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Abstrak :
[ABSTRAK
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 signikan 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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ABSTRACT
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 eective Lagrangian. By using the Euler-Lagrange equation, we will obtain the equation of motion and the eective mass of the system. From the Hamiltonian will obtain the binding energy per nucleon, eective mass, pressure and compressibility. The results show that the exchange term contribution is small on nucleon eective mass of symmetric nuclear matter. But in the other conditions, the signicant contribution are observed on binding energy per nucleon of asymmetric nuclear matter, neutron eective mass, and binding energy per nucleon in asymmetric nuclear matter in low density;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 eective Lagrangian. By using the Euler-Lagrange equation, we will obtain the equation of motion and the eective mass of the system. From the Hamiltonian will obtain the binding energy per nucleon, eective mass, pressure and compressibility. The results show that the exchange term contribution is small on nucleon eective mass of symmetric nuclear matter. But in the other conditions, the signicant contribution are observed on binding energy per nucleon of asymmetric nuclear matter, neutron eective mass, and binding energy per nucleon in asymmetric nuclear matter in low density;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 eective Lagrangian. By using the Euler-Lagrange equation, we will obtain the equation of motion and the eective mass of the system. From the Hamiltonian will obtain the binding energy per nucleon, eective mass, pressure and compressibility. The results show that the exchange term contribution is small on nucleon eective mass of symmetric nuclear matter. But in the other conditions, the signicant contribution are observed on binding energy per nucleon of asymmetric nuclear matter, neutron eective mass, and binding energy per nucleon in asymmetric nuclear matter in low density;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 eective Lagrangian. By using the Euler-Lagrange equation, we will obtain the equation of motion and the eective mass of the system. From the Hamiltonian will obtain the binding energy per nucleon, eective mass, pressure and compressibility. The results show that the exchange term contribution is small on nucleon eective mass of symmetric nuclear matter. But in the other conditions, the signicant contribution are observed on binding energy per nucleon of asymmetric nuclear matter, neutron eective mass, and binding energy per nucleon in asymmetric nuclear matter in low density, 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 eective Lagrangian. By using the Euler-Lagrange equation, we will obtain the equation of motion and the eective mass of the system. From the Hamiltonian will obtain the binding energy per nucleon, eective mass, pressure and compressibility. The results show that the exchange term contribution is small on nucleon eective mass of symmetric nuclear matter. But in the other conditions, the signicant contribution are observed on binding energy per nucleon of asymmetric nuclear matter, neutron eective mass, and binding energy per nucleon in asymmetric nuclear matter in low density]

Abstrak :
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). ......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).

Abstrak :
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.

Abstrak :
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.

Abstrak :
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.