共查询到20条相似文献,搜索用时 46 毫秒
1.
Aristide Sanini 《Rendiconti del Circolo Matematico di Palermo》1992,41(2):165-184
Letf: (M,g)→(N,g′) be a differentiable map between the riemannian manifoldsM andN, M being compact.K. Uhlenbeck pointed out a functionalE
m(f), related to the energy density off, that depends only on the conformal structure ofM.
In this paper we prove thatE
m(f) is stationary with respect to deformations of the riemannian metric ofM if and only iff is weakly conformal; in this casef provides a local minimum ofE
m. 相似文献
2.
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E | arbieary f ∈ E, S(f , e) loheain in w(e)} isomorphic to E° by θ:Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J(E∪ S°) satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J(S°), called the weakly inverse hull of a weakly inverse system (S°, E, θ, φ) with I(∑) ≌ S°, E(∑) ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given. 相似文献
3.
M. Craizer 《Israel Journal of Mathematics》1991,74(2-3):129-168
In this paper, we show that an inner functionf has finite entropy if and only if its derivativef′ lies in the Nevanlinna class. We prove also that the entropy off is given by the average of the logarithm of |f′|. The proof is based on the fact that, evenf being highly discontinuous on the circle, the action off
−n
on Borel subsets is smooth. 相似文献
4.
LetX be a smooth irreducible projective variety over an algebraically closed fieldK andE a vector bundle onX. We prove that, if dimX ≥ 1, there exist a smooth irreducible projective varietyZ overK, a surjective separable morphismf:Z →X which is finite outside an algebraic subset of codimension ≥ 3 inX and a line bundleL onX such that the direct image ofL byf is isomorphic toE. WhenX is a curve, we show thatZ, f, L can be so chosen thatf is finite and the canonical mapH
1(Z, O) →H
1(X, EndE) is surjective.
Dedicated to the memory of Professor K G Ramanathan 相似文献
5.
Summary Let (Ω,A) be a measurable space, let Θ be an open set inR
k
, and let {P
θ; θ∈Θ} be a family of probability measures defined onA. Let μ be a σ-finite measure onA, and assume thatP
θ≪μ for each θ∈Θ. Let us denote a specified version ofdP
θ
/d
μ
byf(ω; θ).
In many large sample problems in statistics, where a study of the log-likelihood is important, it has been convenient to impose
conditions onf(ω; θ) similar to those used by Cramér [2] to establish the consistency and asymptotic normality of maximum likelihood estimates.
These are of a purely analytical nature, involving two or three pointwise derivatives of lnf(ω; θ) with respect to θ. Assumptions of this nature do not have any clear probabilistic or statistical interpretation.
In [10], LeCam introduced the concept of differentially asymptotically normal (DAN) families of distributions. One of the
basic properties of such a family is the form of the asymptotic expansion, in the probability sense, of the log-likelihoods.
Roussas [14] and LeCam [11] give conditions under which certain Markov Processes, and sequences of independent identically
distributed random variables, respectively, form DAN families of distributions. In both of these papers one of the basic assumptions
is the differentiability in quadratic mean of a certain random function. This seems to be a more appealing type of assumption
because of its probabilistic nature.
In this paper, we shall prove a theorem involving differentiability in quadratic mean of random functions. This is done in
Section 2. Then, by confining attention to the special case when the random function is that considered by LeCam and Roussas,
we will be able to show that the standard conditions of Cramér type are actually stronger than the conditions of LeCam and
Roussas in that they imply the existence of the necessary quadratic mean derivative. The relevant discussion is found in Section
3.
This research was supported by the National Science Foundation, Grant GP-20036. 相似文献
6.
John Franks 《Publications Mathématiques de L'IHéS》1990,71(1):105-120
Letf be an orientation preserving diffeomorphism ofR
2 which preserves area. We prove the existence of infinitely many periodic points with distinct rotation numbers around a fixed
point off, provided only thatf has two fixed points whose infinitesimal rotation numbers are not both 0.
We also show that if a fixed pointz off is enclosed in a “simple heteroclinic cycle” and has a non-zero infinitesimal rotation numberr, then for every non-zero rational numberp/q in an interval with endpoints 0 andr, there is a periodic orbit inside the heteroclinic cycle with rotation numberp/q aroundz. 相似文献
7.
Boris Shekhtman 《Journal of Approximation Theory》1996,85(3):343-347
LetEbe a subspace ofC(X) and letR(E)=g/h : g, hE; h>0}. We make a simple, yet intriguing observation: if zero is a best approximation toffromE, then zero is a best approximation toffromR(E). We also prove that if {En} is dense inC(X) then for almost allf(in the sense of category)[formula]That extends the results of P. Borwein and S. Zhou who proved it for the case whenEnis the space of algebraic or trigonometric polynomials of degreen. 相似文献
8.
Liliana Gabriela Gheorghe 《Annali di Matematica Pura ed Applicata》2001,180(2):203-210
We study membership to Schatten ideals S
E
, associated with a monotone Riesz–Fischer space E, for the Hankel operators H
f
defined on the Hardy space H
2(∂D). The conditions are expressed in terms of regularity of its symbol: we prove that H
f
∈S
E
if and only if f∈B
E
, the Besov space associated with a monotone Riesz–Fischer space E(dλ) over the measure space (D,dλ) and the main tool is the interpolation of operators.
Received: December 17, 1999; in final form: September 25, 2000?Published online: July 13, 2001 相似文献
9.
R. J. Cook 《Proceedings Mathematical Sciences》1989,99(2):147-153
Letf(x)=θ1
x
1
k
+...+θ
s
x
s
k
be an additive form with real coefficients, and ∥α∥ = min {|α-u|:uεℤ} denote the distance fromα to the nearest integer. We show that ifθ
1,…,θ
s
, are algebraic ands = 4k then there are integersx
1,…,x
s
, satisfying l ≤x
1,≤ N and ∥f(x)∥ ≤ N
E
, withE = − 1 + 2/e.
Whens = λk, 1 ≤λ ≤ 2k, the exponentE may be replaced byλE/4, and if we drop the condition thatθ
1,…,θ
s
, be algebraic then the result holds for almost all values of θεℝ
s
. Whenk ≥ 6 is small a better exponent is obtained using Heath-Brown’s version of Weyl’s estimate. 相似文献
10.
Michel Talagrand 《Israel Journal of Mathematics》1980,35(1-2):171-176
We construct a Banach spaceE such thatE′ isw
*-separable, andf∈E″/E, which isw
*-continuous on every set ofE′ which is thew
*-closure of a countablebounded set ofE′.
相似文献
11.
We investigateV
f
, the cardinality of the value set of a polynomialf of degreen over a finite field of cardinalityq. It has been shown that iff is not bijective, thenV
f
≤q−(q−1)/n. Polynomials do exist which essentially achieve that bound. We do prove that if the degree off is prime to the characteristic andf is not bijective, then asymptoticallyV
f
≤(5/6)q. We consider related problems for curves and higher dimensional varieties. This problem is related to the number of fixed
point free elements in finite groups, and we prove some results in that setting as well.
Both authors partially supported by the NSF. 相似文献
12.
Let k be a p-adic field of odd residue characteristic and let C be a hyperelliptic (or elliptic) curve defined by the affine equation Y
2=h(X). We discuss the index of C if h(X)=ɛf(X), where ɛ is either a non-square unit or a uniformising element in O
k
and f(X) a monic, irreducible polynomial with integral coefficients. If a root θ of f generates an extension k(θ) with ramification index a power of 2, we completely determine the index of C in terms of data associated to θ. Theorem 3.11 summarizes our results and provides an algorithm to calculate the index for
such curves C.
Received: 14 July 1997 / Revised version: 16 February 1998 相似文献
13.
A. V. Karzanov 《Combinatorica》1985,5(4):325-335
A family ℱ of cuts of an undirected graphG=(V, E) is known to have the weak MFMC-property if (i) ℱ is the set ofT-cuts for someT⊆V with |T| even, or (ii) ℱ is the set of two-commodity cuts ofG, i.e. cuts separating any two distinguished pairs of vertices ofG, or (iii) ℱ is the set of cuts induced (in a sense) by a ring of subsets of a setT⊆V. In the present work we consider a large class of families of cuts of complete graphs and prove that a family from this class
has the MFMC-property if and only if it is one of (i), (ii), (iii). 相似文献
14.
Ferenc Weisz 《Journal of Fourier Analysis and Applications》2009,15(4):463-487
A general summability method, the so-called θ-summability method is considered for Gabor series. It is proved that if the Fourier transform of θ is in a Herz space then this summation method for the Gabor expansion of f converges to f almost everywhere when f∈L
1 or, more generally, when f∈W(L
1,ℓ
∞) (Wiener amalgam space). Some weak type inequalities for the maximal operator corresponding to the θ-means of the Gabor expansion are obtained. Hardy-Littlewood type maximal functions are introduced and some inequalities are
proved for these. 相似文献
15.
For a Bernstein function f the sequence sn=f(1)·...· f(n) is a Stieltjes moment sequence with the property that all powers snc,c>0 are again Stieltjes moment sequences. We prove that
is Stieltjes determinate for c≤ 2, but it can be indeterminate for c>2 as is shown by the moment sequence
, corresponding to the Bernstein function f(s)=s. Nevertheless there always exists a unique product convolution semigroup
such that ρc has moments
. We apply the indeterminacy of
for c>2 to prove that the distribution of the product of p independent identically distributed normal random variables is indeterminate if and only if p≥ 3 相似文献
16.
We investigate the relationships between smooth and strongly smooth points of the unit ball of an order continuous symmetric
function space E, and of the unit ball of the space of τ-measurable operators E(M,t){E(\mathcal{M},\tau)} associated to a semifinite von Neumann algebra (M, t){(\mathcal{M}, \tau)}. We prove that x is a smooth point of the unit ball in E(M, t){E(\mathcal{M}, \tau)} if and only if the decreasing rearrangement μ(x) of the operator x is a smooth point of the unit ball in E, and either μ(∞; f) = 0, for the function f ? SE×{f\in S_{E^{\times}}} supporting μ(x), or s(x
*) = 1. Under the assumption that the trace τ on M{\mathcal{M}} is σ-finite, we show that x is strongly smooth point of the unit ball in E(M, t){E(\mathcal{M}, \tau)} if and only if its decreasing rearrangement μ(x) is a strongly smooth point of the unit ball in E. Consequently, for a symmetric function space E, we obtain corresponding relations between smoothness or strong smoothness of the function f and its decreasing rearrangement μ(f). Finally, under suitable assumptions, we state results relating the global properties such as smoothness and Fréchet smoothness
of the spaces E and E(M,t){E(\mathcal{M},\tau)}. 相似文献
17.
Let M be a closed surface, orientable or non-orientable, and letf be a C° flow onM of which all singular points are isolated. Thenf has the pseudo-orbit tracing property if and only if (i) for anyx ∈ M, both the ωlimit set ω(x) and the α-limit set α(x) ofx contain only one orbit; (ii) for any regular pointx off, if ω(x) is not quasi-attracting, then α(x) is quasi-exclusive; (iii) every saddle point off is strict, and at most 4-forked.
Project supported by the National Natural Science Foundation of China. 相似文献
18.
Eve Bofinger 《Annals of the Institute of Statistical Mathematics》1986,38(1):445-450
Summary The selection oft out ofk populations with parameters θ
i
(i=1, ...,k) is said to result in an ψ-correct decision provided ψ (minimum selected θ)>maximum non-selected θ where ψ(θ) (>θ) is an
increasing function. For the cases of location or scale parameters the minimum probability of ψ-correct decision over the
entire parameter space is shown to be no less than the minimum probability of correct selection over a preference zone determined
by ψ(θ). For other types of parameters this result is shown to be true under certain conditions linking the distribution function
and the ψ function. 相似文献
19.
V. A. Gorelov 《Mathematical Notes》2000,67(2):138-151
We prove a generalization of Shidlovskii’s theorem on the algebraic independence of the values ofE-functions satisfying a system of linear differential equations that is well known in the theory of transcendental numbers.
We consider the case in which the values ofE-functions are taken at singular points of these systems. Using the obtained results, we prove Siegel’s conjecture that, for
the case of first-order differential equations, anyE-function satisfying a linear differential equation is representable as a polynomial in hypergeometricE-functions.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 174–190, February, 2000. 相似文献
20.
Alejandro Illanes 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):483-498
Adendroid is an arcwise connected hereditarily unicoherent continuum. Ashore set in a dendroidX is a subsetA ofX such that, for each ε>0, there exists a subdendroidB ofX such that the Hausdorff distance fromB toX is less then ε andB∩A=θ.
Answering a question by I. Puga, in this paper we prove that the finite union of pairwise disjoint shore subdendroids of a
dendroidX is a shore set. We also show that the hypothesis that the shore subdendroids are disjoint is necessary. It is still unknown
if the union of two closed disjoint shore subsets of a dendroidX is also shore set. 相似文献