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"This book investigates the permutation polynomial (PP) based interleavers for turbo codes, including all the main theoretical and practical findings related to topics such as full coefficient conditions for PPs up to fifth; the number of all true different PPs up to fifth degree; the number of true different PPs under Zhao and Fan sufficient conditions, for any degree (with direct formulas or with a simple algorithm); parallel decoding of turbo codes using PP interleavers by butterfly networks; upper bounds of the minimum distance for turbo codes with PP interleavers; specific methods to design and find PP interleavers with good bit/frame error rate (BER/FER) performance. The theoretical results are explained in great detail to enhance readers’ understanding. The book is intended for engineers in the telecommunications field, but the chapters dealing with the PP coefficient conditions and with the number of PP are of interest to mathematicians working in the field."

"Suatu polinomial atas lapangan hingga dikatakan sebagai polinomial permutasi apabila polinomial tersebut merupakan pemetaan yang satu-satu dan pada dari lapangan hingga ke lapangan hingga itu sendiri. Penentuan suatu polinomial atas lapangan hingga merupakan polinomial permutasi tidaklah mudah. Oleh sebab itu, dilakukan konstruksi polinomial permutasi dengan bentuk tertentu sehingga diperoleh kriteria agar bentuk polinomial tersebut merupakan polinomial permutasi. Pada skripsi ini, dibahas mengenai kriteria polinomial bentuk khusus atas lapangan hingga agar dapat dikatakan sebagai polinomial permutasi. Kriteria tersebut diperoleh melalui kriteria permutasi pada himpunan hingga dan grup hingga.

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A polynomial over a finite field is called a permutation polynomial if the polynomial induces a bijection from the finite field to itself. It is not easy to determine whether an arbitrary polynomial is a permutation polynomial. Hence, constructions of permutation polynomials in several forms have been done to yield the criteria of polynomials to be permutation polynomials. This skripsi discusses about some criteria for a polynomial of special form over finite field to be called a permutation polynomial. These criteria are found by using the criteria for permutation of a finite set and permutation of a finite group."

"Biased towards functional methods, this work presents a polynomial approach to Linear Algebra. Using the shift operator as a central object it makes linear algebra a suitable introduction to other areas of mathematics, particularly operator theory."

"In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far.The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas."

"Suatu graf dikatakan suatu graf jumlah jika terdapat suatu pemetaan satu-satu yang disebut pelabelan jumlah, dari ke himpunan bilangan bulat positif sedemikian sehingga untuk jika dan hanya jika , dimana . Untuk selanjutnya disebut simpul bekerja. Graf terhubung akan membutuhkan beberapa tambahan simpul terisolasi agar memenuhi aturan pelabelan jumlah. Graf jumlah dikatakan graf jumlah eksklusif jika tidak ada simpul bekerja pada graf . Banyak simpul terisolasi minimal sehingga pelabelan jumlah memenuhi pelabelan jumlah eksklusif disebut bilangan jumlah eksklusif, dinotasikan dengan . Suatu pelabelan jumlah eksklusif pada disebut optimal jika . Pada skripsi ini akan ditunjukkan bilangan jumlah eksklusif yang optimal dari graf matahari dengan . Graf korona dengan . Graf hairycycle dengan untuk genap dan dan , dimana menyatakan banyaknya simpul daun yang terhubung pada simpul ke- pada lingkaran.

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A Graph is called a sum graph if there exist an injective labeling called sum labeling, from to a set of positive integers such that if and only if where . A vertex is called a working vertex. Any connected graph will require some additional isolated vertices in order to be sum labeled. Sum graph is said to be exclusive sum graph if contain no working vertex. The smallest number of isolated vertices such that sum labeling is an exclusive sum labeling called exclusive sum number, denoted by In this skripsi, it will be showed optimum exclusive sum number of sun graphs which is corona graphs which is , hairycycle graphs which is for even , , and , where is a number of leaves attached to the -th cycle?s vertex."

"ABSTRAKEra globalisasi tidak dapat menahan besarnya pengaruh kecanggihan teknologi informasi, salah satunya adalah internet. Perkembangan teknologi internet tentu meningkatkan jumlah informasi yang tersedia. Informasi tersebut dapat berupa berita ? berita aktual yang dapat diakses melalui media sosial, seperti Twitter. Oleh karena itu, dibutuhkan suatu cara cepat dan efisien untuk menemukan topik utama dari Twitter. Pendeteksian topik pada dokumen yang sangat besar sulit dilakukan secara manual sehingga dibutuhkan metode otomatis, salah satunya faktorisasi matriks yaitu Nonnegative Matrix Factorization (NMF). Salah satu metode NMF yang telah berhasil dikembangkan dengan komplesitas waktu polinomial adalah P-NMF dengan algoritma AGM yang memiliki asumsi bahwa setiap topik memiliki sedikitnya satu kata yang tidak terdapat pada topik lainnya yang disebut sebagai kata anchor. P-NMF dengan algoritma AGM terdiri dari tiga tahapan, yaitu pembentukan matriks coocurance, pencarian kata anchor, dan recover. Pada penelitian ini akan diterapkan P-NMF dengan Recover KL untuk mendeteksian topik pada twitter, kemudian hasilnya akan dibandingkan dengan LDA dan P-NMF dengan Original Recover. Penelitian menunjukan bahwa P-NMF dengan Recover KL mampu meningkatkan akurasi untuk pendeteksian topik pada Twitter.

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ABSTRACTThe era of globalization can?t withstand the influence of sophistication of information technology, such as Internet. Development of Internet technology would increase the amount of information. The information may be actual news that can be accessed through social media, such as Twitter. Therefore, needed a fast and efficient way to find the main topics of Twitter. Detection topics on very large documents difficult to do manually so it takes automated methods, one of which is nonnegative matrix factorization (NMF). One method that has been successfully developed NMF with polynomial time complexity is P-NMF algorithm AGM which assumes that each topic has at least one word that doesn?t appear on other topics, called anchor words. P-NMF algorithm AGM consists of three steps, the establishment of a matrix coocurance, finding anchor words, and recover. This research will be implemented P-NMF with Recover KL to detect topics on twitter, then the results will be compared with the LDA and P-NMF with Original Recover. Research shows that P-NMF with Recover KL can improve detection accuracy for topics on Twitter."