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"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."

"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."

"This research addresses the problem of finding a minimum Hamming Weight by proposing a left-to-right recoding of integers (from the most significant bit to the less significant one). This representation is the enhanced and modified version of a well-known recoding method called Generalized Non-Adjacent Form (G-NAF). Scanning the digits from the left-to-right is called Modified Generalized Signed Digit Non-Adjacent Form (MGSDNAF), which unlike the G-NAF, presents the ‘nice property’ to be obtained. A ‘nice property’ is one that is based on intuition and is particularly desirable to be obtained in a given context. This processing direction is of great importance because a table of pre-computed values may be used to speed up the scalar multiplication only for that direction. A subsequent advantage is that recoding the exponent in advance is not required. This results in better performances in both running time and memory space. This representation method can reduce the Hamming Weight of integers from about 21.6% for radix 3 to 15.1% for radix 9. These numbers for G-NAF recoding are 16.7% and 8.9% respectively. Comparing these numbers together shows that efficiency of the proposed method in reducing the Hamming Weight is more than the efficiency of G-NAF, which is from 30% (for radix 3) to more than 65% (for radix 9) more efficient in reducing the Hamming Weight. Finally, two radix 3 single scalar multiplication methods for Elliptic Curve Cryptography (ECC), which are based on G-NAF and Left-to-Right MGSDNAF, are compared in order to examine the application of the proposed method in cryptography. The results show that the proposed method can reduce the number of underlying arithmetic operations in single scalar multiplication by 14.1% while G-NAF can only reduce this number by 11.5%."

"Teori elektrodinamika Born-Infeld merupakan teori nonlinear dari teori elektrodinamika Maxwell. Berangkat dari karakterisitik-karakteristik teori Born-Infeld - diantaranya adalah bahwa harga energi-diri berhingga untuk muatan titik dan bahwa medan elektromagnetik di dunia-volume D-brane dideskripsikan oleh teori ini - dan dipasangkan dengan medan gravitasi Einstein (Teori Abelian Einstein-Born-Infeld 6d) penulis mencoba untuk mendeskripsikan mekanisme kompaktifikasi dimensi ekstra, yaitu flux compactification. Hasil dari mekanisme ini adalah persamaan jari-jari ruang dimensi ekstra. Untuk menguji kestabilan ruang dimensi ekstra ini diperlukan penjelasan perspektif 4 dimensi, dimana jari-jari ruang dimensi ekstra dinyatakan oleh sebuah medan dinamik radion dengan potensial stabil. Nilai vakua dari potensial dengan jari-jari dimensi yang terkompaktifikasi ini dapat menunjukkan apakah ruang-waktu 4 dimensi berhubungan dengan ruang-waktu de Sitter, anti de Sitter atau Minkowksi 4 dimensi.

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Born-Infeld electodynamics is a nonlinear theory of Maxwell electrodynamics. Based on some properties of this theory - finite electrostatic self-energy of a point particle and electromagnetic field on the world-volume of D-brane are governed by Born-Infeld theory - and coupled it with Einstein Field, called Einstein-Born-Infeld theory, I attempt to describe flux compactification of extra dimension. The result is an equation of radius of extra dimension. The 4d perspective of this theory is needed to describe the stability of size of the extra dimension, where it will be identified by the effective potential. We can determine what the 4d spacetime is related to, either 4d de Sitter or anti de Sitter spacetime, from the potential vacua of the spacetime."

"This book provides an introduction to Quantum Field Theory (QFT) at an elementary level with only special relativity, electromagnetism and quantum mechanics as prerequisites. Special attention is given to the realization of symmetries in particle physics: global and local symmetries, explicit, spontaneously broken, and anomalous continuous symmetries, as well as discrete symmetries. Beyond providing an overview of the standard model of the strong, weak and electromagnetic interactions and the current understanding of the origin of mass, the text enumerates the general features of renormalization theory as well as providing a cursory description of effective field theories and the problem of naturalness in physics. Among the more advanced topics the reader will find are an outline of the first principles derivation of the CPT theorem and the spin-statistics connection. As indicated by the title, the main aim of this text is to motivate the reader to study QFT by providing a self-contained and approachable introduction to the most exciting and challenging aspects of this successful theoretical framework."