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1.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献
2.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
3.
For natural numbers r,s,q,m,n with s≥r≤q we determine all natural functions g: T
*(J
(r,s,q)(Y, R
1,1)0)*→R for any fibered manifold Y with m-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n with s≥r we determine all natural functions g: T
*(J
(r,s)
(Y, R)0)*→R for any Y as above. 相似文献
4.
Mihnea Colţoiu 《Mathematische Zeitschrift》2007,256(3):461-464
We show the following result: let X be a 1-convex manifold, A its exceptional set, k = dimA and p : Y → X any covering. Then Y can be exhausted by an increasing sequence of smoothly bounded k-convex domains.
相似文献
5.
I. Kocsis 《Acta Mathematica Hungarica》2008,118(4):307-312
Let X ⊂ ℝ be an interval of positive length and define the set Δ = {(x, y) ∈ X × X | x ≧ y}. We give the solution of the equation
which holds for all (x, y) ∈ Δ and (u, υ) ∈ Δ, where the functions F: X → X, G
1: Δ → X, G
2: Δ → X, and G: F(X, X) × F(X, X) → X are continuous and strictly monotonic in each variable.
This research was supported by the Hungarian Scientific Research Fund (OTKA), grant No. T-043080. 相似文献
6.
Vladimir G. Berkovich 《Israel Journal of Mathematics》1995,92(1-3):45-59
Let ϕ:Y →X be a morphism of finite type between schemes of locally finite type over a non-Archimedean fieldk, and letF be an étale constructible sheaf onY. In [Ber2] we proved that if the torsion orders ofF are prime to the characteristic of the residue field ofk then the canonical homomorphisms (R
Q
ϱ*F)an →R
q
ϱ
*
an
F
an are isomorphisms. In this paper we extend the above result to the class of sheavesF with torsion orders prime to the characteristic ofk. 相似文献
7.
N. B. Brodskii 《Mathematical Notes》1999,66(3):283-291
A new method for extending upper semicontinuousUV
n
-valued mappings is introduced. Any upper semicontinuousUV
n
-valued mapping Ψ:A→Y of a closed subsetA of a separable metric spaceX into ann-connected, locallyn-connected complete metric spaceY satisfying the property of disjoint (n+1)-disks is proved to be extendable to an upper semicontinuousUV
n
-valued mapping Ψ′:X→Y such that Ψ′|a=Ψ. As an application, some results aboutn-soft mappings are obtained.
Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 351–363, September, 1999. 相似文献
8.
Let G be a reductive affine group scheme defined over a semilocal ring k. Assume that either G is semisimple or k is normal and noetherian. We show that G has a finite k-subgroup S such that the natural map H
1(R, S) → H
1(R, G) is surjective for every semilocal ring R containing k. In other words, G-torsors over Spec(R) admit reduction of structure to S. We also show that the natural map H
1(X, S) → H
1(X, G) is surjective in several other contexts, under suitable assumptions on the base ring k, the scheme X/k and the group scheme G/k. These results have already been used to study loop algebras and essential dimension of connected algebraic groups in prime
characteristic. Additional applications are presented at the end of this paper.
V. Chernousov was partially supported by the Canada Research Chairs Program and an NSERC research grant. Z. Reichstein was
partially supported by NSERC Discovery and Accelerator Supplement grants. 相似文献
9.
C. Hamburger 《Applied Mathematics and Optimization》1999,40(2):183-190
Finsler's theorem asserts the equivalence of (i) and (ii) for pairs of real quadratic forms f and g on R
n
: (i) f( ξ ) >0 for all ξ≠ 0 with g( ξ ) =0; (ii) f-λ g>0 for some λ∈
R. We prove two extensions: 1. We admit a vector-valued quadratic form g:
R
n
→
R
k
, for which we show that (i) implies that f-λ . . . g>0 on an ( n-k+1 ) -dimensional subspace Y
R
n
for some λ∈
R
k
. 2. In the nonstrict version of Finsler's theorem for indefinite g we replace R
n
by a real
vector
space
X .
Accepted 22 February 1998 相似文献
10.
Jana Maříková 《Israel Journal of Mathematics》2009,171(1):175-195
Let R be a sufficiently saturated o-minimal expansion of a real closed field, let be the convex hull of ℚ in R, and let st: → ℝ
n
be the standard part map. For X ⊆ R
n
define st X:= st (X ∩ ). We let ℝind be the structure with underlying set ℝ and expanded by all sets st X, where X ⊆ R
n
is definable in R and n = 1, 2,.... We show that the subsets of ℝ
n
that are definable in ℝind are exactly the finite unions of sets st X st Y, where X, Y ⊆ R
n
are definable in R. A consequence of the proof is a partial answer to a question by Hrushovski, Peterzil and Pillay about the existence of measures
with certain invariance properties on the lattice of bounded definable sets in R
n
. 相似文献
11.
V. V. Mykhailyuk 《Ukrainian Mathematical Journal》2007,59(7):1110-1113
We prove that, for an arbitrary Baire space X, a linearly ordered compact set Y, and a separately continuous mapping ƒ: X × Y → R, there exists a G
δ-set A ⊆ X dense in X and such that the function ƒ is jointly continuous at every point of the set A × Y, i.e., any linearly ordered compact set is a co-Namioka space.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 1001–1004, July, 2007. 相似文献
12.
A Convenient Subcategory of Tych 总被引:1,自引:1,他引:0
Gábor Lukács 《Applied Categorical Structures》2004,12(4):369-377
A map f:XY between Hausdorff topological spaces is k-continuous if its restriction f|
K
to every compact subspace K of X is continuous. X is called a k
R
-space if every k-continuous function from X to a Tychonoff space is continuous. In this paper we investigate the category of Tychonoff k
R
-spaces, and show that it is Cartesian closed (thus convenient in the sense of Wyler). 相似文献
13.
Piotr Haj?asz 《Mathematische Annalen》2009,343(4):801-823
We prove that Lipschitz mappings are dense in the Newtonian–Sobolev classes N
1,p
(X, Y) of mappings from spaces X supporting p-Poincaré inequalities into a finite Lipschitz polyhedron Y if and only if Y is [p]-connected, π
1(Y) = π
2(Y) = · · · = π
[p](Y) = 0, where [p] is the largest integer less than or equal to p.
This work was supported by the NSF grant DMS-0500966. 相似文献
14.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1987,39(1):611-622
Summary LetX be a standard normal random variable and let σ be a positive random variable independent ofX. The distribution of η=σX is expanded around that ofN(0, 1) and its error bounds are obtained. Bounds are given in terms of E(σ
2V−σ
2−1)
k
whereσ
2Vσ
−2 denotes the maximum of the two quantitiesσ
2 andσ
−2, andk is a positive integer, and of E(σ
2−1)
k
, ifk is even.
The Institute of Statistical Mathematics 相似文献
15.
16.
Meng Wang 《数学学报(英文版)》2012,28(1):145-170
We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition.In the previous paper,we show that the Chern-Simons Higgs equation with parameter λ0 has at least two solutions(uλ1,uλ2) for λ sufficiently large,which satisfy that uλ1→u0 almost everywhere as λ→∞,and that uλ2→∞ almost everywhere as λ→∞,where u 0 is a(negative) Green function on M.In this paper,we study the asymptotic behavior of the solutions as λ→∞,and prove that uλ2-uλ2 converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary M is negative,or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero. 相似文献
17.
We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M
G
. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup. 相似文献
18.
19.
Abstract
Let Λ = {λ
k
} be an infinite increasing sequence of positive integers with λ
k
→∞. Let X = {X(t), t ∈? R
N
} be a multi-parameter fractional Brownian motion of index α(0 < α < 1) in R
d
. Subject to certain hypotheses, we prove that if N < αd, then there exist positive finite constants K
1 and K
2 such that, with unit probability,
if and only if there exists γ > 0 such that
where ϕ(s) = s
N/α
(log log 1/s)
N/(2α), ϕ-p
Λ(E) is the Packing-type measure of E,X([0, 1])
N
is the image and GrX([0, 1]
N
) = {(t,X(t)); ∈? [0, 1]
N
} is the graph of X, respectively. We also establish liminf type laws of the iterated logarithm for the sojourn measure of X.
Supported by the National Natural Science Foundation of China (No.10471148), Sci-tech Innovation Item for Excellent Young
and Middle-Aged University Teachers and Major Item of Educational Department of Hubei (No.2003A005) 相似文献
20.
Oleg T. Izhboldin 《manuscripta mathematica》2000,102(1):41-52
Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 相似文献