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Abstrak :
Optical differentiation is one of many methods in the optical data processing that is useful for, e.g. image contouring. In this thesis, the differentiation filter is caried out based on the spatial filtering techniques. The ob ject is transformed with a Fourier lens to obtain the spatial frequency spectrum of the object at the Fourier plane. A spatial differentiation filter is placed at the Fourier plane. And finally, with another lens the filtered spectrum is transformed back to obtain the output image. The critical step of the experiment is the design and the fabrication of the filter. In this thesis, two kinds of models have been used to approximate the differentiation filters: (1) multi-step function and (2) Gaussian spot. The multi-step function is intended to approximate the first order differentiation filter. However, due to the photographic limitations, the multi-step function has become a single step function or simply a high-pass filter. Nevertheless, the result may be useful as the approximation of the second (not the first) order differentiation. A filter with a diameter of 0.4 mm appears to give a good result for an object consisting of letters of 4 mm high. To obtain the Gaussian spot, a He-Ne laser beam spot with 6328 nm has been used. with several attenuations, the laser beam spot has been recorded with various shutter speeds in an open camera. It appear that the Gaussian filter is a very good approximation of the second order differentiation filter. Compared to the high-pass filter, it gives higher S/N ratio. The Gaussian spot obtained with a shutter speed of 1/4000 and minimum attenuation gives the best image output. However, none of the filters gives the first order differentiation output.

Abstrak :
Bank dipersyaratkan oleh pemerintah untuk mengelola risiko-risiko perbankan, salah satunya adalah risiko operasional. Risiko operasional merupakan salah satu jenis risiko yang melekat pada setiap aktifitas fungsional bank. Bank mengelola risiko operasional dengan cara menghitung kerugian yang diperkirakan sebagai kebutuhan modal bagi risiko operasional (Economic Capital). Loss distribution Approach (LDA) merupakan salah satu metode untuk perhitungan Economic Capital (EC). Dalam metode LDA, bank harus mengestimasi loss severity distribution (distribusi severitas) dan frequency distribution (distribusi frekuensi) kemudian membentuk compound distribution (distribusi majemuk). Nilai EC diperoleh dari Value at Risk (VaR) dari distribusi majemuk dengan tingkat kepercayaan 99,9%. Estimasi distribusi severitas umumnya menggunakan model distribusi tertentu yang telah ada, namun pada banyak kasus kurang baik dalam menggambarkan data. Estimasi distribusi severitas berbasis data diharapkan mampu menjadi solusi permasalahan ini. Salah satu metode yang mengestimasi distribusi severitas dengan berbasis pada data adalah Gaussian Mixture Model (GMM). GMM merupakan suatu metode parametrik untuk mengestimasi fungsi distribusi probabilitas dari suatu variabel acak. Model GMM ini merupakan model kombinasi linear sederhana dari beberapa komponen distribusi Gaussian. Hasil penelitian menunjukkan bahwa GMM mampu menggambarkan data lebih baik dibandingkan dengan menggunakan model distribusi yang ada. Nilai EC yang dihasilkan oleh metode LDA yang distribusi severitasnya menggunakan GMM lebih kecil 2-2,8% dibandingkan nilai EC yang dihasilkan oleh metode LDA yang menggunakan model distribusi tersebut. ......Bank must be able to manage all of banking risk, on of them is operational risk. Operational risk is a risk that come from any functional activity of bank. Bank manage operational risk by calculate estimated risk (Economic Capital). Loss Distribution Approach (LDA) is a popular method to estimate Economic Capital (EC) of operational risk on banking. In LDA method, loss severity distribution (severity distribution) and loss frequency distribution (frequency distribution) must be estimated and then compound distribution is formed from both of them. Through LDA method, the value of EC can be gotten from Value at Risk (VaR) in compound distribution with the level of confidence reaches 99,9%. Severity distribution estimation that used a model on particular distribution cannot describe a data well through. So, Severity distribution estimation based on data is used to solved this problem. One of methode that estimated severity distribution based on data is Gaussian Mixture Model (GMM). GMM is parametric methode that estimate probability density of random variable. Model of GMM is a linear combination of many Gaussian distribution . The result on this research is estimation of severity distribution through GMM is better than existing distribution model in describing the data. The value at EC of LDA method using GMM is smaller 2 % - 2,8 % than the value at EC of LDA using existing distribution model.

Abstrak :
ABSTRAK
Telah dipelajari fotoproduksi pion netral pada proton dengan model Lagrangian effektif dan memperhitungkan faktor bentuk hadronik monopol, dipol, dan gaussian, pada setiap vertex resonan. Amplitudo transisi dihitung untuk setiap kanal mulai dari suku Born, suku vektor messon, dan suku resonan untuk mencari nilai penampang lintang total pada setiap kanalnya. Selanjutnya untuk melihat adanya pengaruh dari faktor bentuk dilakukan dengan cara membandingkannya dengan data eksperimen dengan perhitungan teoritis. Perhitungan faktor bentuk hanya akan diperhitungkan pada suku resonan. Penelitian ini menunjukkan bahwa didapatkan hasil yang lebih baik dengan memperhitungkan faktor bentuk dalam perhitungan total penampang lintang.

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ABSTRACT
There has been investigated about neutral pion photoproduction on protons using effective Lagrangian approach by consider the hadronic form factors monopole, dipole, and gaussian, in each of vertex nucleon resonances. Transition amplitudes are calculated for each channel starting from Born term, vector messon, and resonances term to find the total cross sectional value in each channel. Furthermore, to see the influence of form factors is done by comparing experimental data with theoretical calculation. The calculation will only be taken into nucleon resonances term. This study shows that better results are obtained by counting the form factor in total cross sectional calculations.

Abstrak :
Interaksi hiperon-nukleon (YN) sulit untuk diselidiki sebab kurangnya data dari eksperimen hamburan. Untuk menyelidiki lebih lanjut interaksi ini, kontribusi dari potensial YN perlu diselidiki dalam sistem few-body. Sistem hipernuklir yang terikat paling lemah, hipertriton, diselidiki dalam penelitian ini dengan Gaussian Expansion Method untuk dapat mempelajari struktur dan interaksi YN. Properti-properti dari hiperon Lambda (Λ) dikonfirmasi secara teoretis dengan menggunakan potensial tipe Minnesota. Energi ikat hiperon dari hipertriton ditemukan sebesar 0.19 MeV, relatif terhadap break up threshold d + Λ. Terjadi efek penyusutan pada deuteron, dimana radius rms deuteron berkurang dari 3.85 fm menjadi 3.58 fm, sedang jarak hiperon Λ berada di 9.5 fm. Hal ini mengkonfirmasi struktur halo pada hipertriton, yang mengimplikasikan bahwa sistem deuteron adalah inti nukleus yang dikelilingi oleh hiperon Λ. Hasil perhitungan model juga menghasilkan distribusi kepadatan dari substruktur hipertriton dan fungsi gelombang dari hipertriton, yang berguna untuk diaplikasikan ke perhitungan lebih lanjut. ......The hyperon-nucleon interaction (YN) is difficult to be studied because of the lack in YN scattering data. To better understand this interaction, the contribution from YN potential has to be studied in few-body systems. The lightest bound hypernuclear, hypertriton, is studied with Gaussian Expansion Method to understand its structure and the YN interaction. The properties of Lambda (Λ) hyperon is confirmed theoretically with the Minnesota-type potential. The binding energy of hypertriton is found to be 0.19 MeV, relative to the d +Λ break-up threshold. There appear to be a shrinkage effect on deuteron, where the rms radius of deuteron shrink from 3.85 fm to 3.58 fm, whereas the hyperon Λ is located in 9.5 fm. This confirmed the halo structure of the hypertriton, which implies that the deuteron is the core nucleus with Λ hyperon surrounding it. The calculation results also give the denstiy distribution of hypertriton sub-structures and the wave function of the hypertriton, that is useful to be applied in further calculation.

Abstrak :
Pada proses analisa video, permasalahan deteksi dan identifikasi objek adalah masalah yang sering dijumpai dan menjadi akar masalah yang menyebabkan analisa video masih belum bisa dilakukan secara real time dan diaplikasikan untuk hal yang kompleks. Oleh sebab itu, telah banyak metode yang dikembangkan untuk mengatasi permasalahan tersebut. Salah satu metode yang digunakan untuk identifikasi objek adalah Gaussian Bayes Classifier. Pada skripsi ini dirancang dan disimulasikan identifikasi objek yang berada di tangan dengan menggunakan Gaussian Bayes Classifier. Parameter correctness percentage digunakan untuk menguji performansi dari identifikasi objek (kaleng Green Sands, kaleng Pocari Sweat, dan Biore) yang berada di tangan. Hasil simulasi menunjukkan bahwa hasil pengidentifikasian objek yang memiliki ketepatan pengidentifikasian yang paling paling baik adalah ketika mengidentifikasi antara tidak ada objek dengan objek kaleng Green Sands yang memiliki nilai rata ? rata correct percentage yang mencapai 89% untuk setiap percobaannya dan 94,6% untuk setiap percobaannya saat pengidentifikasian tidak ada objek.

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In video analysis process, problem in object detection and object identification is a common problem and the root problem that causes the video analysis still can?t be used in real time and applied to complex condition. Therefore, many methods have been developed to overcome these problems. One of the methods which is used for object identification is Gaussian Bayes Classifier method. In this thesis is designed and simulated object identification in hand using Gaussian Bayes Classifier. Correctness percentage parameter is used to test the performance of in hand object identification (for object Greend Sands?s can, Pocari Sweat?s can, and Biore) . The simulation result show that identification result which has best accuracy is when identifying between no object and object Green Sands?s can which has average value of correct percentage that reach 89% for each experiment and 94,6% for each experiment when identifying no object.

Abstrak :
Handwritten word segmentation problem is one of many problems in the handwritten wprd recognition field. This segmentation problem will be more complicated if dealing with cursive handwritten words. This paper will discuss a simple approach in segmentation using 1D Gaussian filters having 8 points in length and 4 - 12 in standard deviation as well as those having 12 - 24 points in length 4- 16 in standard deviation can be used effectively for this kind of segmentation.

Abstrak :
Suatu model persebaran litofasies sangat penting dalam proses karakterisasi reservoar. Dengan adanya model kita dapat memperhitungkan nilai keekonomian dari reservoar tersebut termasuk menyusun program pengembangan reservoar selanjutnya, serta dapat pula menjadi masukan sebagai model statik dalam proses simulasi resevoar. Dua metode geostatistik dalam memodelkan fasies telah dilakukan dalam penelitian ini yaitu, sequential indicator simulation dan truncated gaussian simulation. Kedua metode tersebut menggunakan analisa model variogram, namun truncated gaussian simulation memperhitungkan konsep model pengendapan litofasies sementara sequential indicator simulation tidak memperhitungkan konsep tersebut. Untuk memodelkan porositas zona reservoar digunakan metode sequential gaussian simulation. Atribut impedansi akustik digunakan sebagai konstrain dalam setiap pemodelan. Dari hasil penelitian disimpulkan bahwa apabila data sumur yang tersedia terbatas dan pemodelan dikonstrain oleh atribut impedansi akustik, metode truncated gaussian simulation lebih baik dalam memetakan persebaran litofasies dibandingkan dengan metode sequential indicator simulation.

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A model of lithofasies distribution is very important in the process of reservoar characterization. By using this model, we can calculate the economic value of the reservoar. It also can be used as an input static model for reservoar simulation. Two methods of geostatistics stochastic in facies modeling have been done in this research, sequential indicator simulation and truncated gaussian simulation. Both of methods use the variogram model analysis, however truncated gaussian simulation consider the concept of depositional models of lithofasies while sequential indicator simulation not. Sequential gaussian simulation method has been used to model the reservoar porosity zone. Every modelling process use acoustic impedance attribute as litofasies constrain. The study concluded that if the well data is sparse and acoustic impedance has been used as constrain, truncated gaussian method will produced a better model than sequential indicator method.

Abstrak :
The Birnbaum-Sanders (BS) distribution was first introduced in 1969 by Birnbaum and Saunders as a combination of inverse Gaussian distributions with a length-biased inverse Gaussian distribution. Later, in 2008, Ahmed et al. introduced a new parametrization of the BS distribution based on Birnbaum-Sanders, and they also proposed a parameter estimation using the method of moments and regression-quantile estimation. In this paper, we emphasize the Birnbaum-Sanders distribution presented by Ahmed et al., and we develop an EM-algorithm to estimate two unknown parameters of this distribution. The EM-algorithm is a general method used to estimate the parameters when the probability density function is complicated and it is the best alternative for the estimation of a mixture distribution. We assumed that this problem has a missing value, and maximized complete data log-likelihood function instead log-likelihood function because it is analytically easier. Moreover, some simulation experiments were conducted in order to examine the performance of the proposed parameter estimation, and it was observed that the performances were quite satisfactory. Specifically, the MSE, variance and bias tend to decrease as n increases.