共查询到20条相似文献,搜索用时 31 毫秒
1.
Piotr Szuca 《Central European Journal of Mathematics》2013,11(1):170-176
Given a free ultrafilter p on ? we say that x ∈ [0, 1] is the p-limit point of a sequence (x n ) n∈? ? [0, 1] (in symbols, x = p -lim n∈? x n ) if for every neighbourhood V of x, {n ∈ ?: x n ∈ V} ∈ p. For a function f: [0, 1] → [0, 1] the function f p : [0, 1] → [0, 1] is defined by f p (x) = p -lim n∈? f n (x) for each x ∈ [0, 1]. This map is rarely continuous. In this note we study properties which are equivalent to the continuity of f p . For a filter F we also define the ω F -limit set of f at x. We consider a question about continuity of the multivalued map x → ω f F (x). We point out some connections between the Baire class of f p and tame dynamical systems, and give some open problems. 相似文献
2.
R.S. Singh 《Journal of multivariate analysis》1976,6(1):111-122
On the basis of a random sample of size n on an m-dimensional random vector X, this note proposes a class of estimators fn(p) of f(p), where f is a density of X w.r.t. a σ-finite measure dominated by the Lebesgue measure on Rm, p = (p1,…,pm), pj ≥ 0, fixed integers, and for x = (x1,…,xm) in Rm, f(p)(x) = ?p1+…+pm f(x)/(?p1x1 … ?pmxm). Asymptotic unbiasedness as well as both almost sure and mean square consistencies of fn(p) are examined. Further, a necessary and sufficient condition for uniform asymptotic unbisedness or for uniform mean square consistency of fn(p) is given. Finally, applications of estimators of this note to certain statistical problems are pointed out. 相似文献
3.
Lenny Jones 《Journal of Number Theory》2011,131(11):2100-2106
A sequence of prime numbers p1,p2,p3,…, such that pi=2pi−1+? for all i, is called a Cunningham chain of the first or second kind, depending on whether ?=1 or −1 respectively. If k is the smallest positive integer such that 2pk+? is composite, then we say the chain has length k. It is conjectured that there are infinitely many Cunningham chains of length k for every positive integer k. A sequence of polynomials f1(x),f2(x),… in Z[x], such that f1(x) has positive leading coefficient, each fi(x) is irreducible in Q[x] and fi(x)=xfi−1(x)+? for all i, is defined to be a polynomial Cunningham chain of the first or second kind, depending on whether ?=1 or −1 respectively. If k is the least positive integer such that fk+1(x) is reducible in Q[x], then we say the chain has length k. In this article, for polynomial Cunningham chains of both kinds, we prove that there are infinitely many chains of length k and, unlike the situation in the integers, that there are infinitely many chains of infinite length, by explicitly giving infinitely many polynomials f1(x), such that fk+1(x) is the only term in the sequence that is reducible. 相似文献
4.
Krishnaswami Alladi 《Journal of Number Theory》1982,14(1):86-98
Let p(n) denote the smallest prime factor of an integer n>1 and let p(1)=∞. We study the asymptotic behavior of the sum M(x,y)=Σ1≤n≤x,p(n)>yμ(n) and use this to estimate the size of A(x)=max|f|≤1|Σ2≤n<xμ(n)f(p(n))|, where μ(n) is the Moebius function. Applications of bounds for A(x), M(x,y) and similar quantities are discussed. 相似文献
5.
We consider exact and approximate multivariate interpolation of a function f(x 1?,?.?.?.?,?x d ) by a rational function p n,m /q n,m (x 1?,?.?.?.?,?x d ) and develop an error formula for the difference f???p n,m /q n,m . The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. 相似文献
6.
Xiaolong Li 《Bulletin of the Brazilian Mathematical Society》2012,43(1):73-98
For a homoclinic class H(p f ) of f ?? Diff1(M), f?OH(p f ) is called R-robustly entropy-expansive if for g in a locally residual subset around f, the set ?? ? (x) = {y ?? M: dist(g n (x), g n (y)) ?? g3 (?n ?? ?)} has zero topological entropy for each x ?? H(p g ). We prove that there exists an open and dense set around f such that for every g in it, H(p g ) admits a dominated splitting of the form E ?? F 1 ?? ... ?? F k ?? G where all of F i are one-dimensional and non-hyperbolic, which extends a result of Pacifico and Vieitez for robustly entropy-expansive diffeomorphisms. Some relevant consequences are also shown. 相似文献
7.
A. Moudafi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):704-709
We consider a variable Krasnosel’skii-Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping proxλf. The novelty of our approach is that the latter is not non-expansive any longer. We prove that the sequence generated by such algorithm (via the formula xk+1=(1−αk)xk+αkproxλkfxk, where (αk) is a sequence in (0,1)), is an approximate fixed-point of the proximal mapping and converges provided that the function under consideration satisfies a local metric regularity condition. 相似文献
8.
Nikola Sandrić 《Journal of Theoretical Probability》2014,27(3):754-788
We give recurrence and transience criteria for two cases of time-homogeneous Markov chains on the real line with transition kernel p(x,dy)=f x (y?x)?dy, where f x (y) are probability densities of symmetric distributions and, for large |y|, have a power-law decay with exponent α(x)+1, with α(x)∈(0,2). If f x (y) is the density of a symmetric α-stable distribution for negative x and the density of a symmetric β-stable distribution for non-negative x, where α,β∈(0,2), then the chain is recurrent if and only if α+β≥2. If the function x?f x is periodic and if the set {x:α(x)=α 0:=inf x∈? α(x)} has positive Lebesgue measure, then, under a uniformity condition on the densities f x (y) and some mild technical conditions, the chain is recurrent if and only if α 0≥1. 相似文献
9.
Let f be an entire function of exponential type satisfying the condition $ f(z) \equiv e^{i\gamma } e^{i\tau z} \overline {f(\bar z)} $ for some real γ. Lower and upper estimates for ∫ ?∞ ∞ |f′(x)| p dx in terms of ∫ ?∞ ∞ |f(x)| p dx, for such a function f belonging to L p (R), have been known in the case where p ? [1, ∞) and γ = 0. In this paper, these estimates are shown to hold for any p ? (0, ∞) and any real γ. 相似文献
10.
《Finite Fields and Their Applications》2001,7(1):205-237
Let Fq be the finite field of q elements with characteristic p and Fqm its extension of degree m. Fix a nontrivial additive character Ψ of Fp. If f(x1,…, xn)∈Fq[x1,…, xn] is a polynomial, then one forms the exponential sum Sm(f)=∑(x1,…,xn)∈(Fqm)nΨ(TrFqm/Fp(f(x1,…,xn))). The corresponding L functions are defined by L(f, t)=exp(∑∞m=0Sm(f)tm/m). In this paper, we apply Dwork's method to determine the Newton polygon for the L function L(f(x), t) associated with one variable polynomial f(x) when deg f(x)=4. As an application, we also give an affirmative answer to Wan's conjecture for the case deg f(x)=4. 相似文献
11.
Hans Peter Schlickewei 《Journal of Number Theory》1977,9(3):370-380
In his paper [Ann. of Math.96 (1972)] Schmidt applied his results on the n-dimensional Roth theorem to study the n-dimensional Thue equation f(x1,…, xn) = c, and he proved, when f is of norm type, a necessary and sufficient criterion for the Thue equation to have only finitely many solutions. Here we shall study equations f(x1,…, xn) = p1z1 … ptzt and prove the p-adic analog of Schmidt's theorems. 相似文献
12.
Zachary Robinson 《manuscripta mathematica》1993,80(1):45-71
Ap-adic subanalytic set shares with a real subanalytic set the fundamental property that its singular locus is itself subanalytic. Furthermore, given ap-adic subanalytic function ? with domain contained in ? p m , there is an integerL such that for any pointx 0 ∈ ? p m in a neighborhood of whichf is defined,f has a Taylor approximation up to orderL atx 0 if, and only if, ? is analytic aroundx 0. These results extend to thep-adic fields real variables theorems by M. Tamm [21]. 相似文献
13.
S.A McGrath 《Journal of Functional Analysis》1976,23(3):195-198
Let (X, ∑, μ) be a σ-finite measure space and Lp(μ) = Lp(X, ∑, μ), 1 ? p ? ∞, the usual Banach spaces of complex-valued functions. Let {Tt: t ? 0} be a strongly continuous semigroup of positive Lp(μ) operators for some 1 ? p < ∞. Denote by Rλ the resolvent of {Tt}. We show that f?Lp(μ) implies λRλf(x) → f(x) a.e. as λ → ∞. 相似文献
14.
V.P. Gomes Neto 《Journal of Differential Equations》2010,249(11):2822-2865
We consider differential equations which describe pseudospherical surfaces, with associated 1-forms , 1?i?3. We characterize all such equations of type ut=uxxxxx+G(u,ux,…,uxxxx) whose associated 1-forms satisfy fp1=μpf11+ηp, μp,ηp∈R, 2?p?3, in addition to a generic technical assumption. We also classify all of these equations which are independent of any of the real parameters μp, ηp, obtaining as particular cases the fifth-order Korteweg-de Vries, the Sawada-Kotera and the Kaup-Kupershmidt equations. We determine huge classes of equations describing pseudospherical surfaces and their respective linear problems in which particular cases are obtained by merely specifying certain functions which depend on u and its derivatives with respect to x. 相似文献
15.
A. A. Agrachev 《Mathematical Notes》1974,16(4):897-900
We show that if Φ is an arbitrary countable set of continuous functions of n variables, then there exists a continuous, and even infinitely smooth, function ψ(x1,...,xn) such that ψ(x 1, ...,x n ) ?g [? (f 1(x 1, ... ,f f (x n ))] for any function ? from Φ and arbitrary continuous functions g and fi, depending on a single variable. 相似文献
16.
Shaofang Hong 《Linear algebra and its applications》2006,416(1):124-134
Let S = {x1, … , xn} be a set of n distinct positive integers and f be an arithmetical function. Let [f(xi, xj)] denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) of xi and xj as its i, j-entry and (f[xi, xj]) denote the n × n matrix having f evaluated at the least common multiple [xi, xj] of xi and xj as its i, j-entry. The set S is said to be lcm-closed if [xi, xj] ∈ S for all 1 ? i, j ? n. For an integer x > 1, let ω(x) denote the number of distinct prime factors of x. Define ω(1) = 0. In this paper, we show that if S = {x1, … , xn} is an lcm-closed set satisfying , and if f is a strictly increasing (resp. decreasing) completely multiplicative function, or if f is a strictly decreasing (resp. increasing) completely multiplicative function satisfying (resp. f(p) ? p) for any prime p, then the matrix [f(xi, xj)] (resp. (f[xi, xj])) defined on S is nonsingular. By using the concept of least-type multiple introduced in [S. Hong, J. Algebra 281 (2004) 1-14], we also obtain reduced formulas for det(f(xi, xj)) and det(f[xi, xj]) when f is completely multiplicative and S is lcm-closed. We also establish several results about the nonsingularity of LCM matrices and reciprocal GCD matrices. 相似文献
17.
Tauno Metsänkylä 《Journal of Number Theory》1978,10(4):510-522
Let f(x, χ) be the Iwasawa power series for the p-adic L-function Lp(s, χ), where χ is an even nonprincipal character with conductor not divisible by p2 (or by 8, when p = 2). The divisibility by p of the first p coefficients of f(x, χ) is characterized by Kummer type congruences of generalized Bernoulli numbers. Applications to Iwasawa invariants and class numbers of imaginary Abelian fields are discussed. 相似文献
18.
J. Bourgain 《Israel Journal of Mathematics》1992,77(1-2):1-16
We study the almost everythere convergence to the initial dataf(x)=u(x, 0) of the solutionu(x, t) of the two-dimensional linear Schrödinger equation Δu=i? t u. The main result is thatu(x, t) →f(x) almost everywhere fort → 0 iff ∈H p (R2), wherep may be chosen <1/2. To get this result (improving on Vega’s work, see [6]), we devise a strategy to capture certain cancellations, which we believe has other applications in related problems. 相似文献
19.
D. Li 《Journal of Mathematical Sciences》2010,171(1):116-129
We consider a class of nonlinear recurrent systems of the form \( {\Lambda_p} = \frac{1}{p}\sum\limits_{{p_1} = 1}^{p - 1} {f\left( {\frac{{{p_1}}}{p}} \right){\Lambda_{{p_1}}}{\Lambda_{p - {p_1}}}} \), p > 1, where f is a given function on the interval [0, 1] and Λ1 = x is an adjustable real-valued parameter. Under some suitable assumptions on the function f, we show that there exists an initial value x * for which Λ p = Λ p (x * ) → const as p → ∞. More precise asymptotics of Λ p is also derived. 相似文献
20.
Jason P. Bell 《Discrete Mathematics》2007,307(23):3070-3075
A sequence is said to be k-automatic if the nth term of this sequence is generated by a finite state machine with n in base k as input. Regular sequences were first defined by Allouche and Shallit as a generalization of automatic sequences. Given a prime p and a polynomial f(x)∈Qp[x], we consider the sequence , where vp is the p-adic valuation. We show that this sequence is p-regular if and only if f(x) factors into a product of polynomials, one of which has no roots in Zp, the other which factors into linear polynomials over Q. This answers a question of Allouche and Shallit. 相似文献