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Abstrak :
In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.

Abstrak :
Penelitian ini bertujuan untuk mencari gen terdiferensiasi dan informasi biologis dari data ekspresi gen penyakit Alzheimer. Data yang digunakan merupakan data microarray penyakit Alzheimer yang berukuran 54675 peobes × 161 sampel. Data tersebut diperoleh dari National Centre for Biotechnology Information (NCBI) yang dapat diakses melalui laman: http://www.ncbi/nlm.nih.gov/. Gen yang memiliki ekspresi terdiferensiasi diseleksi menggunakan algoritma Delta Relative Deviation dan Absolute Deviation (DARDAD). 7089 gen dengan ekspresi terdiferensiasi pada sampel sakit selanjutnya dianalisis menggunakan metode biclustering. Bicluster didapatkan dengan menggunakan model BicMix yang memodelkan matriks ekspresi gen sebagai perkalian dua parameter ditambah matriks eror. Hasil faktorisasi dari Singular Value Decomposition (SVD) digunakan untuk menginisialisasi proses estimasi parameter model BicMix menggunakan metode iteratif Variational Expectation Maximization (VEM). Hasil bicluster selanjutnya dianalisis menggunakan Gene Ontology dan Disease Ontology. Didapatkan 30 bicluster dan beberapa penyakit yang berkaitan dengan penyakit Alzheimer. ...... The purpose of this research is to find genes that differentially expressed and biologic information from Alzheimer's gene expression data. Microarray data of Alzheimer's disease with 54675 probes × 161 samples were used in this research. Data downloaded from National Centre for Biotechnology Information (NCBI), http://www.ncbi/nlm.nih.gov/. Delta Relative Deviation and Absolute Deviation (DARDAD) were used to find differentially expressed genes. 7089 differentially expressed genes then analyzed using biclustering method with BicMix model. BicMix modeled gene expression matrix data as multiplication two parameters and an error matrix. Parameters in the model estimated using Singular Value Decomposition (SVD) - Variational Expectation Expectation Maximization (VEM). Bicluster result then analyzed using Gene Ontology and Disease Ontology. Result of this research are 30 biclusters and disease that are active in Alzheimer.

Abstrak :
Saat ini penyakit jantung koroner merupakan salah satu penyebab kematian utama di dunia, termasuk di Indonesia. Penyakit jantung koroner adalah salah satu penyakit kardiovaskuler, yaitu masalah gangguan pada jantung dan pembuluh darah. Dampaknya peredaran darah menuju jantung menjadi tidak lancar dan hal ini mengakibatkan penurunan pasokan oksigen ke jantung. Seseorang dapat menderita penyakit jantung koroner karena beberapa faktor risiko antara lain merokok, diabetes dan hipertensi. Oleh karena itu, diperlukan prediksi akurat untuk menentukan apakah seseorang termasuk kategori menderita penyakit jantung koroner berdasarkan faktor – faktor risikonya. Dalam bidang asuransi jika prediksinya cukup akurat maka perusahaan asuransi dapat menyiapkan jenis polis yang tepat untuk calon pemilik polis, terutama bagi calon pemilik polis yang memiliki faktor risiko. Model Bayesian Neural Networks digunakan untuk memprediksi penyakit jantung koroner berdasarkan medical record yang terdiri atas faktor – faktor risiko. Tahap pertama adalah pemilihan model, yaitu membangun model neural networks yang optimal dengan inferensi Bayesian (Bayesian inference) dan metode aproksimasi inferensi variasi (variational inference). Tahap selanjutnya adalah evaluasi model dengan mengukur akurasi hasil prediksi menggunakan matriks confusion, tingkat akurasi (success rate), tingkat precision dan tingkat recall. Model yang diperoleh kemudian dapat digunakan untuk memprediksi penyakit jantung koroner. ......Coronary heart disease is one of the leading causes of death in the world currently, including in Indonesia. By the definition, coronary heart disease is a cardiovascular disease which is a problem of disorders of the heart and blood vessels. The impact is the flow of blood circulation to the heart is faltered. As the result, the supply of oxygen to the heart decreases. Someone can suffer from coronary heart disease due to several risk factors including smoking, diabetes and hypertension. Therefore, an accurate predictions is required to determine whether people are categorized as suffering from coronary heart disease according to their risk factors. In the insurance field if the predictions are accurate enough, the insurance company can prepare the right type of policy for prospective policyholders, particularly for those prospective policyholders who have those risk factors. The Bayesian Neural Networks model is used to predict coronary heart disease according to a medical record that consisting of risk factors. The first stage is model selection, which is building an optimal neural network model with Bayesian inference and the variational inference approximation method. Furthermore, the next stage is model evaluation by measuring the accuracy of the predicted results with the confusion matrix, the accuracy rate (success rate), the level of precision and the level of recall. Then the trained neural network model will be used to predict new data observation.

Abstrak :
This unabridged republication of the 1980 text, an established classic in the field, is a resource for many important topics in elliptic equations and systems and is the first modern treatment of free boundary problems. Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications. They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential equations. Exciting new areas like finance and phase transformations along with more historical ones like contact problems have begun to rely on variational inequalities, making this book a necessity once again.

Abstrak :
The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

Abstrak :
Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The book is motivated by the idea that a full treatment of a variational problem in function spaces would not be complete without a discussion of infinite-dimensional analysis, proper discretization, and the relationship between the two. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Blackcholes model.

Abstrak :
In less than 100 pages, this book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity. Pedregal introduces the reader to Young measures as an important tool in solving vector variational techniques. Readers are encouraged to pursue nonlinear elasticity as one of the best means to apply these techniques. Although there are other books devoted to nonlinear elasticity or variational methods, none are concerned with Young measures as a tool for proving existence results in nonlinear elasticity. In addition, many valuable references are included to direct the reader to other important research.