共查询到20条相似文献,搜索用时 234 毫秒
1.
Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0, 1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c0 ∪ (Q \ Σ)), i.e., there is a homeomorphism h :↓USCC(X) → Q such that h(↓CC(X)) = c0 ∪ (Q \ Σ... 相似文献
2.
Miran Černe 《Arkiv f?r Matematik》2002,40(1):27-45
LetX(-ϱB
m
×C
n
be a compact set over the unit sphere ϱB
m
such that for eachz∈ϱB
m
the fiberX
z
={ω∈C
n
;(z, ω)∈X} is the closure of a completely circled pseudoconvex domain inC
n
. The polynomial hull
ofX is described in terms of the Perron-Bremermann function for the homogeneous defining function ofX. Moreover, for each point (z
0,w
0)∈Int
there exists a smooth up to the boundary analytic discF:Δ→B
m
×C
n
with the boundary inX such thatF(0)=(z
0,w
0).
This work was supported in part by a grant from the Ministry of Science of the Republic of Slovenia. 相似文献
3.
4.
Let X be a Banach space, A : D(A) X → X the generator of a compact C0- semigroup S(t) : X → X, t ≥ 0, D a locally closed subset in X, and f : (a, b) × X →X a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order to make D a viable domain of the semilinear differential equation of retarded type u'(t) = Au(t) + f(t, u(t - q)), t ∈ [to, to + T], with initial condition uto = φ ∈C([-q, 0]; X), is the tangency condition lim infh10 h^-1d(S(h)v(O)+hf(t, v(-q)); D) = 0 for almost every t ∈ (a, b) and every v ∈ C([-q, 0]; X) with v(0), v(-q)∈ D. 相似文献
5.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
6.
Let X be a non-singular complex projective curve of genus ≥3. Choose a point x ∈ X. Let Mx be the moduli space of stable bundles of rank 2 with determinant We prove that the Chow group CHQ1(Mx) of 1-cycles on Mx with rational coefficients is isomorphic to CHQ0(X). By studying the rational curves on Mx, it is not difficult to see that there exits a natural homomorphism CH0(J)→CH1(Mx) where J denotes the Jacobian of X. The crucial point is to show that this homomorphism induces a homomorphism CH0(X)→CH1(Mx), namely, to go from the infinite dimensional object CH0(J) to the finite dimensional object CH0(X). This is proved by relating the degeneration of Hecke curves on Mx to the second term I*2 of Bloch's filtration on CH0(J).
Insong Choe was supported by KOSEF (R01-2003-000-11634-0). 相似文献
7.
A. K. Aleskeviciene 《Lithuanian Mathematical Journal》2005,45(4):359-367
Let X
1, X
2,... be independent identically distributed random variables with distribution function F, S
0 = 0, S
n
= X
1 + ⋯ + X
n
, and Sˉ
n
= max1⩽k⩽n
S
k
. We obtain large-deviation theorems for S
n
and Sˉ
n
under the condition 1 − F(x) = P{X
1 ⩾ x} = e−l(x), l(x) = x
α
L(x), α ∈ (0, 1), where L(x) is a slowly varying function as x → ∞.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 447–456, October–December, 2005. 相似文献
8.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
9.
V. M. Prokip 《Ukrainian Mathematical Journal》2012,63(8):1314-1320
Polynomial n × n matrices A(x) and B(x) over a field
\mathbbF \mathbb{F} are called semiscalar equivalent if there exist a nonsingular n × n matrix P over
\mathbbF \mathbb{F} and an invertible n × n matrix Q(x) over
\mathbbF \mathbb{F} [x] such that A(x) = PB(x)Q(x). We give a canonical form with respect to semiscalar equivalence for a matrix pencil A(x) = A
0x
- A
1, where A
0 and A
1 are n × n matrices over
\mathbbF \mathbb{F} , and A
0 is nonsingular. 相似文献
10.
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
11.
A Banach space X has the alternative Dunford–Pettis property if for every weakly convergent sequences (xn) → x in X and (xn*) → 0 in X* with ||xn|| = ||x||= 1 we have (xn*(xn)) → 0. We get a characterization of certain operator spaces having the alternative Dunford–Pettis property. As a consequence
of this result, if H is a Hilbert space we show that a closed subspace M of the compact operators on H has the alternative Dunford–Pettis property if, and only if, for any h ∈ H, the evaluation operators from M to H given by S ↦ Sh, S ↦ Sth are DP1 operators, that is, they apply weakly convergent sequences in the unit sphere whose limits are also in the unit sphere
into norm convergent sequences. We also prove a characterization of certain closed subalgebras of K(H) having the alternative Dunford-Pettis property by assuming that the multiplication operators are DP1. 相似文献
12.
A. I. Perov 《Functional Analysis and Its Applications》2010,44(1):69-72
Let M be a complete K-metric space with n-dimensional metric ρ(x, y): M × M → R
n
, where K is the cone of nonnegative vectors in R
n
. A mapping F: M → M is called a Q-contraction if ρ (Fx,Fy) ⩽ Qρ (x,y), where Q: K → K is a semi-additive absolutely stable mapping. A Q-contraction always has a unique fixed point x* in M, and ρ(x*,a) ⩽ (I - Q)-1 ρ(Fa, a) for every point a in M. The point x* can be obtained by the successive approximation method x
k
= Fx
k-1, k = 1, 2,..., starting from an arbitrary point x
0 in M, and the following error estimates hold: ρ (x*, x
k
) ⩽ Q
k
(I - Q)-1ρ(x
1, x
0) ⩽ (I - Q)-1
Q
k
ρ(x
1, x
0), k = 1, 2,.... Generally the mappings (I - Q)-1 and Q
k
do not commute. For n = 1, the result is close to M. A. Krasnosel’skii’s generalized contraction principle. 相似文献
13.
Joanna Janczewska 《Central European Journal of Mathematics》2004,2(4):561-572
In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R
k
→Y is a C
2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R
1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R
k
and we describe the solution set of the studied equation in a small neighbourhood of this point. 相似文献
14.
YANG Zhongqiang Department of Mathematics Shantou University Shantou China 《中国科学A辑(英文版)》2005,48(4):469-484
Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable. 相似文献
15.
Frank Jonas 《manuscripta mathematica》1990,67(1):35-39
Zusammenfassung LetD:G→GL(n,C) be an irreducible linear representation of a finite groupG with the characterX. IfD is realizible in Q(ξ
m
) and Q(ξ
m′
) we give a condition for then realizability ofD in Q(ξ(m′)). If the degreen is a prime ≠ 2, we show thatD realizible in Q(ξ
f
), wheref is the conductor of the abelian extensionQ(X)/Q. 相似文献
16.
David Mejzler 《Israel Journal of Mathematics》1987,57(1):1-27
LetX
1, ...,X
n be independent random variables, letF
i be the distribution function ofX
i (1≦i≦n) and letX
1n
≦... ≦X
nn be the corresponding order statistics. We consider the statisticsX
kn, wherek=k(n),k/n → 1 andn−k → ∞. Under some additional restrictions concerning the behaviour of the sequences {a
n>0,b
n,k(n),F
n} we characterize the class of all distribution functionsH such that Prob{(X
kn
−b
n
)/a
n
<x)}→H.
Dedicated to the Memory of N. V. Smirnov (1900–1966) 相似文献
17.
We show the existence of a sequence (λ
n
) of scalars withλ
n
=o(n) such that, for any symmetric compact convex bodyB ⊂R
n
, there is an affine transformationT satisfyingQ ⊂T(B) ⊂λ
n
Q, whereQ is then-dimensional cube. This complements results of the second-named author regarding the lower bound on suchλ
n
. We also show that ifX is ann-dimensional Banach space andm=[n/2], then there are operatorsα:l
2
m
→X andβ:X→l
∞
m
with ‖α‖·‖β‖≦C, whereC is a universal constant; this may be called “the proportional Dvoretzky-Rogers factorization”. These facts and their corollaries
reveal new features of the structure of the Banach-Mazur compactum.
Research performed while this author was visiting IHES. Supported in part by the NSF Grant DMS-8702058 and the Sloan Research
Fellowship. 相似文献
18.
A polynomial Q = Q(X
1, …, X
n
) of degree m in independent identically distributed random variables with distribution function F is an unbiased estimator of a functional q(α
1(F), …, α
m
(F)), where q(u
1, …, u
m
) is a polynomial in u
1, …, u
m
and α
j
(F) is the jth moment of F (assuming the necessary moment of F exists). It is shown that the relation E(Q | X
1 + … + X
n) = 0 holds if and only if q(α
1(θ), …, α
m
(θ)) ≡ 0, where α
j
(θ) is the jth moment of the natural exponential family generated by F. This result, based on the fact that X
1 + … + X
n is a complete sufficient statistic for a parameter θ in a sample from a natural exponential family of distributions F
θ(x) = ∫−∞
x
e
θu−k(θ)
dF(u), explains why the distributions appearing as solutions of regression problems are the same as solutions of problems for
natural exponential families though, at the first glance, the latter seem unrelated to the former. 相似文献
19.
Further Results on Finitely Generated Projective Modules 总被引:1,自引:0,他引:1
Tong Suo Wu 《数学学报(英文版)》2002,18(2):225-228
In this paper, the exchange rings R whose primitive factor rings are artinian are studied. The following results are proved: for any exchange ring R and any two-sided ideal I of R, K
0(π) : K
0(R)→K
0(R/I) is a group epimorphism with the kernel {[P]−[Q] |P = PI, Q = QI}; there is an isomorphism of ordered groups from K
0(R) to the gorup of all such functions ƒ
P
: X→Q(P∈p(R)), where X is the set of all primitive ideals of R and Q, the rational integers.
Received February 2, 1999, Accepted December 9, 1999 相似文献
20.
Dominique Arlettaz 《Central European Journal of Mathematics》2004,2(1):50-56
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism
b
n
: π
n
(X)→H
n
(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π
n
(X)→E
n
(X), F
n
(X)→(E∧F)
n
(X), F
n
(X)→H
n
(X;π
0
F) and F
n
(X)→H
n+t
(X;π
t
F) for other cohomology theories E
*(−) and F
*(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in
terms of the order of the Postnikov invariants of the spectrum F. 相似文献