共查询到20条相似文献,搜索用时 32 毫秒
1.
Let μ be a real measure on the line such that its Poisson integral M( z) converges and satisfies| M( x+ iy)| Ae−cyα, y→+∞,for some constants A, c>0 and 0<α1. We show that for 1/2<α1 the measure μ must have many sign changes on both positive and negative rays. For 0<α1/2 this is true for at least one of the rays, and not always true for both rays. Asymptotical bounds for the number of sign changes are given which are sharp in some sense. 相似文献
2.
Suppose that G is a graph with n vertices and m edges, and let μ be the spectral radius of its adjacency matrix.Recently we showed that if G has no 4-cycle, then μ2- μn-1, with equality if and only if G is the friendship graph.Here we prove that if m9 and G has no 4-cycle, then μ2m, with equality if G is a star. For 4 m8 this assertion fails. 相似文献
3.
In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given k 4 and L 3 there are only finitely many arithmetic progressions of the form with xi , gcd( x0, xl) = 1 and 2 li L for i = 0, 1, …, k − 1. Furthermore, we show that, for L = 3, the progression (1, 1,…, 1) is the only such progression up to sign. Our proofs involve some well-known theorems of Faltings [9], Darmon and Granville [6] as well as Chabauty's method applied to superelliptic curves. 相似文献
4.
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following: 1. , for 1a5, a≠2. 2. A8. 3. PSL(3,4)e, for 1e10. 4. A5×PSL(3,4)e, for 1e10. Based on this result, we virtually show that if G is an ah-group with π( G) 2,3,5,7 , then F( G)≠1, or equivalently, that G has an abelian normal subgroup.In addition, we show that if G is an ah-group of minimal size which is not isomorphic to S3, then the non-abelian socle of G is either trivial or isomorphic to one of the following: 1. , for 3a5. 2. PSL(3,4)e, for 1e10. Our research lead us to interesting results related to transitivity and homogeneousity in permutation groups, and to subgroups of wreath products of form Z2Sn. These results are of independent interest and are located in appendices for greater autonomy. 相似文献
6.
New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1 dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms. 相似文献
7.
We consider boolean circuits C over the basis Ω={,} with inputs x1, x2,…, xn for which arrival times are given. For 1 in we define the delay of xi in C as the sum of ti and the number of gates on a longest directed path in C starting at xi. The delay of C is defined as the maximum delay of an input.Given a function of the form f(x1,x2,…,xn)=gn−1(gn−2(…g3(g2(g1(x1,x2),x3),x4)…,xn−1),xn) | where gjΩ for 1jn−1 and arrival times for x1,x2,…,xn, we describe a cubic-time algorithm that determines a circuit for f over Ω that is of linear size and whose delay is at most 1.44 times the optimum delay plus some small constant. 相似文献
8.
We develop a general context for the computation of the determinant of a Hankel matrix
Hn = (
αi+j)0i,jn, assuming some suitable conditions for the exponential (or ordinary) generating function of the sequence (
αn)
n0. Several well-known particular cases are thus derived in a unified way.
相似文献
9.
Let
μbe a Gaussian measure (say, on
Rn) and let
K,
LRnbe such that
Kis convex,
Lis a “layer” (i.e.,
L={
x:
ax,
ub} for some
a,
bRand
uRn), and the centers of mass (with respect to
μ) of
Kand
Lcoincide. Then
μ(
K∩
L)
μ(
K)·
μ(
L). This is motivated by the well-known “positive correlation conjecture” for symmetric sets and a related inequality of Sidak concerning confidence regions for means of multivariate normal distributions. The proof uses the estimate
Φ(
x)> 1−((8/
π)
1/2/(3
x+(
x2+8)
1/2))
e−x2/2,
x>−1, for the (standard) Gaussian cumulative distribution function, which is sharper than the classical inequality of Komatsu.
相似文献
10.
It is shown that the fundamental polynomials for (0, 1, …, 2
m+1) Hermite–Fejér interpolation on the zeros of the Chebyshev polynomials of the first kind are non-negative for −1
x1, thereby generalising a well-known property of the original Hermite–Fejér interpolation method. As an application of the result, Korovkin's 10theorem on monotone operators is used to present a new proof that the (0, 1, …, 2
m+1) Hermite–Fejér interpolation polynomials of
fC[−1, 1], based on
nChebyshev nodes, converge uniformly to
fas
n→∞.
相似文献
11.
An efficient method to generate all edge sets
XE of a graph
G=(
V,
E), which are vertex-disjoint unions of cycles, is presented. It can be tweaked to generate (i) all cycles, (ii) all cycles of cardinality 5, (iii) all chordless cycles, (iv) all Hamiltonian cycles.
相似文献
12.
Let
m and
n be positive integers with
n2 and 1
mn−1. We study rearrangement-invariant quasinorms
R and
D on functions
f: (0, 1)→
such that to each bounded domain
Ω in
n, with Lebesgue measure |
Ω|, there corresponds
C=
C(|
Ω|)>0 for which one has the Sobolev imbedding inequality
R(
u*(|
Ω|
t))
CD(|
mu|* (|
Ω|
t)),
uCm0(
Ω), involving the nonincreasing rearrangements of
u and a certain
mth order gradient of
u. When
m=1 we deal, in fact, with a closely related imbedding inequality of Talenti, in which
D need not be rearrangement-invariant,
R(
u*(|
Ω|
t))
CD((d/d
t) ∫
{x
n : |u(x)|>u*(|Ω| t)} |(
u)(
x)| d
x),
uC10(
Ω). In both cases we are especially interested in when the quasinorms are optimal, in the sense that
R cannot be replaced by an essentially larger quasinorm and
D cannot be replaced by an essentially smaller one. Our results yield best possible refinements of such (limiting) Sobolev inequalities as those of Trudinger, Strichartz, Hansson, Brézis, and Wainger.
相似文献
14.
Let 1<
p<∞, and
k,
m be positive integers such that 0(
k−2
m)
pn. Suppose Ω
Rn is an open set, and Δ is the Laplacian operator. We will show that there is a sequence of positive constants
cj such that for every
f in the Sobolev space
Wk,p(Ω), for all
xΩ except on a set whose Bessel capacity
Bk−2m,p is zero.
相似文献
15.
In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2
nu1 (HSOLSSOM(2
nu1)). For
u2, necessary conditions for existence of such an HSOLSSOM are that
u must be even and
n3
u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1)
n9 and
n3
u/2+1 or (2)
n263 and
n2(
u-2). In this paper we show that in (1) the condition
n9 can be extended to
n30 and that in (2), the condition
n263 can be improved to
n4, except possibly for 19 pairs (
n,
u), the largest of which is (53,28).
相似文献
16.
Let
I be a finite interval,
,
and 1
p∞. Given a set
M, of functions defined on
I, denote by
the subset of all functions
yM such that the
s-difference
is nonnegative on
I,
τ>0. Further, denote by
the Sobolev class of functions
x on
I with the seminorm
x(r)Lp1. We obtain the exact orders of the Kolmogorov and the linear widths, and of the shape-preserving widths of the classes
in
Lq for
s>
r+1 and (
r,
p,
q)≠(1,1,∞). We show that while the widths of the classes depend in an essential way on the parameter
s, which characterizes the shape of functions, the shape-preserving widths of these classes remain asymptotically ≈
n-2.
相似文献
17.
We compute the best constants of approximation by entire functions of spherical type and by trigonometric polynomials of spherical degree on classes of functions
f satisfying the condition Δ
kfLp1, where
p=1 or 2 and Δ is the Laplace operator.
相似文献
18.
The continuity conditions at the endpoints of interpolation theorems,
TaBjMj aAj for
j=0, 1, can be written with the help of the approximation functional:
E(
t,
Ta;
B1,
B0)
L∞M0 aA0 and
E(
t,
Ta;
B0,
B1)
L∞M1 aA1. As a special case of the results we present here we show that in the hypotheses of the interpolation theorem the
L∞ norms can be replaced by BMO(
+) norms. This leads to a strong version of the Stein-Weiss theorem on interpolation with change of measure. Another application of our results is that the condition
fL0, i.e.,
f*
L∞, where
f*(
γ)=
μ{|
f|>
γ} is the distribution function of
f, can be replaced in interpolation with
L(
p,
q) spaces by the weaker
f*BMO(
+).
相似文献
19.
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg
recurrences. We assume that the reflection coefficients tend to some complex number
a with 0<
a<1. The orthogonality measure
μ then lives essentially on the arc {
eit :
αt2
π−
α} where
sin
with
α(0,π). Under the certain rate of convergence it was proved in (Golinskii
et al. (
J. Approx. Theory96 (1999), 1–32)) that
μ has no mass points inside this arc. We show that this result is sharp in a sense. We also examine the case of the whole unit circle and some examples of singular continuous measures given by their reflection coefficients.
相似文献
20.
A graph
G is (
m,
n)-
linked if for any two disjoint subsets
R,
BV(
G) with |
R|
m and |
B|
n,
G has two disjoint connected subgraphs containing
R and
B, respectively. We shall prove that a planar graph with at least six vertices is (3,3)-linked if and only if
G is 4-connected and maximal.
相似文献