共查询到20条相似文献，搜索用时 281 毫秒
1.
Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:
where (λ
n
) is a sequence of positive steps. Algorithm may be viewed as the discretized equation of a nonlinear oscillator subject to friction. We prove that, if 0 ∈ int (A(0)) (condition of dry friction), then the sequence (x
n
) generated by is strongly convergent and its limit x
∞ satisfies 0 ∈ A(0) + B(x
∞). We show that, under a general condition, the limit x
∞ is achieved in a finite number of iterations. When this condition is not satisfied, we prove in a rather large setting that
the convergence rate is at least geometrical. 相似文献
2.
We analyze polynomials P
n
that are biorthogonal to exponentials
, in the sense that
Here α>−1. We show that the zero distribution of P
n
as n→∞ is closely related to that of the associated exponent polynomial
More precisely, we show that the zero counting measures of {P
n
(−4nx)}
n=1∞ converge weakly if and only if the zero counting measures of {Q
n
}
n=1∞ converge weakly. A key step is relating the zero distribution of such a polynomial to that of the composite polynomial
under appropriate assumptions on {Δ
n,j
}.
相似文献
3.
4.
A. I. Aptekarev J. S. Dehesa A. Martínez-Finkelshtein R. Yáñez 《Constructive Approximation》2009,30(1):93-119
Given a nontrivial Borel measure on ℝ, let p
n
be the corresponding orthonormal polynomial of degree n whose zeros are λ
j
(n), j=1,…,n. Then for each j=1,…,n,
with
defines a discrete probability distribution. The Shannon entropy of the sequence {p
n
} is consequently defined as
In the case of Chebyshev polynomials of the first and second kinds, an explicit and closed formula for
is obtained, revealing interesting connections with number theory. In addition, several results of numerical computations
exemplifying the behavior of
for other families are presented.
相似文献
5.
J. V. Manojlović 《Lithuanian Mathematical Journal》2009,49(1):71-92
We consider a class of fourth-order nonlinear difference equations of the form
where α and β are the ratios of odd positive integers, and {p
n
} and {q
n
} are positive real sequences defined for all
satisfying the condition
We classify the nonoscillatory solutions of (Ω) and establish necessary and/or sufficient conditions for the existence of
nonoscillatory solutions with specific asymptotic behavior.
Supported by Ministry of Science, Technology and Development of Republic of Serbia – Grant No. 144003. 相似文献
6.
Let {xn}n∈ℕ be a sequence in [0, 1]d , {λn}n∈ℕ a sequence of positive real numbers converging to 0, and δ > 1. The classical ubiquity results are concerned with the computation of the Hausdorff dimension of limsup-sets of the form
Let μ be a positive Borel measure on [0, 1]d , ρ 2 (0, 1] and α > 0. Consider the finer limsup-set
We show that, under suitable assumptions on the measure μ, the Hausdorff dimension of the sets Sμ(ρ, δ, α) can be computed. Moreover, when ρ < 1, a yet unknown saturation phenomenon appears in the computation of the Hausdorff dimension of Sμ(ρ, δ, α). Our results apply to several classes of multifractal measures, and S(δ) corresponds to the special case where μ is a monofractal measure like the Lebesgue measure.
The computation of the dimensions of such sets opens the way to the study of several new objects and phenomena. Applications
are given for the Diophantine approximation conditioned by (or combined with) b-adic expansion properties, by averages of some Birkhoff sums and branching randomwalks, as well as by asymptotic behavior
of random covering numbers. 相似文献
7.
We consider the computation of stable approximations to the exact solution of nonlinear ill-posed inverse problems F(x) = y with nonlinear operators F : X → Y between two Hilbert spaces X and Y by the Newton type methods
in the case that only available data is a noise of y satisfying with a given small noise level . We terminate the iteration by the discrepancy principle in which the stopping index is determined as the first integer such that
with a given number τ > 1. Under certain conditions on {α
k
}, {g
α
} and F, we prove that converges to as and establish various order optimal convergence rate results. It is remarkable that we even can show the order optimality
under merely the Lipschitz condition on the Fréchet derivative F′ of F if is smooth enough. 相似文献
8.
Sun Zhonghua Qi Wenfeng 《高校应用数学学报(英文版)》2007,22(4):469-477
Let Z/(pe) be the integer residue ring modulo pe with p an odd prime and integer e ≥ 3. For a sequence (a) over Z/(pe), there is a unique p-adic decomposition (a) = (a)0 (a)1·p … (a)e-1 ·pe-1, where each (a)i can be regarded as a sequence over Z/(p), 0 ≤ i ≤ e - 1. Let f(x) be a primitive polynomial over Z/(pe) and G' (f(x), pe) the set of all primitive sequences generated by f(x) over Z/(pe). For μ(x) ∈ Z/(p)[x] with deg(μ(x)) ≥ 2 and gcd(1 deg(μ(x)),p- 1) = 1,set ψe-1 (x0, x1,…, xe-1) = xe-1·[ μ(xe-2) ηe-3 (x0, x1,…, xe-3)] ηe-2 (x0, x1,…, xe-2),which is a function of e variables over Z/(p). Then the compressing map ψe-1: G'(f(x),pe) → (Z/(p))∞,(a) (→)ψe-1((a)0, (a)1,… ,(a)e-1) is injective. That is, for (a), (b) ∈ G' (f(x), pe), (a) = (b) if and only if ψe - 1 ((a)0, (a)1,… , (a)e - 1) =ψe - 1 ((b)0,(b)1,… ,(b)e-1). As for the case of e = 2, similar result is also given. Furthermore, if functions ψe-1 and ψe-1 over Z/(p) are both of the above form and satisfy ψe-1((a)0,(a)1,… ,(a)e-1) = ψe-1((b)0,(b)1,… ,(b)e-1) for (a),(b) ∈ G'(f(x),pe), the relations between (a) and (b), ψe-1 and ψe-1 are discussed. 相似文献
9.
L. V. Rozovsky 《Journal of Mathematical Sciences》2009,159(3):341-349
Let Sn = X1 + · · · + X
n
, n ≥ 1, and S
0 = 0, where X
1, X
2, . . . are independent, identically distributed random variables such that the distribution of S
n/B
n converges weakly to a nondeoenerate distribution F
α
as n → ∞ for some positive B
n
. We study asymptotic behavior of sums of the form
where
a function d(t) is continuous at [0,1] and has power decay at zero,
Bibliography: 13 titles.
Translated from Zapiski Nauchnylch Serninarov POMI, Vol. 361, 2008, pp. 109–122. 相似文献
10.
Jin Deng 《应用数学学报(英文版)》2006,22(1):163-170
In this paper, a nonlinear difference system {xn=βxn-1＋f（yn-κ）,yn=βyn-1＋f（xn-κ）,n∈N is considered a,nd sufficient conditions for the existe~lce of the stable 2κ ＋ 1 periodic solution are obtained. 相似文献
11.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
wherea
i
≠0 is integer,i=1,2…,s. In 1979, Schmidt proved that if ∈>0 then there is a large constantC(k,∈) such that fors>C(k,∈) the equationf(X)=0 has a nontrivial, integer solution in σ1, σ2, …, σ3,x
1,x
2, …,x
3 satisfying
Schmidt did not estimate this constantC(k,∈) since it would be extremely large. In this paper, we prove the following result 相似文献
12.
周英告 《高校应用数学学报(英文版)》2003,18(1):53-58
§ 1 ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) ) ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ… 相似文献
13.
Oscillation criteria for all solutions of the first order delay difference equation of the form
where {pn} is a sequence of nonnegative real numbers and k is a positive integer are established especially in the case that the well-known oscillation conditions
are not satisfied.
Dedicated to Professor Y.G. Sficas on the occasion of his 60h birthday 相似文献
14.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n（2 ＋ ∑i^n=1 mi）. 相似文献
15.
Yisheng Song 《Positivity》2009,13(4):643-655
In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by
, where f is a Lipschitz strong pseudocontractive mapping and {βn}, {αn} satisfy (i); (ii) ; (iii).
相似文献
16.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
and
almost surely for any continuity point x of G and for any bounded Lipschitz function f: R → R.
相似文献
17.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
We also show that
where ω(n) is the number of distinct prime divisors of n and p denotes prime numbers. These estimates improve several results from [6, 9].
Received: 23 November 2006 相似文献
18.
Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a
n
, 1;x
1), with
andnth approximant
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相似文献
19.
Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(4):611-622
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation
20.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
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