共查询到20条相似文献,搜索用时 31 毫秒
1.
Zeng Fanping 《数学学报(英文版)》1998,14(4):457-462
LetP andAC be two primary sequences with min{P, AC}≥RLR
∞,ρ(P) and ρ(AC) be the eigenvalues ofP andAC, respectively. Letf∈C
0
(I, I) be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved thatf has the kneading sequenceK(f)≥(RC)
*m
*P if λ≥(ρ(P))1/2m, andK(f)>(RC)
*m*AC*E for any shift maximal sequenceE if λ>(ρ(AC))1/2m. The value of (ρ(P))1/2m or (ρ(AC))1/2m is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.
Project supported by the National Natural Science Foundation of China 相似文献
2.
G. Baikunth Nath 《Annals of the Institute of Statistical Mathematics》1977,29(1):259-273
Summary Let (X, Y) be bivariate normally distributed with means (μ
1,μ
2), variances (σ
1
2
,σ
2
2
) and correlation betweenX andY equal to ρ. Let (X
i
,Y
i
) be independent observations on (X,Y) fori=1,2,...,n. Because of practical considerations onlyZ
i
=min (X
i
,Y
i) is observed. In this paper, as in certain routine applications, assuming the means and the variances to be known in advance,
an unbiased consistent estimator of the unknown distribution parameter ρ is proposed. A comparison between the traditional
maximum likelihood estimator and the unbiased estimator is made. Finally, the problem is extended to multivariate normal populations
with common mean, common variance and common non-negative correlation coefficient. 相似文献
3.
LetB be a compact convex body symmetric around0 in ℝ2 which has nonempty interior, i.e., the unit ball of a two-dimensional Minkowski space. The self-packing radiusρ(m,B) is the smallestt such thatt
B can be packed withm translates of the interior ofB. Form≤6 we show that the self-packing radiusρ(m,B)=1+2/α(m,B) whereα(m,B) is the Minkowski length of the side of the largest equilateralm-gon inscribed inB (measured in the Minkowski metric determined byB). We showρ(6,B)=ρ(7,B)=3 for allB, and determine most of the largest and smallest values ofρ(m,B) form≤7. For allm we have
相似文献
4.
Q. X. Yang 《Proceedings Mathematical Sciences》2005,115(3):347-368
In this paper, we characterize the symbol in Hormander symbol classS
ρ
m
,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kerneldistribution property for the symbol in the symbol classS
ρ
m
,δ (m ∈R, ρ > 0, δ≥ 0) which is more general than known results ; for non-regular symbol operators, we establish sharp L2-continuity which is better than Calderón and Vaillancourt’s result, and establishL
p
(1 ≤p ≤∞) continuity which is new and sharp. Our new idea is to analyse the symbol operators in phase space with relative wavelets,
and to establish the kernel distribution property and the operator’s continuity on the basis of the wavelets coefficients
in phase space. 相似文献
5.
The problem of finding a solution of the Neumann problem for the Laplacian in the form of a simple layer potential Vρ with unknown density ρ is known to be reducible to a boundary integral equation of the second kind to be solved for density.
The Neumann problem is examined in a bounded n-dimensional domain Ω+ (n > 2) with a cusp of an outward isolated peak either on its boundary or in its complement Ω− = R
n
\Ω+. Let Γ be the common boundary of the domains Ω±, Tr(Γ) be the space of traces on Γ of functions with finite Dirichlet integral over R
n
, and Tr(Γ)* be the dual space to Tr(Γ). We show that the solution of the Neumann problem for a domain Ω− with a cusp of an inward peak may be represented as Vρ−, where ρ− ∈ Tr(Γ)* is uniquely determined for all Ψ− ∈ Tr(Γ)*. If Ω+ is a domain with an inward peak and if Ψ+ ∈ Tr(Γ)*, Ψ+ ⊥ 1, then the solution of the Neumann problem for Ω+ has the representation u
+ = Vρ+ for some ρ+ ∈ Tr(Γ)* which is unique up to an additive constant ρ0, ρ0 = V
−1(1). These results do not hold for domains with outward peak. 相似文献
6.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
7.
Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aw of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aw)=1/d.tr(Aρ).It is proved that the set of all C^*-algebras of sections of locally trivial C^*-algebra bundles over S^2 with fibres Aω has a group sturcture,denoted by π1^s(Aut(Aω)),which is isomorphic to Zif Ed>1 and {0} if d>1.Let Bcd be a cd-homogeneous C^*-algebra over S^2×T^2 of which no non-trivial matrix algebra can be factored out.The spherical noncommutative torus Sρ^cd is defined by twisting C^*(T2×Z^m-2) in Bcd ×C^*(Z^m-3) by a totally skew multiplier ρ on T^2×Z^m-2。It is shown that Sρ^cd×Mρ∞ is isomorphic to C(S^2)×C^*(T^2×Z^m-2,ρ)× Mcd(C)×Mρ∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p. 相似文献
8.
Denny H. Leung 《Israel Journal of Mathematics》2001,121(1):247-264
The space WeakL
1 consists of all Lebesgue measurable functions on [0,1] such thatq(f)=supcλ{t:|f(t)|>c} c>0 is finite, where λ denotes Lebesgue measure. Let ρ be the gauge functional of the convex hull of the unit ball {f:q(f)≤1} of the quasi-normq, and letN be the null space of ρ. The normed envelope of WeakL
1, which we denote byW, is the space (WeakL
1/N, ρ). The Banach envelope of WeakL
1,
, is the completion ofW. We show that
is isometrically lattice isomorphic to a sublattice ofW. It is also shown that all rearrangement invariant Banach function spaces are isometrically lattice isomorphic to a sublattice
ofW. 相似文献
9.
In the present paper, the embedding problem is considered for number fields with p-groups whose kernel is either of two groups
with two generators α and β and with the following relations: (1) αρ=1, αρ=1, [α,β,β]=1, [α,β,α,α]=1, or (2) αρ=[α, β α], βρ=1, [α,β,β]=1. It is shown that for the solvability of the original embedding problem it is necessary and sufficient to have the solvability
of the associated Abelian and local problems for all completions of the base fields. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 120–126.
Translated by V. V. Ishkhanov. 相似文献
10.
Allen Weitsman 《Israel Journal of Mathematics》2001,124(1):327-331
Letw=f(z) be a univalent harmonic mapping of the annulus {ρ≤|z|≤1} onto the annulus {σ≤|w|≤1}. It is shown thatσ≤1/(1+(ρ
2/2)(logρ)2). 相似文献
11.
Consider the Cauchy problem ∂u(x, t)/∂t = ℋu(x, t) (x∈ℤd, t≥ 0) with initial condition u(x, 0) ≡ 1 and with ℋ the Anderson Hamiltonian ℋ = κΔ + ξ. Here Δ is the discrete Laplacian, κ∈ (0, ∞) is a diffusion constant,
and ξ = {ξ(x): x∈ℤ
d
} is an i.i.d.random field taking values in ℝ. G?rtner and Molchanov (1990) have shown that if the law of ξ(0) is nondegenerate,
then the solution u is asymptotically intermittent.
In the present paper we study the structure of the intermittent peaks for the special case where the law of ξ(0) is (in the
vicinity of) the double exponential Prob(ξ(0) > s) = exp[−e
s
/θ] (s∈ℝ). Here θ∈ (0, ∞) is a parameter that can be thought of as measuring the degree of disorder in the ξ-field. Our main result
is that, for fixed x, y∈ℤ
d
and t→∈, the correlation coefficient of u(x, t) and u(y, t) converges to ∥w
ρ∥−2
ℓ2Σz ∈ℤd
w
ρ(x+z)w
ρ(y+z). In this expression, ρ = θ/κ while w
ρ:ℤd→ℝ+ is given by w
ρ = (v
ρ)⊗
d
with v
ρ: ℤ→ℝ+ the unique centered ground state (i.e., the solution in ℓ2(ℤ) with minimal l
2-norm) of the 1-dimensional nonlinear equation Δv + 2ρv log v = 0. The uniqueness of the ground state is actually proved only for large ρ, but is conjectured to hold for any ρ∈ (0, ∞).
empty
It turns out that if the right tail of the law of ξ(0) is thicker (or thinner) than the double exponential, then the correlation
coefficient of u(x, t) and u(y, t) converges to δ
x, y
(resp.the constant function 1). Thus, the double exponential family is the critical class exhibiting a nondegenerate correlation
structure.
Received: 5 March 1997 / Revised version: 21 September 1998 相似文献
12.
We present the bi-Hamiltonian structure and Lax pair of the equation ρt = bux+(1/2)[(u
2
−ux
2
)ρ]x, where ρ = u − uxx and b = const, which guarantees its integrability in the Lax pair sense. We study nonsmooth soliton solutions of this equation and show
that under the vanishing boundary condition u → 0 at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions. 相似文献
13.
I. E. Chyzhykov 《Ukrainian Mathematical Journal》2007,59(7):1088-1109
For arbitrary 0 ≤ σ ≤ ρ ≤ σ + 1, we describe the class A
σ
ρ
of functions g(z) analytic in the unit disk
= {z : ∣z∣ < 1} and such that g(z) ≠ 0, ρT[g] = σ, and ρM[g] = ρ, where
14.
Le Anh Vinh 《Annals of Combinatorics》2011,15(3):541-547
Using Fourier analysis, Covert, Hart, Iosevich, and Uriarte-Tuero (2008) showed that if the cardinality of a subset of the
2-dimensional vector space over a finite field with q elements is ≥ ρq
2, with
q-1/2 << r £ 1{q^{-1/2} \ll \rho \leq 1}
then it contains an isometric copy of ≥ cρq
3 triangles. In this note, we give a graph theoretic proof of this result. 相似文献
15.
Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C
ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ3 of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC
1 cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes
based on finite elements of this type. 相似文献
16.
Bifurcations of rough heteroclinic loop with two saddle points 总被引:7,自引:0,他引:7
The bifurcation problems of rough 2-point-loop are studied for the case p11 > λ11, p21 < λ21, P11p21 <λ111λ21. where - pi1 < 0 and λi1 > 0 are the pair of principal eigenvalues of unperturbed system at saddle point pi, i = 1,2. Under the transversal and nontwisted conditions, the authors obtain some results of the existence of one 1-periodic orbit, one 1-periodic and one 1-homoclinic loop, two 1-periodic orbits and one 2-fold 1-periodic orbit. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation graph is drawn. 相似文献
17.
P. J. Kim 《Annals of the Institute of Statistical Mathematics》1976,28(1):267-275
Summary Adequacy of the Smirnov approximation to P (D
mn
≧c/mn), of the exact distribution of the two sample Kolmogorov-Smirnov criterion,D
mn
,m<=n is examined. The main finding is that accuracy depends as much on the sample sizes,m andn, as on the ratio, ρ=m/n. The Smirnov approximation is good whenn is an integer multiple ofm, especiallyn=m, 2m; poor otherwise. This contrasts with the Smirnov approximation to P (D
mn
>c/mn), where this ordering is reversed, the cases forn=m, 2m being poor. The merit of continuity correction, of order ofn
−1 in theD
mn
scale, is demonstrated for the Smirnov approximation, .1≦ρ, as well as for the Kolmogorov approximation, ρ<.1. As an argument
for the optimum choice of ρ, the casen=m+1 is shown to have much to recommend it over the casen=m. Finally the usefulness of theχ
2 distribution with 2 degress of freedom is illustrated as an approximation to the Smirnov distribution.
This study was in part supported by USPHS-NIH Grant number 2 DO4 AH 0167 07 PHT Development Project. 相似文献
18.
Daan Krammer 《Inventiones Mathematicae》2000,142(3):451-486
We study a linear representation ρ:B
n
? GL
m
(Z[q
±1,t
±1]) with m=n(n-1)/2. We will show that for n=4, this representation is faithful. We prove a relation with the new Charney length function. We formulate a conjecture implying
that ρ is faithful for all n.
Oblatum 15-VI-1999 & 24-II-2000?Published online: 18 September 2000 相似文献
19.
We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (ℝ
d
, g), d ≥ 3, when the metric g is non-trapping and approaches the Euclidean metric like 〈x〉−ρ
with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial
data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric is radial with ρ > 1 for d = 3. 相似文献
20.
We introduce and study a classl
1
dom
(ρ) ofl
1-embeddable metrics corresponding to a given metric ρ. This class is defined as the set of all convex combinations of ρ-dominated
line metrics. Such metrics were implicitly used before in several constuctions of low-distortion embeddings intol
p
-spaces, such as Bourgain’s embedding of an arbitrary metric ρ onn points withO(logh) distortion. Our main result is that the gap between the distortions of embedding of a finite metric ρ of sizen intol
2 versus intol
1
dom
(ρ) is at most
, and that this bound is essentially tight. A significant part of the paper is devoted to proving lower bounds on distortion
of such embeddings. We also discuss some general properties and concrete examples.
Research by J. M. supported by Charles University grants No. 158/99 and 159/99. Part of the work by Y. R. was done during
his visit at the Charles University in Prague partially supported by these grants, by the grant GAČR 201/99/0242, and by Haifa
University grant for Promotion of Research. 相似文献
|