term and resonance term in the calculation of the observable data."