Yazar "Ratiu, Andrei V." seçeneğine göre listele

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    A notion of robustness and stability of manifolds
    (Academic Press Inc Elsevier Science, 2008-06-01) Deniz, Ali; Koçak, Şahin; Ratiu, Andrei V.
    Starting from the notion of thickness of Parks we define a notion of robustness for arbitrary subsets of R-k and we investigate its relationship with the notion of positive reach of Federer. We prove that if a set M is robust, then its boundary a M is of positive reach and conversely (under very mild restrictions) if partial derivative M is of positive reach, then M is robust. We then prove that a closed non-empty robust set in R-k (different from R-k) is a codimension zero submanifold of class C-1 with boundary. As a partial converse we show that any compact codimension zero submanifold with boundary of class C-2 is robust. Using the notion of robustness we prove a kind of stability theorem for codimension zero compact submanifolds with boundary: two such submanifolds, whose boundaries are close enough (in the sense of Hausdorff distance), are diffeomorphic. (C) 2007 Elsevier Inc. All rights reserved.
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    Chaotic n-dimensional euclidean and hyperbolic open billiards and chaotic spinning planar billiards
    (2008) Ratiu, Andrei V.
    We propose a new method to handle the n-dirnensional billiard problem in the exterior of a finite mutually disjoint union of convex (but not necessarily strictly convex) smooth obstacles without eclipse in the Euclidean or hyperbolic n-space, and we prove that there exist trajectories visiting the obstacles in any given doubly infinite prescribed order (with the obvious restriction of no consecutive repetition). As an interesting variant of planar billiards, we consider spinning obstacles and particles and prove that any forward sequence of obstacles has a trajectory that follows it.© 2008 Society for Industrial and Applied Mathematics.
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    Hiperbolik uzayda bazı ideal çokyüzlülerin hacimleri üzerine
    (Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik, 2002) Ratiu, Andrei V.; Deniz, Ali
    -Öz:-3-boyutlu hiperbolik uzayda, hacim hesabında sıkça kullanılan Lobachevsky fonksiyonu Extra close brace or missing open brace JI(theta)=?intt0hetalog|2sinx|dx şeklinde tanımlanır. Hiperbolik uzayda düzgün, ideal dörtyüzlünün hacminin 3JI(fracpi3) oldu