Legendre transformations of curves
نویسندگان
چکیده
منابع مشابه
Legendre Transformations of Curves
In a recent paper of Wintner [l ], an extension is made of a classical theorem on the Legendre transformation of a convex function (for details of the proof, see [3], and for related results, cf. [4; 5]). His assumptions are that the function be strictly convex and of class C1. Here we shall prove a more general result which eliminates both of these restrictions and shows that, in a sense, they...
متن کاملDegree Elevation of Interval Bezier Curves Using Legendre-Bernstein Basis Transformations
This paper presents a simple matrix form for degree elevation of interval Bezier curve using LegendreBernstein basis transformations. The four fixed Kharitonov's polynomials (four fixed Bezier curves) associated with the original interval Bezier curve are obtained. These four fixed Bezier curves are expressed in terms of the Legendre polynomials. The process of degree elevations r times are app...
متن کاملL-functions of Twisted Legendre Curves
Let K be a global field of char p and let Fq be the algebraic closure of Fp in K. For an elliptic curve E/K with non-constant j-invariant, the L-function L(T,E/K) is a polynomial in 1+T ·Z[T ]. For any N > 1 invertible in K and finite subgroup T ⊂ E(K) of order N , we compute the mod N reduction of L(T,E/K) and determine an upper-bound for the order of vanishing at 1/q, the so-called analytic r...
متن کاملLegendre elliptic curves over finite fields
Throughout this paper, q > 1 denotes a power of an odd prime number p, and k is a field. Given two elliptic curves E/k and E′/k, all morphisms from E to E′ are understood to be defined over k. In particular, we simply write End(E) for the ring of all endomorphisms of E/k. The notation E ≃ E′ indicates that E is isomorphic to E′, and E ∼ E′ means that E and E′ are isogenous. The endomorphism of ...
متن کاملDiscontinuous Transformations and Lorenz Curves
In this study we reconsider the effect of variable transformations on the redistribution of income. Under the assumption that the theorems should hold for all income distributions, earlier given conditions are both necessary and sufficient. Different versions of the conditions are compared. We also consider the consequences if we drop the explicit continuity restriction on the transformations. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1954
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1954-0066704-x