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"Kuantisasi Lagrangian model point-coupling bergantung densitas menghasilkan Lagrangian Hartree-Fock yang terdiri atas suku direct dan exchange. Identitas Fierz diaplikasikan pada suku exchange agar bisa disusun bersama dengan suku direct membentuk Lagrangian efektif. Dengan menggunakan persamaan Euler-Lagrange akan didapat persamaan gerak dan massa efektif sistem. Dari Hamiltonian sistem diperoleh energi ikat sistem per nukleon, massa efektif, tekanan dan kompresibilitas. Dari hasil yang diperoleh, kontribusi suku exchange kecil pada massa efektif nukleon materi nuklir simetrik. Namun pada keadaan lain, kontribusi yang signifikan terlihat pada energi ikat per nukleon di materi nuklir simetrik dan materi netron, massa efektif materi netron, dan energi ikat per nukleon pada densitas rendah dari materi netron.

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Point-coupling model Lagrangian is quantized to obtain the Hartree-Fock Lagrangian which contained direct and exchange terms. Fierz identity applied to the exchange term to be rearranged together with the direct term to obtain the effective Lagrangian. By using the Euler-Lagrange equation, we will obtain the equation of motion and the effective mass of the system. From the Hamiltonian will obtain the binding energy per nucleon, effective mass, pressure and compressibility. The results show that the exchange term contribution is small on nucleon effective mass of symmetric nuclear matter. But in the other conditions, the significant contribution are observed on binding energy per nucleon of asymmetric nuclear matter, neutron effective mass, and binding energy per nucleon in asymmetric nuclear matter in low density."

"Pada skripsi ini dibahas mengenai model SEIR penyebaran penyakit Tuberkulosis den- gan adanya proses reinfeksi dan reaktivasi. Dari model matematika ini, dapat diperoleh nilai bilangan reproduksi dasar atau basic reproduction number (R0) yang merupakan ambang batas dimana penyakit dikatakan endemik atau tidak dalam populasi. Kemudian model dianalisis dan didapatkan dua jenis titik keseimbangan, yaitu titik keseimbangan bebas penyakit (Disease-Free Equilibrium) dan titik keseimbangan endemik (Endemic Equilibrium). Tetapi, pada skripsi ini akan dianalisis titik keseimbangan bebas penyakit saja. Dengan syarat γ = 0 didapatkan Fungsi Lyapunov dan kemudian dengan Teorema Lasalle dapat ditunjukan bahwa titik DFE tersebut seimbang secara global. Selain itu, dilakukan juga analisis sensitivitas basic reproduction number (R0) terhadap 2 parameter yaitu: peluang seseorang terinfeksi TB laten (p) dan laju reaktivasi (α), serta simulasi dari model dengan variasi nilai R0 untuk menggambarkan perilaku dan kestabilan di sekitar titik keseimbangan.

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This undergraduate thesis discussed. SEIR model of tubercolusis spread with reinfection and reactivation .In this model, basic reproduction number(Ro) will be obtained, which is the threshold whether the disease is said to be endemic or not in the population. Then the model is analysed and two types of equilibrium points is obtained, which are the Disease-Free Equilibrium and Endemic Equilibriu. But, this thesis only the Disease-Free Equilibrium will be analysed. With condition of γ = 0 obtained a Lyapunov Function and then by Lasalle Theorem it is shown that the DFE is globally stable. In addition, sensitivity analysis of the basic reproduction number (R0) towards 2 parameter is also carried out which are: the probability people infected by latent TB (p) and reactivation rate (α). As well as simulation of the model with variation of R0 to describe the behavior and stability around the equilibrium point."

"Buku teks kalkulus yang sangat populer ini terbit dalam dua jilid dan menjadi salah satu buku wajib utama di sebagian besar perguruan tinggi di Indonesia) tetap merupakan buku teks utama paling ringkas yang ada saat ini namun tetap mencakup semua materi yang dibutuhkan oleh, dan dengan tingkat kedalaman yang cocok untuk para mahasiswa teknik, sains, dan matematika. Buku yang ringkas namun jelas ini membantu mahasiswa memahami konsep-konsep penting kalkulus tanpa harus bersusah payah dan kesulitan berkutat dengan materi-materi yang terlalu dalam namun tidak terlalu dibutuhkan. Isinya akurat tanpa perlu berlebihan, terkini tanpa harus ikut-ikutan tren. Penulis menggunakan aplikasi, grafik dan teknologi komputer dengan efektif; ideal untuk dosen yang ingin pembahasan tepat dan ringkas."

"Kompaktifikasi dimensi ekstra 5D dengan suku kinetik hukum pangkat (power law), telah berhasil menggulung satu dimensi ekstra, serta memperoleh informasi radius dan kestabilannya. Namun dari kajian tersebut didapatkan kompaktifikasi yang bersifat anti-de sitter (Ads) pada empat dimensi. Hal yan menunjukkan bahwa lagrangian yang dipilih belum sesuai dengan lagrangian alam semesta tempat kita berada yang mengharuskan bersifat de sitter (dS).

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The 5D extra dimension compatibility with the power law kinetic terms, has succeeded in rolling an extra dimension, and obtained information on its radius and stability. However, from this study, it was found that anti-de sitter compactification (Ads) in four dimensions was obtained. This shows that the selected lagrangian does not match the universe we are in, which requires it to be de sitter (dS)."

"A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator-splitting methods such as alternating-methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite-element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods additionally used to study them. These ideas are then applied to specific classes of mechanical problems."

"This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems."

"Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The book is motivated by the idea that a full treatment of a variational problem in function spaces would not be complete without a discussion of infinite-dimensional analysis, proper discretization, and the relationship between the two.The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Blackcholes model."