منابع مشابه
Polynomial iteration in characteristic p ∗ †
Let f(x) = ∑d s=0 asx s ∈ Z[x] be a polynomial with ad 6≡ 0 mod p. Take z ∈ Fp and let Oz = {fi(z)}i∈Z+ ⊂ Fp be the orbit of z under f , where fi(z) = f(fi−1(z)) and f0(z) = z. For M < |Oz|, we study the diameter of the partial orbit Oz,M = {z, f(z), f2(z), . . . , fM−1(z)} and prove that diam Oz,M & min { M c log logM , Mp , M 1 2p 1 2 } , where ‘diameter’ is naturally defined in Fp and c depe...
متن کاملCharacteristic Polynomial
A [ An−1 + p1A n−2 + · · ·+ pn−1 In ] = −pn In . Since A is nonsingular, pn = (−1)n det(A) 6= 0; thus the result follows. Newton’s Identity. Let λ1, λ2, . . . , λn be the roots of the polynomial K(λ) = λ + p1λ n−1 + p2λ n−2 + · · · · · ·+ pn−1λ+ pn. If sk = λ k 1 + λ k 2 + · · ·+ λn, then pk = − 1 k (sk + sk−1 p1 + sk−2 p2 + · · ·+ s2 pk−2p1 + s1 pk−1) . Proof. From K(λ) = (λ − λ1)(λ − λ2) . . ...
متن کاملChaotic iteration for polynomial constraints
In this paper we argue for an alternative way of designing solvers based on interval arithmetic. We achieve constraint propagation over real numbers using chaotic iteration, a general and basic technique used for computing limits of iterations of nite sets of functions. This is carried out in two steps: rst involving computationally \cheap" functions for reducing constraint satisfaction problem...
متن کاملRelationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...
متن کاملSingularities in characteristic 0 and characteristic p
1 Characteristic 0 We start with a basic question: given a polynomial f ∈ C[z1, · · · , zn] with a singularity at 0, how can we measure the “singularness” of this polynomial in a precise way? In other words: we can look at various singularities and see intuitively that some singularities are worse than others. For instance, it feels like a transverse self-intersection is probably not as bad as ...
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: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.08.018