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1.
Di Zhao 《中国科学A辑(英文版)》1999,42(9):897-904
LetM be a compact Riemann manifold with the Ricci curvature ≽ - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies
. Moreover if
, then
相似文献
2.
Deh-phone Kung Hsing 《Annali di Matematica Pura ed Applicata》1976,109(1):235-245
Summary We consider the system(L):
, t ⩾ p, y(t)=f(t), t⩽0, where y is an n-vector and each Ai, B(t) are n × n matrices. System(L) generates a semigroup by means of Ttf(s)=y (t+s, f), f(s) ∈ BCl(− ∞, 0]. Under some hypotheses concerning the roots ofdet
where
is the Laplace transform of B(t), the asymptotic behavior of y(t) is discussed. Two typical results are: Theorem 3.1: suppose
∥B(t)∥ ɛ L1[0, ∞),
thendet
forRe λ>0 iff for every ɛ>0 there is an Mɛ>0 such that ∥Ttf∥l ⩽ ⩽ Mɛ
exp [ɛt]∥f∥l for t ⩾ 0. Corollary 3.1.1: suppose
exp [at]B(t) ∈ ∈ L1[0, ∞) for some a>0 anddet
forRe λ>−a. Then the solution of(L) is exponentially asymptotically stable.
Entrata in Redazione il 21 marzo 1975.
The author is grateful to ProfessorC. Corduneanu for suggesting this problem and for many helpful discussions during the preparation of the paper. 相似文献
3.
In studying local harmonic analysis on the sphere Sn, R.S. Strichartz introduced certain zonal functions ϕ2(d(x, y)) which satisfy the equation
, where Δz is the Laplace operator and δ−y the Dirac measure. The explicit expression of the constant a (λ) is given by R.S. Strichartz in the case that n is odd. Appyling
the Apéry identity, we show in this paper that
for n even, where wn-1 is the surface area of Sn-1,
.
The author's research was supported by a grant from NSFC. 相似文献
4.
Amitai Regev 《Israel Journal of Mathematics》1999,113(1):15-28
The numbers
% MathType!End!2!1!, λ ⊢n appear in the enumeration of various objects, as well as coefficients inS
nrepresentations associated with products of higher commutators. We study their asymptotics asn→∞ and show that if (λ1, λ2, …)≈(α
1,α
2, …)n, if (λ′1, λ′2, …)≈(β
1,β
2, …)n and ifγ=1− Σ
k⩽1(α
k⩽1+β
k⩽1), then
% MathType!End!2!1!.
Work partially supported by N.S.F. Grant No. DMS 94-01197. 相似文献
5.
Extensions of some inequalities 总被引:2,自引:0,他引:2
ChenDaoqi 《高校应用数学学报(英文版)》2001,16(3):241-243
Abstract. By using a simple analytic method the following inequalities are proved: 相似文献
6.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
By a constructive argument, we prove that for any k = 1, 2, • • •, if ε is small enough, then the above problem has positive a solution uε concentrating at k distinct points which tending to the boundary of Ω as ε goes to 0+. 相似文献
7.
Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics
Yu. G. Safarov 《Journal of Mathematical Sciences》1988,40(5):645-652
Let j be the eigenvalues of a positive elliptic pseudodifferential operator of order m > 0 on a closed compact d-dimensional C-manifold and let N()=#{j:jm}. It is shown that for each > 0 we have
相似文献
8.
Xianling Fan Shao-Gao Deng 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):255-271
We study the existence and multiplicity of positive solutions for the inhomogeneous Neumann boundary value problems involving
the p(x)-Laplacian of the form
9.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献 10.
K. A. Kopotun 《分析论及其应用》1995,11(2):41-58
Some estimates for unconstrained and convex polynomial approximation in the uniform metric are obtained. These results are
given in terms of the Ditzian-Totik moduli of smoothness
, ≤1 with
. The construction of the approximating polynomials does not depend on λ. 相似文献
11.
A. E. Shishkov 《Journal of Mathematical Sciences》1999,97(3):4066-4084
The paper deals with localization properties of solutions to the Cauchy problem with the initial data u0(x) ∈ L2(ℝn) for a wide class of equations in the divergence form. This class contains, e.g., the following equation:
12.
De Li LI Andrew ROSALSKY Andrei VOLODIN 《数学学报(英文版)》2007,23(4):599-612
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
(i) lim sup n→∞ ||Sn||/an〈∞ a.s.and
∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent;
(ii) For all constants λ ∈ [0, ∞),
lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
13.
A. Michael Alphonse 《Journal of Fourier Analysis and Applications》2000,6(4):449-456
In this paper we prove that the maximal commutator of singular integral operator [b, T]* satisfies the inequality:
14.
L. Yu Kolotilina 《Journal of Mathematical Sciences》1998,89(6):1690-1693
Let A=(aij)
i,j
n
=1 be a Hermitian matrix and let
denote its eigenvalues. If
, k<n, then A is known to be block diagonal. We show that this result easily follows from the Cauchy interlacing theorem,
generalize it by introducing a convex strictly monotone function f(t), and prove that in the positivedefinite case, the matrix
diagonal entries can be replaced by the diagonal entries of a Schur complement. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 153–158.
Translated by L. Yu. Kolotilina. 相似文献
15.
16.
ON A CLASS OF BESICOVITCHFUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION
This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given byB(t) := ∞∑k=1 λs-2k sin(λkt),where 1 < s < 2, λk > 0 tends to infinity as k →∞ and λk satisfies λk 1/λk ≥λ> 1. The results show thatlimk→∞ log λk 1/log λk = 1is a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions.For the fractional Riemann-Liouville differential operator Du and the fractional integral operator D-v,the results show that if λ is sufficiently large, then a necessary and sufficient condition for box dimension of Graph(D-v(B)),0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)),0 < u < 2 - s, to be s uis also lim k→∞logλk 1/log λk = 1. 相似文献
17.
Letf(z) be a real entire function of genus 1*, δ≥0, and suppose that for each ε>0, all but a finite number of the zeros off(z) lie in the strip |Imz| ≤δ+ε. Let λ be a positive constant such that
. It is shown that for each ε>0, all but a finite number of the zeros of the entire function
lie in the strip
and if Δ2 < 2λ, then all but a finite number of the zeros of e−λD2
f(z) are real and simple. As a consequence, de Bruijn's question whether the functions eγ
t
2,λ>0, are strong universal factors is answered affirmatively.
The authors wish to acknowledge the financial support of the Korea Research Foundation made in the program year of (1998–2000). 相似文献
18.
We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary, λ is a positive real number, and the continuous functions p
1, p
2, and q satisfy 1 < p
2(x) < q(x) < p
1(x) < N and for any . The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that any is an eigenvalue, while any is not an eigenvalue of the above problem. 相似文献
19.
Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞|aj| 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj+tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}. 相似文献
20.
G. Kuba 《Archiv der Mathematik》2002,79(6):534-542
Let
(z ∈ ℝ). Further let λ denote a large real parameter. We show that for arbitrary real numbersk and α withk>=2.7013 and 0<α≦1,
|