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"Tugas akhir ini membahas visualisasi optimisasi fungsi non-Iinier tanpa kendala dengan fungsi berbenruk polinomial dua variabel. Metode yang digunakan yaitu metode iteratif Newton dan D-F-P (Davidon-Fletcher-Powell). Visualisasi digambarkan berupa kontur ketinggian untuk tiap titik iterasi yang diperoleh dari kedua metode tersebut. Dengan visualisasi cara kerja kedua metode akan lebih mudah dipahami."

"Tugas akhir ini meninjau visualisasi grafis penyelesaian optimisasi fungsi non linier tanpa kendala dengan metode penurunan tercuram(sfepest descentd) dan gradien sekawam (coniugate grandien). Visualisasi grafis diatas ditampilkan dalam bentuk penggambarakn kurva ketinggiaunn titik-titik yang diperoleh dalam setiap proses iterasi. Melalui visualisas grafis ini diharapkana kan mempermudah terrcapainya pemahaman mengenai arah pencarian, pengambilan panjang langkah optimum dalam satu iterasi untuk masing-masing metode. Disamping itu juga dapat dilihat dengan mudah gerakan dari suatu titik ke titik lain Hingga mencapai titik optimum."

"Penelitian ini meneliti bagaimana penerapan analisis FAR untuk untuk menentukan remunerasi sesuai Arm?s Length Principle di Indonesia. Penelitian dilakukan terhadap teori tentang analisis FAR dan prakteknya di negara Jerman, Amerika dan Indonesia.Dari penelitian terhadap teori dan praktek dilapangan ditemukan bahwa Analisis FAR merupakan faktor penting dalam menentukan remunerasi sesuai Arm's Length Principle. Analisa FAR digunakan untuk memahami transaksi afiliasi yang diperiksa sehingga pihak yang akan diuji melalui pembanding yang potensial akan dapat ditentukan. Penentuan pembanding internal atau pembanding eksternal akan bergantung pada kemiripan karakeristik FAR yang dihasilkan melalui pengulangan proses analisis FAR transaksi/pihak yang dibandingkan oleh pembanding potensial.Penelitian menghasilkan flowchart langkah-langkah yang harus dilakukan dalam analisis FAR dengan mempertimbangkan faktor-faktor penyesuaian yang dapat diandalkan, hirarki perbandingan dan faktor perbandingan lainnyadalam penetapan pembanding yang dapat diandalkan dan dipercaya. Pertimbangan ketiga faktor tersebut akan membantu penentuan metode transfer pricing terbaik untuk menentukan remunerasi sesuai Arm?s Length Principle.Penelitian ini menyimpulkan bahwa di Indonesia perlu ditetapkan langkahlangkah dalam membuat analisis FAR dan analisis FAR terintegrasi dalam grup (?Value chain?) agar Agar Wajib Pajak dapat menentukan remunerasi sesuai Arm's Length Principle di Indonesia. Ketika proses analisis FAR telah dilakukan terhadap Wajib Pajak dalam suatu industri, maka akan dapat terbentuk suatu pembanding yang dikenal dengan nama "benchmark".

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This research is about the application of functional analysis to determine the arm?s length principle renumeration in Indonesia. This research is done to the functional analysis theory and practice in Jerman, USA and Indonesia.Functional analysis is an important factor to determine the arm?s length principle renumeration. The functional analysis is used to understand the afiliated transaction so that the potential comparable will depend on functional characteristic that is found through the repeatence of functional analysis transaction or tested party compare to the potential comparable.This research result the flowchart of step that should be done in functional analysis by considering the adjustment factors that is reliable, the comparable hierarchy and other comparable factors in determining the reasonable and reliable comparable. Those three factors will help determining the best transfer pricing method to determine the arm?s length principle renumeration.This research concluded that it is needed to determined the step in making the functional analysis and value chain analysis in Indonesia so that the tax payers can determine the arm?s length principle renumeration. When functional analysis is done to the tax payers in the same industry, it will create a comparison that is known as "benchmark"."

"Pencarian solusi pada sistem persamaan non-linier dapat dilakukan dengan cara langsung maupun tidak langsung. Salah satu cara tidak langsung yang digunakan adalah metode numerik. Metode Newton merupakan salah satu metode numerik untuk mencari solusi pada sistem persamaan non-linier. Metode Newton-like merupakan improvisasi dari Metode Newton, yang memiliki sebuah parameter berupa bilangan real yang berperan sebagai pengontrol kecepatan konvergensinya. Metode ini bersifat konvergen kuadratik, serta dianggap lebih baik daripada metode Newton untuk matriks Jacobi yang mendekati singular pada vektor inisial. Simulasi numerik dilakukan pada Metode Newton dan Newton-like dengan menggunakan lima sistem persamaan non-linier, yang masing-masingnya menggunakan empat nilai real untuk parameter pada Newton-like. Vektor inisial didapat dengan membuat nilai determinan Matriks Jacobi pada sistem persamaan non-linier mendekati nol. Berdasarkan simulasi numerik yang telah dilakukan, metode Newton-like secara umum lebih cepat konvergen daripada metode Newton. Kemudian, dari masing-masing sistem dapat ditentukan ada atau tidaknya sebuah nilai parameter optimal pada Metode Newton-like.

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Finding solutions on systems of non linear equations can be done by direct or indirect way. One of the inderect way is numerical methods. Newton method is one of the numerical methods to find solutions on systems of non linear equations. Newton like is an improvement of Newton method, which has a real parameter as the convergence speed regulator. This method is quadratic convergent, and considered better than Newton for Jacobian that is close to singular on initial vector.

Numerical simulations are performed on Newton and Newton like using five systems of non linear equations, which each system using four real values for the parameter on Newton like. The initial vector is obtained by making the determinant of Jacobian on systems close to zero. Newton like are generally faster than Newton Method. Later, from each system can be determined whether or not an optimal value on Newton like Method. "

"This book provides a comprehensive and in-depth treatment of one of the most important control problems: the nonlinear output regulation problem. It contains up-to-date research results and algorithms and tools for approaching and solving the output regulation problem and other related problems, such as robust stabilization of nonlinear systems. The author also offers personal insights about solving the output regulation problem. Output regulation is a general mathematical formulation of many control problems encountered in daily life including cruise control of automobiles, landing and takeoff of aircraft, manipulation of robot arms, orbiting of satellites, and speed regulation of motors."

"Umbi porang (Amorphophallus muelleri Blume) mengandung senyawa glukomanan yang berpotensi sebagai bahan pangan fungsional penunjang terapi pada penyakit diabetes melitus tipe 2 (T2DM). Namun, masih diperlukannya optimasi proses dalam pembuatan tepung porang untuk meningkatkan kualitas tepung yang lebih baik. Penelitian ini bertujuan untuk meningkatkan kualitas tepung porang yang memenuhi standar eksport beberapa negara sebagai bahan pangan fungsional. Pembuatan tepung porang dilakukan dengan terlebih dahulu melakukan uji pendahulan untuk melihat pengaruh variasi perbandingan pelarut, waktu perendaman dan pemanasan. Kemudian dari hasil uji pendahuluan diperoleh hasil bahwa rentang waktu perendaman adalah 1-3 jam, perbandingan pelarut menggunakan penambahan volume etanol sedangkan NaCl dan NaHSO3 dibuat tetap, dan variasi pemanasan tidak dilakukan karena menyebabkan kerusakan produk. Hasil dari penelitian ini diperoleh kondisi optimum untuk meningkatkan kualitas tepung porang adalah pada perendaman secara simultan dengan perbandingan Etanol 50%: NaCl 8%: NaHSO3 2% (4:2:2) selama 2 jam. Pada kondisi optimum tersebut dapat meningkatkan kadar glukomanan dari 59,53 ± 0,02% menjadi 85,55 ± 0,01%, meningkatakn nilai derajat putih dari 74,68 ± 0,31 menjadi 85,45 ± 0,50 dan menurunkan kadar kalsium oksalat dari 17,44 ± 0,57 mg/100g menjadi 2,34 ± 0,31 mg/100g. Hasil evaluasi tepung porang yang dibuat pada kondisi optimum telah memenuhi syarat kualitas standar SNI 7939:2020 (Indonesia), Committee on Food Chemicals Codex, CAS: 37220-17-0 (Amerika), Commission Directive 2001/30/EC: E 425(ii) (Eropa), dan standar NY/T 494-2002 (China). Aktivitas antioksidan dengan metode DPPH pada tepung porang hasil optimasi (IC50 = 35,14 ± 0,43 μg/mL) lebih kuat dibanding tepung porang sebelum optimasi (IC50 = 61,29 ± 0,14 μg/mL). Aktivitas penghambatan enzim α-glukosidase tepung porang hasil optimasi (IC50 = 60,57 ± 0,72 μg/mL) lebih kuat dibanding tepung poran sebelum optimasi (IC50 = 77,89 ± 0,87 μg/mL). Bedasarkan hasil tersebut metode perendaman secara simultan dengan perbandingan Etanol 50%: NaCl 8%: NaHSO3 2% (4:2:2) selama 2 jam dapat meningkatkan kualitas tepung porang dan dapat digunakan sebagai bahan pangan fungsional.

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Porang tubers (Amorphophallus muelleri Blume) contain glucomannan which has the potential to be a functional food to support therapy in type 2 diabetes mellitus (T2DM). However, an optimization process is still needed in making porang flour to improve the quality of the flour. This research aims to improve the quality of porang flour which meets export standards in several countries as a functional food. The making of porang flour was done by carrying out preliminary tests to see the effect of variations in solvent ratio, soaking time, and heating. From the preliminary test, it was found that the immersion time range was 1-3 hours, additional volume of ethanol was used in solvent ratio while NaCl and NaHSO3 were kept constant, and heating variations were not carried out since they caused product damage. The results of this research showed that soaking the flour with a ratio 50% of Ethanol: 8% of NaCl: 2% of NaHSO3 (4:2:2) for 2 hours simultaneously as the optimum condition to improve the quality of the flour. This optimum conditions, increase the glucomannan content from 59.53 ± 0.02% to 85.55 ± 0.01%, increase the white degree value from 74.68 ± 0.31 to 85.45 ± 0.50, and reduce the calcium oxalate from 17.44 ± 0.57 mg/100g to 2.34 ± 0.31 mg/100g. The evaluation results of porang flour made under optimum conditions have passed the standard quality requirements of SNI 7939:2020 (Indonesia), Committee on Food Chemicals Codex, CAS: 37220-17-0 (America), Commission Directive 2001/30/EC: E 425(ii) (Europe), and NY/T 494-2002 (China). The antioxidant activity using the DPPH method in optimized porang flour (IC50 = 35.14 ± 0.43 μg/mL) is stronger than porang flour before optimization (IC50 = 61.29 ± 0.14 μg/mL). The α-glucosidase enzyme inhibitory activity of optimized porang flour (IC50 = 60.57 ± 0.72 μg/mL) is stronger than porang flour before optimization (IC50 = 77.89 ± 0.87 μg/mL). Based on these results, the simultaneous soaking method with a ratio of 50% of Ethanol: 8% of NaCl: 2% of NaHSO3 (4:2:2) for 2 hours can improve the quality of porang flour and can be used as a functional food."

"Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering."

"This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition. Part I presents the Navier-Stokes equations of viscous incompressible fluids and the main boundary-value problems usually associated with these equations. The case of the flow in a bounded domain with periodic or zero boundary conditions is studied and the functional setting of the equation as well as various results on existence, uniqueness, and regularity of time-dependent solutions are given. Part II studies the behavior of solutions of the Navier-Stokes equation when t approaches infinity and attempts to explain turbulence. Part III treats questions related to numerical approximation. In the Appendix, which is new to the second edition, concepts of inertial manifolds are described, definitions and some typical results are recalled, and the existence of inertial systems for two-dimensional Navier-Stokes equations is shown."