منابع مشابه
Algorithms for projecting points onto conics
We study the problem of projecting 2D points onto quadratic curves (ellipses, hyperbolas, parabolas). We investigate various projection algorithms focusing on those that are mathematically proven to produce (or converge to) correct results in all cases. Our tests demonstrate that thosemaybe still unfit for practical use due to large computational errors. We present two new algorithms that are n...
متن کاملA Family of Conics and Three Special Ruled Surfaces
In [5] the authors presented a family F = {ck | k ∈ R} of conics. The conics ck are gained by offsetting from a given conic c0 with proportional distance functions kδ(t). We investigate certain properties of F and give the correct version of a result claimed in [5]: The distance function is unique (up to a constant factor) only if c0 is not a parabola. Furthermore we deal with the surfaces that...
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Let K ⊆ R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence of this, we can show that the set of points with a unique coding is a graph-directed selfsimi...
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Self-similar fractals arise as the unique attractors of iterated function systems (IFSs) consisting of finitely many contracting similarities satisfying an open set condition. Each point x in such a fractal F arising from an IFS S is naturally regarded as the “outcome” of an infinite coding sequence T (which need not be unique) over the alphabet Σk = {0, . . . , k − 1}, where k is the number of...
متن کاملThe Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp
Let p be a prime number, Fp be a finite field, and let k ∈ Fp. In this paper, we consider the number of rational points on conics Cp,k : x − ky = 1 over Fp. We proved that the order of Cp,k over Fp is p− 1 if k is a quadratic residue mod p and is p+1 if k is not a quadratic residue mod p. Later we derive some results concerning the sums ∑ C [x] p,k(Fp) and ∑ C [y] p,k(Fp), the sum of x− and y−c...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1903
ISSN: 0002-9947
DOI: 10.2307/1986416