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1.
In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I—convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also
give an example to show that the classical Korovkin Theory does not work but the theory works in I—convergence sense.
相似文献
2.
Torsten Ekedahl 《Arkiv f?r Matematik》1984,22(1):185-239
Summary Due to the length this work is published in two parts. The second part will appear in Vol 23: 1 of this journal.
Part 1 has the subtitle “Duality for the de Rham—Witt complex” and Part 2 is entitled “A Künneth formula for the Hodge—Witt complex”. 相似文献
3.
M. I. D’yachenko 《Russian Mathematics (Iz VUZ)》2008,52(5):32-40
Earlier we introduced a continuous scale of monotony for sequences (classes M α, α ≥ 0), where, for example, M 0 is the set of all nonnegative vanishing sequences, M 1 is the class of all nonincreasing sequences, tending to zero, etc. In addition, we extended several results obtained for trigonometric series with monotone convex coefficients onto more general classes. The main result of this paper is a generalization of the well-known Hardy—Littlewood theorem for trigonometric series, whose coefficients belong to classes M α, where α ∈ ( $ \tfrac{1} {2} Earlier we introduced a continuous scale of monotony for sequences (classes M
α, α ≥ 0), where, for example, M
0 is the set of all nonnegative vanishing sequences, M
1 is the class of all nonincreasing sequences, tending to zero, etc. In addition, we extended several results obtained for
trigonometric series with monotone convex coefficients onto more general classes. The main result of this paper is a generalization
of the well-known Hardy—Littlewood theorem for trigonometric series, whose coefficients belong to classes M
α, where α ∈ (, 1). Namely, the following assertion is true.
Let α ∈ (, 1), < p < 2, a sequence a ∈ M
α, and . Then the series cos nx converges on (0,2π) to a finite function f(x) and f(x) ∈ L
p
(0,2π).
Original Russian Text ? M.I. D’yachenko, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Matematika, 2008, No.
5, pp. 38–47. 相似文献
4.
Broué and Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to the π-block theory of
a π-separable group, defines the nilpotency of a π-block, and proves that there is a unique B
π′-character in a nilpotent π-block.
This work was partially supported by the National Natural Science Foundation of China (Grant No. 10771132) and Beijing Educational
Committee (Grant No. Km200510028002) 相似文献
5.
J. J. Macys 《Lithuanian Mathematical Journal》2005,45(3):284-291
We consider the factorial quotients (2n − 1)!!/(2n)!! in connection with the Wallis formula n
−1(2n)!!2/(2n − 1)!!2 → π. We improve the Wallis inequalities (n + 1/2)−1(2n)!!2/(2n − 1)!!2 < π < n
−1(2n)!!2/(2n − 1)!!2 for π and obtain new estimates of factorial quotients with error order not worse than 1/n
2.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 349–358, July–September, 2005. 相似文献
6.
Stochastic 2-D Navier—Stokes Equation 总被引:1,自引:0,他引:1
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
7.
The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera
equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power
and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z
0 are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also
determined.
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8.
Christiansen 《Constructive Approximation》2008,19(1):1-22
Abstract. We consider the indeterminate Stieltjes moment problem associated with the q -Laguerre polynomials. A transformation of the set of solutions, which has all the classical solutions as fixed points, is
established and we present a method to construct, for instance, continuous singular solutions. The connection with the moment
problem associated with the Stieltjes—Wigert polynomials is studied; we show how to come from q -Laguerre solutions to Stieltjes—Wigert solutions by letting the parameter α —> ∞ , and we explain how to lift a Stieltjes—Wigert solution to a q -Laguerre solution at the level of Pick functions. Based on two generating functions, expressions for the four entire functions
from the Nevanlinna parametrization are obtained. 相似文献
9.
Model selection for regression on a fixed design 总被引:1,自引:0,他引:1
Yannick Baraud 《Probability Theory and Related Fields》2000,117(4):467-493
We deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic
design points. For this end, we consider some collection of finite dimensional linear spaces (models) and the least-squares
estimator built on a data driven selected model among this collection. This data driven choice is performed via the minimization
of some penalized model selection criterion that generalizes on Mallows' C
p
. We provide non asymptotic risk bounds for the so-defined estimator from which we deduce adaptivity properties. Our results
hold under mild moment conditions on the errors. The statement and the use of a new moment inequality for empirical processes
is at the heart of the techniques involved in our approach.
Received: 2 July 1997 / Revised version: 20 September 1999 / Published online: 6 July 2000 相似文献
10.
Let T ∈ ℒ(X) be a bounded operator on a complex Banach space X. If V is an open subset of the complex plane such that λ-T is of Kato-type for each λ ∈ V, then the induced mapping f(z) ↦ (z-T)f(z) has closed range in the Fréchet space of analytic X-valued functions on V. Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to
a sharper estimate of Nagy’s spectral residuum of T. Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and Putinar and the theory of coherent analytic
sheaves. 相似文献
11.
We extend the results of Pollard [4] and give asymptotic estimates for the norm of the Fourier—Gegenbauer projection operator
in the appropriate weighted L
p
space. In particular, we settle the question of whether the projection is bounded for p=(2λ+1)/λ and p=(2λ+1)/(λ+1) , where λ is the index for the family of Gegenbauer polynomials under consideration.
March 19, 1997. Date revised: June 3, 1998. Date accepted: August 1, 1998. 相似文献
12.
We study the Bloch constant for Κ-quasiconformal holomorphic mappings of the unit ball B of C
n
. The final result we prove in this paper is: If f is a Κ-quasiconformal holomorphic mappig of B into C
n
such that det(f′(0)) = 1, then f(B) contains a schlicht ball of radius at least
where C
n
> 1 is a constant depending on n only, and as n→∞.
Received June 24, 1998, Accepted January 14, 1999 相似文献
13.
Liviu C. Florescu 《Central European Journal of Mathematics》2007,5(4):619-638
We introduce two notions of tightness for a set of measurable functions — the finite-tightness and the Jordan finite-tightness
with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness)
to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov
theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of measurable
mappings on a finite family of sets of small measure. In the Euclidean case, the Jordan finite-tight sets form a subclass
of finite-tight sets for which the finite family of sets of small measure is composed by d-dimensional intervals. The main result affirms that each tight set H ⊆ W
1,1 for which the set of the gradients ∇H is a Jordan finite-tight set is relatively compact in measure. This result offers very good conditions to use fiber product
lemma for obtaining a relaxed lower semicontinuity condition.
相似文献
14.
The limit as ɛ→ 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is
shown that limit value functions exist and solve in a viscosity sense a Hamilton—Jacobi equation. The Hamiltonian of this
equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and
the limit Hamilton—Jacobi equation are applicable in cases where the reduction of order, namely setting ɛ = 0 , does not yield an optimal behavior.
Accepted 18 November 1999 相似文献
15.
含有p拉普拉斯算子方程的解的存在性研究 总被引:3,自引:0,他引:3
By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978), the abstract result on the existence of a solution u ∈ Lp (Ω) to nonlinear equations involving p-Laplacian operator △p, where 2N/N 1 < p < ∞ and N (≥ 1 )denotes the dimension of RN,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result ,some new techniques are used. 相似文献
16.
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
17.
The concepts of ℒ*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the ℒ*-inverse
semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups.
We shall also provide a constructed example for the ℒ*-inverse semigroups by using the left wreath products. 相似文献
18.
M. Hărăguş 《Journal of Nonlinear Science》1998,8(4):353-374
Summary. For a certain class of partial differential equations in cylindrical domains, we show that all small time-dependent solutions
are described by a reduced system of equations on the real line, which contains nonlocal terms. As an application, we investigate
the system describing nonlinear water waves travelling on the free surface of an inviscid fluid. Two-dimensional gravity waves
are characterized by the parameter λ , the inverse square of the Froude number. For λ close to the critical value λ
0
=1 , we obtain a reduced system of four nonlocal equations. We show that the terms of lowest order in μ=λ-1 lead to the Korteweg—de Vries equation for the lowest-order approximation of the free surface.
Received February 23, 1994; final revision received October 13, 1997; accepted for publication October 16, 1997. 相似文献
19.
B. Al-Nashef 《Acta Mathematica Hungarica》2002,97(1-2):115-120
The following two decomposition theorems are obtained. (1) A function f is α-continuous if and only if f is pre-continuous and αα-continuous, (2) A function f is semi-continuous if and only if f is spr-continuous and αLC-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
本文利用文[2,3]的引理和算子L(a,c)f(z)的一些性质.结合Hadamard乘积,研究了算子L(a,c)f(z),获得了L(a,c)f(z)∈S*(β)和L(a,c)f(z)∈K(β)的充分条件,推广了文[2,3]的相关结论. 相似文献