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"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%."

"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)."

"Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime number theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included."

"ABSTRAKTelah dibuat Heterostruktur Sumur Kuantum Selaput Tipis ZnS-ZnO yang mempunyai sela energi (Eg) = 0.95 eV, pada temperatur kamar. bahan tersebut merupakan Semikonduktor dan mempunyai sifat transisi tidak langsung (indirect transition). Pembuatannya dilakukan dengan jalan evaporasi termal, pada tingkat kevakuman antara 1.5 - 8 x l0-6 mbar. Untuk membuat sebuah sampel dilakukan beberapa kali evaporasi. Dengan menggunakan alat UV-VIS-NIR untuk dipelajari sifat optis (absorpsi dan transmitans) pada panjang gelombang 250 nm sld 1.800 nm, untuk 7 Lapisan perlapis 100 Angstrom. Selain itu dilakukan juga pengukuran sifat elektris (I-V) dengan menggunakan sebuah rangkaian DC. Ternyata cuplikan-cuplikan yang dibuat menunjukkan adanya hambatan negatif dan penerowongan resonans di dalam sumur kuantum heterostruktur selaput tipis ZnS-ZnO yang dipelajari. Besar kemungkinan telah terbentuk superlatis untuk struktur yang terdiri baik dari 3 (tiga), 5 (lima) maupun 7 (tujuh) lapis, sebagian dapat dijelaskan dari pola kurva-kurva karakteristik elektris (I-V) masing-masing. "