共查询到20条相似文献,搜索用时 15 毫秒
1.
Jean-Christophe Bourgoin 《Calculus of Variations and Partial Differential Equations》2006,25(4):469-489
In this paper, we investigate the minimality of the map
from the Euclidean unit ball Bn to its boundary 핊n−1 for weighted energy functionals of the type Ep,f = ∫Bn f(r)‖∇ u‖p dx, where f is a non-negative function. We prove that in each of the two following cases:
Mathematics Subject Classification (2000) 58E20; 53C43 相似文献
i) | p = 1 and f is non-decreasing, |
ii) | p is integer, p ≤ n−1 and f = rα with α ≥ 0, the map minimizes Ep,f among the maps in W1,p(Bn, 핊n−1) which coincide with on ∂ Bn. We also study the case where f(r) = rα with −n+2 < α < 0 and prove that does not minimize Ep,f for α close to −n+2 and when n ≥ 6, for α close to 4−n. |
2.
Subhash J. Bhatt 《Proceedings Mathematical Sciences》2006,116(2):161-173
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C
*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A
∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C
*-crossed productC
*(ℝ,E(A), α) of the enveloping Σ-C
*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK
*(S(ℝ, A∞, α)) =K
*(C
*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC
*-algebra defined by densely defined differential seminorms is given. 相似文献
3.
K. L. Avetisyan 《Potential Analysis》2008,29(1):49-63
We study anisotropic mixed norm spaces h(p,q,α) consisting of n-harmonic functions on the unit polydisc of by means of fractional integro-differentiation including small 0 < p < 1 and multi-indices α = (α
1,...,α
n
) with non-positive α
j
≤ 0. As an application, two different Bloch spaces of n-harmonic functions are characterized.
相似文献
4.
Anm-consecutive-k-out-of-n:F system is a system ofn linearly arranged components which fails if and only if at leastm non-overlapping sequences ofk components fail, when there arek distinct components with failure probabilitiesq
i
fori=1,...,k and where the failure probability of thej-th component (j=rk+i (1 ≤i ≤k) isq
j
=q
i
, we call this system by anm-consecutive-k-out-of-n:F system with cycle (or period)k. In this paper we give a formula of the failure probability ofm-consecutive-k-out-of-n:F system with cyclek via the failure probability of consecutive-k-out-of-n:F system. 相似文献
5.
Paul Arne ?stv?r 《K-Theory》2004,31(4):345-355
Let X be a connected based space and p be a two-regular prime number. If the fundamental group of X has order p, we compute the two-primary homotopy groups of the homotopy fiber of the trace map A(X) → TC(X) relating algebraic K-theory of spaces to topological cyclic homology. The proof uses a theorem of Dundas and an explicit calculation of the cyclotomic
trace map K(ℤ[Cp])→ TC(ℤ[Cp]). 相似文献
6.
S. J. Bhatt 《Proceedings Mathematical Sciences》2001,111(1):65-94
UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform
topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through
the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC
c
(G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC
∞-elementsC
∞(A), the analytic elementsC
ω(A) as well as the entire analytic elementsC
є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI
α is constructed satisfyingA =C*-ind limI
α; and the locally convex inductive limit ind limI
α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK
a
ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible. 相似文献
7.
Antonio Sedeo-Noda Carlos Gonzlez-Martín 《European Journal of Operational Research》2010,202(3):628-635
We address the problem of finding the K best path trees connecting a source node with any other non-source node in a directed network with arbitrary lengths. The main result in this paper is the proof that the kth shortest path tree is adjacent to at least one of the previous (k-1) shortest path trees. Consequently, we design an O(f(n,m,Cmax)+Km) time and O(K+m) space algorithm to determine the K shortest path trees, in a directed network with n nodes, m arcs and maximum absolute length Cmax, where O(f(n,m,Cmax)) is the best time needed to solve the shortest simple paths connecting a source node with any other non-source node. 相似文献
8.
Katrin Schumacher 《Czechoslovak Mathematical Journal》2009,59(3):637-648
Given a domain Ω of class C
k,1, k ∈ ℕ, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of in the sense
that (∂/∂x
n
)α(x′, 0) = − N(x′) and that still is of class C
k,1. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class C
k,1. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class
of Muckenhoupt weights. 相似文献
9.
E. G. Straus 《Israel Journal of Mathematics》1963,1(4):221-223
For any two positive integersk, l and anyɛ>0 there exists anN(k, l, ɛ) so that given anyl convex bodiesC
1, …,C
l symmetric about the origin inE
n withn≧N there exists a subspaceE
k so that eachC
i intersectsE
k, or has a projection intoE
k, in a set which is nearly spherical (asphericity <ɛ). The measure of the totality ofE
k which intersect a given body inE
n in a nearly ellipsoidal set is considered and an affine invariant measure is introduced for that purpose. 相似文献
10.
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
11.
Larry Guth 《Geometric And Functional Analysis》2007,17(4):1139-1179
We prove that a bounded open set U in has k-width less than C(n) Volume(U)
k/n
. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in . In particular, we estimate the smallest (n – 1)-dilation of any degree 1 map between two n-dimensional rectangles. For any pair of rectangles, our estimate is accurate up to a dimensional constant C(n). We give examples in which the (n – 1)-dilation of the linear map is bigger than the optimal value by an arbitrarily large factor.
Received: January 2006, Revision: May 2006, Accepted: June 2006 相似文献
12.
M. V. Medvedeva 《Mathematical Notes》1998,64(5):616-621
In this paper we study functions belonging to the classesV
ε and ΛBV, which are encountered in the theory of Fourier trigonometric series. Necessary and sufficient conditions for the embedding
of the classesH
ω in the classesV
ϕ and ABV are obtained.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 713–719, November, 1998.
This research was supported by the program “Leading Scientific Schools” under grant No. 96/97-15-96073. 相似文献
13.
C(n, k) is a graph obtained from n-cycle by adding edges v
i
v
i+k
(i = 1, 2,...,n, i + k (mod n)). There are several known results on the crossing numbers of the Cartesian products of C(n, k) (n ≤ 7) with paths, cycles and stars. In this paper we extend these results, and show that the crossing number of the Cartesian
product of C(8, 2) with P
n
is 8n.
Yuanqiu Huang: Research supported by NSFC (10771062) and New Century Excellent Talents in University (NCET-07-0276).
Jinwang Liu: Research supported by NSFC (10771058) and Hunan NSFC(O6jj20053). 相似文献
14.
Henry Teicher 《Journal of Theoretical Probability》1995,8(4):779-793
Conditions are obtained for (*)E|S
T
|γ<∞, γ>2 whereT is a stopping time and {S
n=∑
1
n
,X
j
ℱ
n
,n⩾1} is a martingale and these ensure when (**)X
n
,n≥1 are independent, mean zero random variables that (*) holds wheneverET
γ/2<∞, sup
n≥1
E|X
n
|γ<∞. This, in turn, is applied to obtain conditions for the validity ofE|S
k,T
|γ<∞ and of the second moment equationES
k,T
2
=σ
2
EΣ
j=k
T
S
k−1,j−1
2
where
and {X
n
, n≥1} satisfies (**) and
,n≥1. The latter is utilized to elicit information about a moment of a stopping rule. It is also shown for i.i.d. {X
n
, n≥1} withEX=0,EX
2=1 that the a.s. limit set of {(n log logn)−k/2
S
k,n
,n≥k} is [0,2
k/2/k!] or [−2
k/2/k!] according ask is even or odd and this can readily be reformulated in terms of the corresponding (degenerate kernel)U-statistic
. 相似文献
15.
It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1|
k
summability implies |A|
k
summability wherek≥1. In the present paper, we consider the converse implication. 相似文献
16.
In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f
n
(x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ℝ,G∈C
m
(J
n+1, ℝ) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces
and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence,
uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in
reference in different aspects. 相似文献
17.
K. Kubilius 《Lithuanian Mathematical Journal》1999,39(3):251-261
The uniform distance between the solution of a nonlinear equation driven by a functionh with boundedp-variation and its Milstein-type approximation is estimated by δ
n
v γ
p
(n) v γ
p
2
(n), where δ
n
=max(t
k
−t
k−1
) is the maximum step size of the approximation on the interval [0,T], γ
p
(n)=max υ
p
1/p
(h;[t
k-1,t
k
]), 1 <p < 2, and υ
p
(h;[t
k-1,t
k
]) is thep-variation of the functionh on [t
k-1,t
k]. In particular, ifh is a Lipschitz function of order α, then the uniform distance has the bound δ
n
α
for δn <1.
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius; Vilnius Technical University, Saulétekio 11, 2054 Vilnius,
Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 317–330, July–September, 1999. 相似文献
18.
19.
Let (GA)
n
[k](a), A
n
(a), G
n
(a) be the third symmetric mean of k degree, the arithmetic and geometric means of a
1, …, a
n
(a
i
> 0, i = 1, …, n), respectively. By means of descending dimension method, we prove that the maximum of p is k−1/n−1 and the minimum of q is n/n−1(k−1/k)
k/n
so that the inequalities {fx505-1} hold. 相似文献
20.
Li Wenxia 《数学学报(英文版)》1998,14(4):487-494
Corresponding to the irreducible 0–1 matrix (a
ij
)
n×n
, take similitude contraction mappingsϕ
ij
for eacha
ij
=1, ina
ij
=1, in R
d
with ratio 0<r
ij
<1. There are unique nonempty compact setsF
1,…,F
n
satisfying for each1≤i≤n, F
i. We prove that open set condition holds if and only ifF
i
is ans-set for some1≤i≤n, wheres is such that the spectral radius of matrix (r
ij
3
)
n x n
is 1.
Partly supported by Natural Science Foundation of China, and partly by Natural Science Foundation of Hubei Province 相似文献