共查询到20条相似文献,搜索用时 31 毫秒
1.
Rafael López 《Monatshefte für Mathematik》1999,127(2):155-169
We study constant mean curvature compact surfaces immersed in hyperbolic space with non-empty boundary (=H-surfaces). We prove that the only H-surfaces with boundary circular and 0≤∣H∣≤1, are the umbilical examples. When the surface is embedded, conditions to be umbilical are given. Finally, we characterize
umbilical surfaces bounded by a circle among all H-discs with small area.
Received 27 March 1997; in final form 11 June 1998 相似文献
2.
Wen-Bin Zhang 《Monatshefte für Mathematik》2003,15(1):319-353
We extend the mean-value theorems for multiplicative functions f on additive arithmetic semigroups, which satisfy the condition ∣f(a)∣≤1, to a wider class of multiplicative functions f for which ∣f(a)∣ is bounded in some average sense, via Halász’s method in classical probabilistic number theory. 相似文献
3.
Wen-Bin Zhang 《Monatshefte für Mathematik》2003,138(4):319-353
We extend the mean-value theorems for multiplicative functions f on additive arithmetic semigroups, which satisfy the condition ∣f(a)∣≤1, to a wider class of multiplicative functions f for which ∣f(a)∣ is bounded in some average sense, via Halász’s method in classical probabilistic number theory.
Received October 18, 2001; in final form April 11, 2002 相似文献
4.
Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials
V. V. Savchuk 《Ukrainian Mathematical Journal》2006,58(12):1904-1915
On concentric circles T
ϱ
= {z ∈ ℂ: ∣z∣ = ϱ}, 0 ≤ ϱ < 1, we determine the exact values of the quantities of the best approximation of holomorphic functions of the Bergman
class A
p
, 2 ≤ p ≤ ∞, in the uniform metric by algebraic polynomials generated by linear methods of summation of Taylor series. For 1 ≤ p < 2, we establish exact order estimates for these quantities.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1674–1685, December, 2006. 相似文献
5.
Jan Malý 《manuscripta mathematica》1994,85(1):419-428
Summary New lower semicontinuity results for quasiconvex integrals. In particular, under certain structure conditions and growth 0≤F(ξ)≤C(∣≤∣
q
) the functional ∫
Ω
F(∇u)dx is proved to be lower semicontinuous onW
1,q
with respect to the weak convergence inW
1,p, p≥q−1.
Research supported by the grant No. 201/93/2171 of Czech Grant Agency (GAČR) and by the grant No. 364 of Charles University
(GAUK).
This article was processed by the author using the Springer-VerlagTex P Jourlg marco package 1991. 相似文献
6.
S. Zaidman 《Annali dell'Universita di Ferrara》1968,13(1):33-36
Riassunto Nel presente lavoro si considera una classe di simboli non-omogenei, più generale di quella introdotta nel [3]; per operatori
pseudo-differenzialiEl(x,D) associati a tali simboli si considera il commutatore con l'operatore di Friedrichs Ψ(D) associato a una funzione Ψ(ξ) che gode di alcune speciali proprietà; prendendo inoltre una funzione ζ(ξ) nulla per ∣≤∣⩽1/2
e=1 per |ξ|≥1, si dimostra usando una tecnica dovuta a H?rmander [1] che l'operatore ζ(D)[Ψ(D),El(x,D)] è di ordine ≤-1/2.
Résumé Dans ce travail on considère une classe de symboles non-homogènes plus générale de celle introduite dans [3]; pour les opérateurs pseudo-différentielsEl(x,D) associés à tels symboles on considère le commutateur [Ψ(D),El(x,D)] avec l'opérateur de Friedrichs Ψ(D) associé à une fonction Ψ(ξ) jouissant de certaines propriétés spéciales. En prenant ensuite une fonction ζ(ξ) nulle pour ∣≤∣⩽1/2 e=1 et =1 pour |ξ|≥1, on démontre avec une technique de H?rmander [1] que l'opérateur ζ(D)[Ψ(D),El(x,D)] est d'ordre ≤-1/2.相似文献
7.
Abstract
We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval I of length ∣I∣ ≫ q
1/2+∈. Similar results are obtained for the distribution of ordered pairs (x, x
−1) with x a primitive λ-root, and for the number of primitive λ-roots satisfying inequalities such as |x − x
−1| ≤ B.
(Dedicated to Professor Wang Yuan on the occasion of his 75th birthday)
*Project supported by the National Natural Science Foundation of China (No.19625102) and the 973 Project of the Ministry of
Science and Technology of China. 相似文献
8.
V. V. Arestov 《Ukrainian Mathematical Journal》2010,62(3):331-342
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment
[–1, 1] with respect to a measure, or, more precisely, with respect to the functional μ(f) = mes{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1}. We also discuss an analogous problem with respect to the integral functionals ∫–11 φ (∣f (x)∣) dx for functions φ that are defined, nonnegative, and nondecreasing on the semiaxis [0, +∞). 相似文献
9.
G. Dziuk 《Numerische Mathematik》1990,58(1):603-611
Summary An Algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of Poisson problems on a series of surfaces. This gives a new method to solve Plateau's problem forH-surfaces. 相似文献
10.
LetH
i, 1 ≤ i ≤n be complex finite-dimensional Hilbert spaces of dimension di,1 ≤ i ≤n respectively withd
i ≥ 2 for everyi. By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using
a key lemma of Jaikumar [1] we show that every unitary operator on the tensor productH =H
1 ⊗H
2 ⊗... ⊗H
n can be expressed as a composition of a finite number of unitary operators living on pair productsH
i ⊗H
j,1 ≤i,j ≤n. An estimate of the number of operators appearing in such a composition is obtained.
Dedicated to Prof. A.K. Roy on his 62nd birthday. 相似文献
11.
Let H be a complex Hilbert space of dimension greater than 2, and B(H) denote the Banach algebra of all bounded linear operators on H. For A, B ∈ B(H), define the binary relation A ≤* B by A*A = A*B and AA* = AB*. Then (B(H), “≤*”) is a partially ordered set and the relation “≤*” is called the star order on B(H). Denote by Bs(H) the set of all self-adjoint operators in B(H). In this paper, we first characterize nonlinear continuous bijective maps on B
s
(H) which preserve the star order in both directions. We characterize also additive maps (or linear maps) on B(H) (or nest algebras) which are multiplicative at some invertible operator. 相似文献
12.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,43(2):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣. 相似文献
13.
Let K be either the rational number field
\Bbb Q{\Bbb Q} or an imaginary quadratic field. We give irrationality results for the number q = ?n=1¥rn/(qn-rl)\theta=\sum_{n=1}^{\infty}{r^n}/(q^n-r^l), where q (∣q∣ > 1) is an integer in K, r∈ K
× (∣r∣ < ∣q∣), and
1 £ l ? \Bbb Z1\le l\in{\Bbb Z} with q
n
≠ r
l (n ≥ 1). 相似文献
14.
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (H
p,q
(φ1), H
u,v
(φ2)) for the values of p, q, u, v in three cases: (i) 0 < p ≤ u ≤ ∞, 0 < q ≤ min(1, v) ≤ ∞. (ii) v = ∞, 0 < p ≤ u ≤ ∞, 1 ≤ u, q ≤ ∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤ ∞, and 0 < p ≤ u ≤ ∞ or 1 ≤ p, u ≤ ∞. The first case extends the result of Blasco, Jevtić, and Pavlović in one variable. The third case generalizes partly
the results of Jevtić, Jovanović, and Wojtaszczyk to higher dimensions.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
15.
R. Balasubramanian K. Ramachandra A. Sankaranarayanan 《Proceedings Mathematical Sciences》1992,102(1):1-12
For suitable functionsH = H(T) the maximum of|(ζ(σ + it))
z
| taken overT≤t≤T + H is studied. For fixed σ(1/2≤σ≤l) and fixed complex constantsz “expected lower bounds” for the maximum are established. 相似文献
16.
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all
root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M
2)−χ(M
10/(1−χ(M
2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M
2)−χ(M
2)/(1−χ(M
2)). Also we construct, for each integer n≥3, an example of a map f: K
n
→N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time. 相似文献
17.
The linear discrepancy of a partially ordered set P = (X, ≺) is the minimum integer l such that ∣f(a) − f(b)∣ ≤ l for any injective isotone and any pair of incomparable elements a, b in X. It measures the degree of difference of P from a chain. Despite of increasing demands to the applications, the discrepancies of just few simple partially ordered sets
are known. In this paper, we obtain the linear discrepancy of the product of two chains. For this, we firstly give a lower
bound of the linear discrepancy and then we construct injective isotones on the product of two chains, which show that the
obtained lower bound is tight. 相似文献
18.
Hiroshi Nakano 《Graphs and Combinatorics》2001,17(4):707-716
Let Γ be a distance-regular graph of diameter d. The height of Γ is defined by h = max{j∣p
d
d,j
≠ 0}. Let e, f be positive integers such that e < f and e + f≤d, and let d = 2e + s for some positive integer s. We show that if k
e
= k
f
, h≤ 2s and the height h is even, then Γ is an antipodal 2-cover.
Received: October 23, 1997 Final version received: July 31, 2000 相似文献
19.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,138(1):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣.
Supported in part by NSF DMS-0074531.
Received February 14, 2002; in revised form July 18, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
20.
For each positive integer k, the radix representation of the complex numbers in the base –k+i gives rise to a lattice self-affine tile T
k
in the plane, which consists of all the complex numbers that can be expressed in the form ∑
j≥1
d
j
(–k+i)–j
, where d
j
∈{0, 1, 2, ...,k
2}. We prove that T
k
is homeomorphic to the closed unit disk {z∈C:∣z∣ ≤ 1} if and only if k ≠ 2.
The first author is supported by Youth Project of Tianyuan Foundation (10226031) and Zhongshan University Promotion Foundation
for Young Teachers (34100-1131206); the second author is supported by National Science Foundation (10041005) and Guangdong
Province Science Foundation (011221) 相似文献