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1.
We obtain the asymptotic behaviour for the L
norm of the first eigenfunction of the Dirichlet Laplace operator on a conic sector over a geodesic disc
in
as
. We are led to conjecture that for an open, bounded and convex set D with inradius and diameter d,
where
and
相似文献
2.
Let
be the Dirichlet integral and
the Brownian motion on R. Let be a finite positive measure in the Kato class and
the additive functional associated with . We prove that for a regular domain D of R
d
where
D
is the exit time from D. As an application, we consider the integrability of Wiener functional exp (
). 相似文献
\beta )\;\; = \;\; - \inf \left\{ {\tfrac{1}{2}D(u,u):u \in C_0^\infty (D)\int_D {u^2 {\text{d}}} \mu = 1} \right\} \hfill \\ {\text{ for any }}x \in D, \hfill \\ \end{gathered} $$ " align="middle" vspace="20%" border="0"> |
3.
Let (
) be a regular Dirichlet form on L2(X;m) and {Px}x X the Hunt process generated by (
). Let be a signed 'smooth measure' associated with (
) and At the continuous additive functional corresponding to the measure . Under some conditions on (
) and , we shall prove that
where
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4.
In this paper, we consider a problem of the form
where d3, f is a positive locally Lipschitz bounded function and g is assumed to change sign. We give some conditions of integral type to get the existence of positive solutions for large enough. 相似文献
5.
Denote by
the class of all triangle-free
graphs on n vertices and
m edges. Our main result is
the following sharp threshold, which answers the question for
which densities a typical triangle-free graph is bipartite. Fix
> 0 and let
. If
n/2 m (1 – ) t
3, then almost
all graphs in
are not bipartite, whereas if
m (1 + )t
3, then almost
all of them are bipartite. For m (1 + )t
3, this allows
us to determine asymptotically the number of graphs in
. We also obtain corresponding
results for C
-free graphs, for any
cycle C
of fixed odd length.
Forschergruppe Algorithmen, Struktur, Zufall
supported by Deutsche Forschungsgemeinschaft grant FOR
413/1-1 相似文献
6.
For semigroups (e
tA
)
t0 of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type
0$$
" align="middle" border="0">
, where
denotes the trace class. As an application we present higher order analogues of results due to E.B. Davies, B. Simon and M. van den Berg of the type
0$$
" align="middle" border="0">
, for certain unbounded domains
, e.g. spiny urchin domains. 相似文献
7.
Given two disjoint subsets T
1 and
T
2 of
nodes in an undirected 3-connected graph G = (V, E) with node set
V and arc set
E, where
and
are even numbers, we
show that V can be
partitioned into two sets V
1 and
V
2
such that the graphs induced by V
1 and
V
2 are
both connected and
holds for each
j = 1,2. Such a partition can
be found in
time. Our proof relies
on geometric arguments. We define a new type of convex
embedding of k-connected
graphs into real space R
k-1 and prove that for
k = 3 such an embedding
always exists.
1 A preliminary version
of this paper with title Bisecting Two Subsets in 3-Connected
Graphs appeared in the Proceedings of the 10th Annual
International Symposium on Algorithms and Computation, ISAAC
99, (A. Aggarwal, C. P. Rangan, eds.), Springer LNCS 1741,
425–434, 1999. 相似文献
8.
Matching Polynomials And Duality 总被引:2,自引:0,他引:2
Let G be a simple graph on n vertices. An r-matching in G is a set of r independent edges. The number of r-matchings in G will be denoted by p(G, r). We set p(G, 0) = 1 and define the matching polynomial of G by
and the signless matching polynomial of G by
.It is classical that the matching polynomials of a graph G determine the matching polynomials of its complement
. We make this statement more explicit by proving new duality theorems by the generating function method for set functions. In particular, we show that the matching functions
and
are, up to a sign, real Fourier transforms of each other.Moreover, we generalize Foatas combinatorial proof of the Mehler formula for Hermite polynomials to matching polynomials. This provides a new short proof of the classical fact that all zeros of µ(G, x) are real. The same statement is also proved for a common generalization of the matching polynomial and the rook polynomial. 相似文献
9.
We obtain the new exact Kolmogorov-type inequality
for 2-periodic functions
and any k, r N, k < r. We present applications of this inequality to problems of approximation of one class of functions by another class and estimates of K-functional type. 相似文献
10.
We investigate the relationship between the constants K(R) and K(T), where
is the exact constant in the Kolmogorov inequality, R is the real axis, T is a unit circle,
is the set of functions x L
p(G) such that x
(r) L
s(G), q, p, s [1, ], k, r N, k < r, We prove that if
thenK(R) = K(T),but if
thenK(R) K(T); moreover, the last inequality can be an equality as well as a strict inequality. As a corollary, we obtain new exact Kolmogorov-type inequalities on the real axis. 相似文献
11.
We study the existence of classical (non-collision) T-periodic
solutions of the Hamiltonian system
where
and
is a T-periodic function in t which has a
singularity at
like
Under suitable conditions on H, we prove that if
then (HS) possesses at least one
non-collision solution and if
then the generalized solution of (HS) obtained in [5] has at most
one time of collision in its period. 相似文献
12.
Suppose that X is a Banach space, K denotes the set of real numbers R or the set of nonnegative real numbers R
{+},
is a family of linear operators from X into X such that T
0=I is the identity operator in X,
for all
, and there exists M such that
for all
. The expression
is called the rth order modulus of continuity of an element x with step h in the space X with respect to the family A(K). The properties of
are studied. Bibliography: 3 titles. 相似文献
13.
T. D. Porter 《Combinatorica》1992,12(3):317-321
For a graphG, let (U,V)=max{e(U), e(V)} for a bipartition (U, V) ofV(G) withUV=V(G),UV=Ø. Define (G)=min(U,V
){(U,V)}. Paul Erds conjectures
. This paper verifies the conjecture and shows
.This work was part of the author's Ph. D. thesis at the University of New Mexico. Research Partially supported by NSA Grant MDA904-92-H-3050. 相似文献
14.
We obtain a strengthened version of the Kolmogorov comparison theorem. In particular, this enables us to obtain a strengthened Kolmogorov inequality for functions x L
x
(r), namely,
where
k, r N, k < r, and
r
is a perfect Euler spline of order r. Using this inequality, we strengthen the Bernstein inequality for trigonometric polynomials and the Tikhomirov inequality for splines. Some other applications of this inequality are also given. 相似文献
15.
Zhen-Qing Chen 《Potential Analysis》1996,5(4):383-401
Let D be an open set in d and E be a relatively closed subset of D having zero Lebesgue measure. A necessary and sufficient integral condition is given for the Sobolev spaces W
1,2 (D) and W
1,2(D\E) to be the same. The latter is equivalent to (normally) reflecting Brownian motion (RBM) on
being indistinguishable (in distribution) from RBM on
. This integral condition is satisfied, for example, when E has zero (d–1)-dimensional Hausdorff measure. Therefore it is possible to delete from D a relatively closed subset E having positive capacity but nevertheless the RBM on
is indistinguishable from the RBM on
, or equivalently, W
1,2(D\E)=W1,2(D). An example of such kind is: D=2 and E is the Cantor set. In the proof of above mentioned results, a detailed study of RBMs on general open sets is given. In particular, a semimartingale decomposition and approximation result previously proved in [3] for RBMs on bounded open sets is extended to the case of unbounded open sets.Research supported in part by NSF Grant DMS 86-57483. 相似文献
16.
We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p [1, ], the following unimprovable inequality holds for functions
:
where
and
r
is the perfect Euler spline of order r. 相似文献
17.
E. Bolthausen 《Probability Theory and Related Fields》1986,72(2):305-318
Summary LetX
i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of
is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums
under the law transformed by the density exp
. 相似文献
18.
Existence and Stability Results for Renormalized Solutions to Noncoercive Nonlinear Elliptic Equations with Measure Data 总被引:1,自引:0,他引:1
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is
where is a bounded open subset of , , is the so-called Laplace operator, , is a Radon measure with bounded variation on , , , and belong to the Lorentz spaces , and , respectively. In particular we prove the existence result under the assumption that , is small enough and , with . We also prove a stability result for renormalized solutions to a class of noncoercive equations whose prototype is with . 相似文献
19.
Marian Nowak 《Czechoslovak Mathematical Journal》2000,50(2):401-414
Let
be a real Banach space and let E be an ideal of L
0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function
, defined by
, belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology
the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. 相似文献
20.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2002,42(4):425-448
LetA be a positive self-adjoint operator and letB be anm-accretive operator which isA-small with a relative bound less than one. LetH=A+B, thenH is well-defined on dom(H)=dom(A) andm-accretive. IfB is a strictlym-accretive operator obeying
then for the Trotter product formula we prove that
(and similar forH
*) asn, uniformly int0. We also show that: (a) theA-smallness ofB guarantees the condition (1) for (0,1/2), i.e. the estimate (2) holds for (0,1/2); (b) ifB is strictlym-sectorial, then there are sufficient conditions ensuring the relation (1) for =1/2, that implies (2); (c) ifB isA-small,m-sectorial and such that dom(A
1/2) is a subset of the formdomain ofB, then again (2) is valid for =1/2. 相似文献
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