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1.
For given analytic functions ϕ(z) = z + Σ
n=2∞ λ
n
z
n
, Ψ(z) = z + Σ
n=2∞ μ with λ
n
≥ 0, μ
n
≥ 0, and λ
n
≥ μ
n
and for α, β (0≤α<1, 0<β≤1), let E(φ,ψ; α, β) be of analytic functions ƒ(z) = z + Σ
n=2∞
a
n
z
n
in U such that f(z)*ψ(z)≠0 and
for z∈U; here, * denotes the Hadamard product. Let T be the class of functions ƒ(z) = z - Σ
n=2∞|a
n
| that are analytic and univalent in U, and let E
T
(φ,ψ;α,β)=E(φ,ψ;α,β)∩T. Coefficient estimates, extreme points, distortion properties, etc. are determined for the class E
T
(φ,ψ;α,β) in the case where the second coefficient is fixed. The results thus obtained, for particular choices of φ(z) and ψ(z), not only generalize various known results but also give rise to several new results.
University of Bahrain, Isa Town, Bahrain. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1162–1170,
September, 1997. 相似文献
2.
We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition
where 0≤σ<+∞ and η is a positive function continuously differentiable on [0; +∞) and such thatxη′(x)/η(x)→0 asx→+∞.
Drohobych Pedagogic University, Drohobych. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 904–909,
July, 1999. 相似文献
3.
Mümün Can 《数学学报(英文版)》2004,20(2):193-200
In this work, Rademacher‘s two questions about Dedekind sums are applied to the Hardy sums s2(h,κ) and s3(h,κ). Some relations between these sums are obtained and some inequalities are given. 相似文献
4.
A. N. Tikhomirov 《Siberian Advances in Mathematics》2009,19(3):211-223
Let X:= (X
jk
) denote a Hermitian random matrix with entries X
jk
which are independent for all 1 ≤ j ≤ k. We study the rate of convergence of the expected spectral distribution function of the matrix X to the semi-circular law under the conditions E
X
jk
= 0, E
X
jk
2 = 1, and E|X
jk
|2+η
≤ M
η
< ∞, 0 < η ≤ 2. The bounds of order $
O(n^{ - \frac{\eta }
{{2 + \eta }}} )
$
O(n^{ - \frac{\eta }
{{2 + \eta }}} )
for 1 ≤ η ≤ 2, and those of order $
O(n^{ - \frac{{2\eta }}
{{(2 + \eta )(3 - \eta )}}} )
$
O(n^{ - \frac{{2\eta }}
{{(2 + \eta )(3 - \eta )}}} )
for 0 < η ≤ 1, are obtained. 相似文献
5.
Yuefei Wang 《Journal d'Analyse Mathématique》1997,71(1):87-102
Let f(z) be a meromorphic function in the plane. If ψ(t)/t andp(t) are two positive, continuous and non-decreasing functions on [1,∞) with ∫
1
∞
dt/ψ(t) = ∞ and ∫
1
∞
dt/p(t) = ∞, then
asr → ∞ outside a small exceptional set, provided that the divergence of the integral ∫
1
r
dt/ψ(t) is slow enough. The same forms for the logarithmic derivative and for the ramification term are obtained. It is shown by
example that the estimates are best possible.
Author supported by Max-Planck-Gesellschaft Z.F.D.W and by NSFC. 相似文献
6.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}The aim of this study is to prove global existence of classical solutions for systems of the form
\frac?u?t -a Du=-f(u,v){\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)} ,
\frac?v?t -b Dv=g(u,v){\frac{\partial v}{\partial t} -b \Delta v=g(u,v)} in (0, +∞) × Ω where Ω is an open bounded domain of class C
1 in
\mathbbRn{\mathbb{R}^n}, a > 0, b > 0 and f, g are nonnegative continuously differentiable functions on [0, +∞) × [0, +∞) satisfying f (0, η) = 0, g(x,h) £ C j(x)eahb{g(\xi,\eta) \leq C \varphi(\xi)e^{\alpha {\eta^\beta}}} and g(ξ, η) ≤ ψ(η)f(ξ, η) for some constants C > 0, α > 0 and β ≥ 1 where j{\varphi} and ψ are any nonnegative continuously differentiable functions on [0, +∞) such that j(0)=0{\varphi(0)=0} and limh? +¥hb-1y(h) = l{ \lim_{\eta \rightarrow +\infty}\eta^{\beta -1}\psi(\eta)= \ell} where ℓ is a nonnegative constant. The asymptotic behavior of the global solutions as t goes to +∞ is also studied. For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates
and Lyapunov functional methods. 相似文献
7.
In this paper, we consider a differentiable multiobjective optimization problem with generalized cone constraints (for short,
MOP). We investigate the relationship between weakly efficient solutions for (MOP) and for the multiobjective optimization
problem with the modified objective function and cone constraints [for short, (MOP)
η
(x)] and saddle points for the Lagrange function of (MOP)
η
(x) involving cone invex functions under some suitable assumptions. We also prove the existence of weakly efficient solutions
for (MOP) and saddle points for Lagrange function of (MOP)
η
(x) by using the Karush-Kuhn-Tucker type optimality conditions under generalized convexity functions. As an application, we
investigate a multiobjective fractional programming problem by using the modified objective function method. 相似文献
8.
Inspired by Riemann’s work on certain quotients of the Dedekind Eta function, in this paper we investigate the value distribution
of quotients of values of the Dedekind Eta function in the complex plane, using the form , where A
j-1 and A
j
are matrices whose rows are the coordinates of consecutive visible lattice points in a dilation XΩ of a fixed region Ω in , and z is a fixed complex number in the upper half plane. In particular, we show that the limiting distribution of these quotients
depends heavily on the index of Farey fractions which was first introduced and studied by Hall and Shiu. The distribution
of Farey fractions with respect to the value of the index dictates the universal limiting behavior of these quotients. Motivated
by chains of these quotients, we show how to obtain a generalization, due to Zagier, of an important formula of Hall and Shiu
on the sum of the index of Farey fractions.
A. Zaharescu is supported by National Science Foundation Grant DMS-0456615. 相似文献
9.
Analysis of FETI methods for multiscale PDEs 总被引:2,自引:0,他引:2
In this paper, we study a variant of the finite element tearing and interconnecting (FETI) method which is suitable for elliptic
PDEs with highly heterogeneous (multiscale) coefficients α(x); in particular, coefficients with strong variation within subdomains and/or jumps that are not aligned with the subdomain
interfaces. Using energy minimisation and cut-off arguments we can show rigorously that for an arbitrary (positive) coefficient
function the condition number of the preconditioned FETI system can be bounded by C(α) (1 + log(H/h))2 where H is the subdomain diameter and h is the mesh size, and where the function C(α) depends only on the coefficient variation in the vicinity of subdomain interfaces. In particular, if varies only mildly in a layer Ω
i,η
of width η near the boundary of each of the subdomains Ω
i
, then , independent of the variation of α in the remainder Ω
i
\Ω
i,η
of each subdomain and independent of any jumps of α across subdomain interfaces. The quadratic dependence of C(α) on H/η can be relaxed to a linear dependence under stronger assumptions on the behaviour of α in the interior of the subdomains.
Our theoretical findings are confirmed in numerical tests.
C. Pechstein was supported by the Austrian Science Funds (FWF) under grant F1306. 相似文献
10.
J. Sunklodas 《Acta Appl Math》2008,102(1):87-98
In the present paper, we consider L
1 bounds for asymptotic normality for the sequence of r.v.’s X
1,X
2,… (not necessarily stationary) satisfying the ψ-mixing condition. The L
1 bounds have been obtained in terms of Lyapunov fractions which, in a particular case, under finiteness of the third moments
of summands and the finiteness of ∑
r≥1
r
2
ψ(r), are of order O(n
−1/2), where the function ψ participates in the definition of the ψ-mixing condition.
相似文献
11.
Let Γ be a regular curve and Lp(Γ),1<p<+∞, be the class of all complex-valued functions f defined on Γ which are such that |f|p is integrable in sense of Lebesgue. In this work, we define the kth p-Faber polynomial Fk.p(z), the kth p-Faber principle part ≈Fk.p(1/z) for Γ, and defined the nth p-Faber-Laurent rational function Rn,p(f, z) and p-generalized modulus of continuity Ωp of a function f of Lp(Γ). We investigate some properties of Fk.p(z) and ≈Fk.p(1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ωp in the mean of functions of Lp(Γ) by the rational functions Rn.p(.,z). 相似文献
12.
Ramesh C. Gupta Mohammad Ahsanullah 《Annals of the Institute of Statistical Mathematics》2004,56(4):721-732
In this paper, we attempt to characterize a distribution by means ofE[ψ(X
k
+s:n)|X
k:n
=z]g(z), under some mild conditions on ψ(·) andg(·). An explicit result is provided in the case ofs=1 and a uniqueness result is proved in the case ofs=2. For the general case, an expression is provided for the conditional expectation. Similar results are proved for the record
values, both in the continuous as well as in the discrete case (weak records). 相似文献
13.
B. I. Peleshenko 《Ukrainian Mathematical Journal》2005,57(11):1741-1762
We prove theorems on interpolation of quasilinear operators of weak type (ϕ0, ψ0, ϕ0, ψ1) in Lorentz spaces. The operators under study are analogs of the Calderón operator and the Benett operator for concave and
convex functions ϕ0(t), ψ0(t), ϕ1(t), and ψ1(t).
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1490–1507, November, 2005. 相似文献
14.
We describe sequences of zeros of functions ƒ ≠ 0 that are analytic in the right half-plane and satisfy the condition |ƒ(z)| ≤ 0(1) exp (σ| z |η(| z |)), 0 ≤ <+ ∞, Re z > 0, where η: [0; + ∞) → (- ∞; + ∞) is a function of bounded variation.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1169–1176, September, 1998. 相似文献
15.
E. G. Goluzina 《Journal of Mathematical Sciences》2006,137(3):4774-4779
The paper studies the region of values Dm,1(T) of the system {ƒ(z1), ƒ(z2), …, ƒ(zm), ƒ(r)}, m e 1, where zj (j = 1, 2, …,m) are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0 (j = 1, 2, …,m), and r, 0 < r < 1, is fixed, in the class T of functions ƒ(z) = z+a2z2+ ⋯ regular in the disk U and satisfying in the latter the condition Im ƒ(z) Imz > 0 for Im z ≠ 0. An algebraic characterization of the set Dm,1(T) in terms of nonnegative-definite Hermitian forms is given, and all the boundary functions are described. As an implication,
the region of values of ƒ(zm) in the subclass of functions from the class T with prescribed values ƒ(zk) (k = 1, 2, …,m − 1) and ƒ(r) is determined. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 24–33. Original article submitted June 13, 2005. 相似文献
16.
Von Neumann-Jordan Constants of Absolute Normalized Norms on C^n 总被引:1,自引:0,他引:1
In this note, we give some estimations of the Von Neumann-Jordan constant C
N J
(∥·∥ψ) of Banach space (ℂ
n
, ∥·∥ψ), where ∥·∥ψ is the absolute normalized norm on ℂ
n
given by function ψ. In the case where ψ and φ are comparable, n=2 and C
N J
(∥·∥ψ)=1, we obtain a formula of computing C
N J
(∥·∥ψ). Our results generalize some results due to Saito and others.
Received May 11, 2002, Accepted November 20, 2002
This work is partly supported by NNSF of China (No. 19771056) 相似文献
17.
Eve Bofinger 《Annals of the Institute of Statistical Mathematics》1986,38(1):445-450
Summary The selection oft out ofk populations with parameters θ
i
(i=1, ...,k) is said to result in an ψ-correct decision provided ψ (minimum selected θ)>maximum non-selected θ where ψ(θ) (>θ) is an
increasing function. For the cases of location or scale parameters the minimum probability of ψ-correct decision over the
entire parameter space is shown to be no less than the minimum probability of correct selection over a preference zone determined
by ψ(θ). For other types of parameters this result is shown to be true under certain conditions linking the distribution function
and the ψ function. 相似文献
18.
We study a class of nonlinear evolutionary equations generated by an elliptic pseudo-differential operator, and with nonlinearity
of the form G(u
x
) where cη2 ≤ G(η) ≤ Cη2 for large |η|.
For the evolution in spaces of periodic functions with zero mean we demonstrate existence of a universal absorbing set and
compact attractor. Furthermore, we show that the attractor is of a finite Hausdorf dimension. The dissipation mechanism for
the class of equations studied in the paper is akin to the nonlinear saturation in the Kuramoto-Sivashinsky equation. A similar
generalization of the Kuramoto-Sivashinsky equation was studied by Nicolaenko et al. under the assumption of a purely quadratic nonlinearity and reflection invariance of both: the equation and solutions.
相似文献
19.
In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank.
Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) =
1/45(26n3 -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n2 + 1, and the class number of quadratic number field K2 = Q(vq) is 1. 相似文献
20.
Let Γ be the set of all permutations of the natural series and let α = {α j}
j∈ℕ, ν = {νj}
j∈ℕ, and η = {ηj}
j∈ℕ be nonnegative number sequences for which
is defined for all γ:= {γ(j)}
j∈ℕ ∈ Γ and η ∈ l
p. We find
in the case where 1 < p < ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1430–1434, October, 2005. 相似文献