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Abstrak :
Di dalam Geometri Lobachevsky, ada sedikitnya dua garis yang sejajar dengan suatu garis yang diberikan melalui suatu titik di luar garis yang diberikan tersebut. Namun, di Geometri Euclid, hanya ada tepat satu garis yang sejajar dengan suatu garis yang diberikan melalui suatu titik di luar garis yang diberikan tersebut. Perbedaan sifat kesejajaran tersebut mengakibatkan perbedaan-perbedaan lain antara Geometri Lobachevsky dan Geometri Euclid. Di dalam skripsi ini, dipelajari beberapa karakteristik poligon dan fungsi luas di Geometri Lobachevsky, terutama perbedaannya dengan Geometri Euclid. Struktur geometri yang diperhatikan hanyalah geometri dalam bidang. ...... In Lobachevskian Geometry, there are at least two lines parallel to a given line through a given point not on the line. But, in Euclidian Geometry, there’s only a single line parallel to a given line through a given point not on the line. The parallelism characteristics difference implies other differences between Lobachevskian Geometry and Euclidean Geometry. In this thesis, some characteristics of polygons and area function in Lobechevskian Geometry are studied, especially differences compared to Euclidean Geometry. Geometric structure considered is only plane geometry.

Abstrak :
Penelitian ini menitikberatkan kepada perancangan dan realisasi bentukan 3D scaffold menggunakan biomaterial (PLA) dengan variasi ukuran dan geometri tertentu. Variasi parameter tersebut akan menghasilkan scaffold dengan porositas tertentu yang memiliki korelasi terhadap nilai modulus elastisitas (E) yang diuji melalui uji tekan (compressive test). Sistem fabrikasi fuse deposition modelling (FDM) digunakan untuk fabrikasi scaffold dibantu dengan CAD software dalam proses perancangannya. Melalui pengolahan data eksperimen, dihasilkan bahwa persentase porositas berbanding terbalik dengan nilai E yang dihasilkan pada masing-masing ukuran dan geometri scaffold. Dari penelitian yang dilakukan, scaffold yang dihasilkan memiliki porositas berkisar 24%-77% dengan modulus elastisitas berkisar 1,6-4,5 Mpa. ...... This research focuses on the design and realization of 3D scaffold using biomaterial (PLA) with certain variations in size and geometry. Variations of these parameters will result in a certain scaffold with a porosity that have a correlation to the value of the modulus of elasticity (E) were tested via compressive test. Fabrication system fuse deposition modeling (FDM) used for scaffold fabrication assisted by CAD software in the design process. Through processing of the experimental data, resulting that the percentage of porosity is inversely proportional to the value of E is generated for each size and geometry of the scaffold. From the research, the resulting scaffold has a porosity ranging from 24% -77% with a modulus of elasticity ranging from 1.6 to 4.5 MPa.

Abstrak :
Geometri hiperbolik H^n, n>=2, merupakan salah satu contoh geometri non-Euclid. Pada artikelnya, Jeffers (2000) memberikan teorema mengenai bijeksi yang mempertahankan geodesik. Teorema tersebut menyatakan bahwa bijeksi yang mempertahankan geodesik di H^n adalah isometri. Pada kajian ini diberikan rincian bukti teorema di bidang hiperbolik H^2 dengan menggunakan model upper half plane. ......Hyperbolic geometry H^n, n>=2, is one of the example of non-Euclid Geometry. In his article, Jeffers (2000) present a theorem regarding bijection that preserves geodesic. The theorem states that bijection which preserves geodesic in H^n is an isometry. In this paper the proof of theorem in hyperbolic plane H^2 will be given with detail using upper half plane model.

Abstrak :
This book presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos.