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1.
Haiou Tan 《Analysis Mathematica》2000,26(2):119-132
Let be a normal function on [0, 1), B
n
the unit ball of C
n
, and A
p
(B
n
) the weighted Bergman spaces on B
n
with weight . The purpose of this paper is to discuss some relations among A
p
(B
n
), weighted Bergman kernels, and Carleson measures on B
n
. 相似文献
2.
Conservative weightings and ear-decompositions of graphs 总被引:1,自引:0,他引:1
András Frank 《Combinatorica》1993,13(1):65-81
A subsetJ of edges of a connected undirected graphG=(V, E) is called ajoin if |CJ||C|/2 for every circuitC ofG. Answering a question of P. Solé and Th. Zaslavsky, we derive a min-max formula for the maximum cardinality of a joint ofG. Namely, =(+|V|–1)/2 where denotes the minimum number of edges whose contraction leaves a factor-critical graph.To study these parameters we introduce a new decomposition ofG, interesting for its own sake, whose building blocks are factor-critical graphs and matching-covered bipartite graphs. We prove that the length of such a decomposition is always and show how an optimal join can be constructed as the union of perfect matchings in the building blocks. The proof relies on the Gallai-Edmonds structure theorem and gives rise to a polynomial time algorithm to construct the optima in question. 相似文献
3.
Let
be a d - dimensional Markov family corresponding to a uniformly elliptic second order divergence form operator. We show that for any quasi continuous in the Sobolev space
the process (X) admits under P
x a decomposition into a martingale additive functional (AF) M
and a continuous AF A
of zero quadratic variation for almost every starting point x if q=2, for quasi every x if q>2 and for every
if is continuous, d=1 and
or d>1 and q>d. Our decomposition enables us to show that in the case of symmetric operator the energy of A
equals zero if q=2 and that the decomposition of (X) into the martingale AF M
and the AF of zero energy A
is strict if
for some q>d. Moreover, our decomposition provides a probabilistic representation of A
. 相似文献
4.
Shi Ronghua 《应用数学学报(英文版)》1985,2(2):154-160
In this paper we prove the following main results:
Theorem A. If bind (G)3/2, thenG–u has a Hamiltonian circuit for every vertexu of graphG
i, unlessG belongs either to two classesH
1 andH
2 of graphs or to some smaller order graphs with |V(G)|17.
Theorem B. If bind (G)3/2 and the maximum degree (G)>(n–1)/2, |V(G)|=n>17, thenG is pancyclic (i.e., it contains a circuit of every lengthm, 3m|V(G)|). 相似文献
5.
Jean Legras 《Numerische Mathematik》1966,8(1):14-28
Sommaire La solution stricte d'un système différentiel linéaire à coefficients constants [d /d t] = [A] [] + [f (t) ] est donnée par: [ (t)]= [eAt] [ (0) ] + f [eA(t–)] [f (T) ] d .Cette relation, utilisée dans une méthode de pas à pas, permet le calcul de [(t+u)] en fonction de [(t)]. La mise en oeuvre numérique de cette formule nécessite le calcul de [eA] et de l'intégrale de matrice du second membre.Le sujet de cette étude est la mise au point de techniques d'approximation permettant le calcul effectif de [e
Aµ] et de l'intégrale de matrice par des méthodes qui peuvent s'adapter en particulier aux systèmes différentiels à très grand nombre d'inconnues, qui apparaissent par exemple dans l'approximation par discrétisation enx ety, de l'équation aux dérivées partielles, dite de la chaleur. 相似文献
6.
In this paper we consider the anisotropic perimeter
defined on subsets E2, where the anisotropy is a (possibly non-symmetric) norm on 2 and E is the exterior unit normal vector to E.We consider quasi-minimal sets E (which include sets with prescribed curvature) and we prove that E(E) is locally a bi-Lipschitz curve and the singular set (E) is closed and discrete.We then classify the global P-minimal sets. In particular we find that global minimal sets may have a singular point if and only if {1} is a triangle or a quadrilateral and that sets with two singularities exist if and only if {1} is a triangle.We finally show that the boundary of a subset of 2, which locally minimizes the anisotropic perimeter, plus a volume term (prescribed constant curvature) is contained, up to a translation and a rescaling, in the boundary of the Wulff shape determined by the anisotropy. Mathematics Subject Classification (2000) 74N05, 49N60 相似文献
7.
Mark C. Ho 《Integral Equations and Operator Theory》1997,29(3):301-312
In this paper, we will use the Birkhoff's ergodic theorem to do some finer analysis on the spectral properties of slant Toeplitz operators. For example, we will show that if is an invertibleL
function on the unit circle, then almost every point in (A
*
) is not an eigenvalue ofA
*
. More specifically, we will show that the point spectrum ofA
*
is contained in a circle with positive radius. 相似文献
8.
Sanming Zhou 《Czechoslovak Mathematical Journal》1998,48(1):45-53
Let G be a graph with order p, size q and component number . For each i between p – and q, let
be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H
is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M
j() and m
j() be the invariants defined by
. It is proved that both M
p–() and m
p–(;) interpolate over
, if is continuous with respect to AET, and that M
j() and m
j() interpolate over
, if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized. 相似文献
9.
IfY is a finite graph then it is known that every sufficiently large groupG has a Cayley graph containing an induced subgraph isomorphic toY. This raises the question as to what is sufficiently large. Babai and Sós have used a probabilistic argument to show that |G| > 9.5 |Y|3 suffices. Using a form of greedy algorithm we strengthen this to
(2 + \sqrt 3 )|Y|^3 $$
" align="middle" border="0">
. Some related results on finite and infinite groups are included. 相似文献
10.
Erik Valtonen 《manuscripta mathematica》1989,63(1):45-68
LetR be a commutative ring with 1 andM anR-module. If:M
R
MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR
M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR
M; in particular, we are interested in some homological properties ofR
M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR
M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM
*, where the isomorphism is given by the adjoint of. 相似文献
11.
LetX, Y be finite sets and suppose thatF is a collection of pairs of sets (F, G),FX,GY satisfying |FF|s, |GG|t and |FF|+|GG|s+t+1 for all (F, G),F, GF. Extending a result of Sali, we determine the maximum ofF. 相似文献
12.
A subset X of a group G is said to be large (on the left) if, for any finite set of elements g1,l... ,gkin G, an intersection of the subsets giX=gimid x in X is not empty, that is, limits{i=1}
{k}giX . It is proved that a group in which elements of order 3 form a large subset is in fact of exponent 3. This result follows from the more general theorem on groups with a largely splitting automorphism of order 3, thus answering a question posed by Jaber amd Wagner in [1]. For groups with a largely splitting automorphism of order 4, it is shown that if His a normal -invariant soluble subgroup of derived length d then the derived subgroup [H,H] is nilpotent of class bounded in terms of d. The special case where =1 yields the same result for groups that are largely of exponent 4. 相似文献
13.
14.
Edward A. Bertram 《Israel Journal of Mathematics》1984,47(4):335-344
In 1955 R. Brauer and K. A. Fowler showed that ifG is a group of even order >2, and the order |Z(G)| of the center ofG is odd, then there exists a strongly real) elementx∈G−Z whose centralizer satisfies|C
G(x)|>|G|1/3. In Theorem 1 we show that every non-abeliansolvable groupG contains an elementx∈G−Z such that|C
G(x)|>[G:G′∩Z]1/2 (and thus|C
G(x)|>|G|1/3). We also note that if non-abelianG is either metabelian, nilpotent or (more generally) supersolvable, or anA-group, or any Frobenius group, then|C
G(x)|>|G|1/2 for somex∈G−Z. In Theorem 2 we prove that every non-abelian groupG of orderp
mqn (p, q primes) contains a proper centralizer of order >|G|1/2. Finally, in Theorem 3 we show that theaverage
|C(x)|, x∈G, is ≧c|G|
1/3 for metabelian groups, wherec is constant and the exponent 1/3 is best possible. 相似文献
15.
A topological graph is a graph G=(V, E) on a topological space V such that the edge set E is a closed subset of the product space V x V. If the graph contains no infinite independent set then, by a well-known theorem of Erdös, Dushnik and Miller, for any infinite set LV, there is a subset LL of the same oardinality |L| = |L| such that the restriction G L is a complete graph. We investigate the question of whether the same conclusion holds if we weaken the hypothesis and assume only that some dense subset AV does not contain an infinite independent set. If the cofinality cf (|L|)>|A|, then there is an L as before, but if cf (|L|)<-|A|, then some additional hypothesis seems to be required. We prove that, if the graph GA is a comparability graph and A is a dense subset, then for any set LV such that cf (|L|)>, there is a subset LL of size |L|=|L| such that GL is complete. The condition cf (|L|)> is needed.Research supported by NSERC grant #A5198. 相似文献
16.
LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. 相似文献
17.
Let G be an abelian
group of order n. The
critical number c(G) of G is the smallest
s such that the subset sums
set (S) covers all G for eachs ubset
SG\{0} of cardinality |S|s. It has been recently proved that, if
p is the smallest prime
dividing n and
n/p is composite, then
c(G)=|G|/p+p–2, thus establishing a conjecture of
Diderrich.We characterize the critical sets with |S|=|G|/p+p–3 and (S)=G, where p3 is the smallest prime dividing
n, n/p is composite and
n7p2+3p.We also extend a result of Diderrichan d Mann by proving
that, for n67, |S|n/3+2 and S=G
imply (S)=G. Sets of cardinality
for which
(S) =G are also characterized when
n183, the smallest prime
p dividing
n is odd and
n/p is composite. Finally we
obtain a necessary and sufficient condition for the equality
(G)=G
to hold when |S|n/(p+2)+p, where p5, n/p is composite and
n15p2.* Work partially supported by the Spanish Research
Council under grant TIC2000-1017 Work partially supported by the Catalan Research
Council under grant 2000SGR00079 相似文献
18.
19.
Circular Chromatic Number and
Mycielski Graphs 总被引:7,自引:0,他引:7
As a natural generalization of graph coloring, Vince
introduced the star chromatic number of a graph
G and denoted it by
*(G). Later, Zhu called it circular
chromatic number and denoted it by c(G). Let (G)
be the chromatic number of G.
In this paper, it is shown that if the complement of
G is non-hamiltonian, then
c(G)=(G). Denote by M(G)
the Mycielski graph of G.
Recursively define Mm(G)=M(Mm–1(G)). It was conjectured that if
mn–2, then c(Mm(Kn))=(Mm(Kn)). Suppose that
G is a graph on n vertices.
We prove that if
, then
c(M(G))=(M(G)). Let S be the set of vertices of degree
n–1 in
G. It is proved that if
|S| 3, then
c(M(G))=(M(G)), and if |S| 5, then c(M2(G))=(M2(G)), which implies the known results of
Chang, Huang, and Zhu that if n3, c(M(Kn))=(M(Kn)), and if
n5, then
c(M2(Kn))=(M2(Kn)).* Research supported by Grants from National Science
Foundation of China and Chinese Academy of
Sciences. 相似文献
20.
Huanyin Chen 《Southeast Asian Bulletin of Mathematics》2001,25(2):209-216
In this paper, we show that if rings A and B are (s, 2)-rings, then so is the ring of a Morita context (A, B, M, N, , ). Also we get analogous results for unit 1-stable ranges and GM-rings. These give new classes of rings satisfying such stable range conditions.2000 Mathematics Subject Classification: 16U99 16E50 相似文献