Algorithms and identities for (p, q)-Bézier curves via (p, q)-Blossom Abstract In this paper, a new variant of the blossom, the (p, q)-blossom, is introduced, by altering the diagonal property of the standard blossom. This (p, q)-blossom is has been adapted for developing identities and algorithms for (p, q)-Bernstein bases and (p, q)-Bézier curves. We generate several new identities including ...

The n-dimensional cube Q is the graph whose vertices are the subsets of {1, . . . , n} where two such vertices are adjacent if and only if their symmetric difference is a singleton. Clearly Q is an n-connected graph of diameter and radius n. Write M = n2n−1 = e(Q) for the size of Q. Let Q̃ = (Qt) M 0 be a random Q -process. Thus Qt is a spanning subgraph of Q n of size t, and Qt is obtained from...

We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of form q(x1,?,xn)=m, where q is a non-degenerate integral quadratic n?3 variables and m non-zero integer. This gives asymptotic formulas density points taking coprime polynomial values, which quantitative version arithmetic purity strong approximation off infinity quadrics.

Abstract We introduce two properties: strong R-property and $C(q)$ -property, describing a special way of divergence nearby trajectories for an abstract measure-preserving system. show that systems satisfying the are disjoint (in sense Furstenberg) with -property. Moreover, we if $u_t$ is unipotent flow on $G/\Gamma $ $\Gamma irreducible, then satisfies -property provided not form $h_t\times \o...

During the workshop entitled “Discrete Tomography”, held in Volkrange on March 22, 1999, A. Kuba presented the open problem of reconstructing discrete sets satisfying the properties of connectivity and convexity by projections taken along many directions. In this paper, we study this problem, considering a similar property of discrete sets: the Q-convexity. In fact this property contains a cert...

During the workshop entitled “Discrete Tomography”, held in Volkrange on March 22, 1999, A. Kuba presented the open problem of reconstructing discrete sets satisfying the properties of connectivity and convexity by projections taken along many directions. In this paper, we study this problem, considering a similar property of discrete sets: the Q-convexity. In fact this property contains a cert...

Let p be a prime and K a number field of degree p. We count the number of elliptic curves, up to K-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup, or that it has an isogeny of prescribed degree. We also study the following question: for a given n such that |Y0(n)(Q)| > 0, does every elliptic curve over K with ...

We establish some notation. Let N be prime and set S = SpecZ[1/2N ]. Denote by XQ = X0(N)/Q and JQ = J0(N) the usual modular curve and its Jacobian over Q, where we normalize the embedding XQ →֒ JQ by requiring ∞ 7→ 0. XQ is the generic fiber of the (smooth) S-curve X = X0(N)/S , and JQ has Néron model J = NéronS(J0(N)), which is in fact an abelian scheme over S. The Néron mapping property gives...

In this paper we propose a definition and construction of a new family of one-way candidate functions RN : Q N → Q , where Q = {0, 1, . . . , s− 1} is an alphabet with s elements. Special instances of these functions can have the additional property to be permutations (i.e. one-way permutations). These one-way functions have the property that for achieving the security level of 2 computations i...

The paper gives an upper bound on the size of a q-ary code of length n that has the k-identifiable parent property. One consequence of this bound is that the optimal rate of such a code is determined in many cases when q →∞ with k and n fixed.