共查询到20条相似文献,搜索用时 15 毫秒
1.
Fang Liping 《数学学报(英文版)》1998,14(1):139-144
Letf be a holomorphic self-map of the punctured plane ℂ*=ℂ\{0} with essentially singular points 0 and ∞. In this note, we discuss the setsI
0(f)={z ∈ ℂ*:f
n
(z) → 0,n → ∞} andI
∞(f)={z ∈ ℂ*:f
n
(z) → 0,n → ∞}. We try to find the relation betweenI
0(f),I
∞(t) andJ(f). It is proved that both the boundary ofI
0(f) and the boundary ofI
∞)f) equal toJ(f),I
0(f) ∩J(f) ≠ θ andI
∞(f) ∩J(f) ≠ θ. As a consequence of these results, we find bothI
0(f) andI
∞(f) are not doubly-bounded.
Supported by the National Natural Science Foundation of China 相似文献
2.
P. Penner 《Algebra Universalis》1981,13(1):307-314
Following W. Taylor we define a hyperidentity ∈ to be formally the same as an identity (e.g.,F(G(x, y, z), G(x, y, z))=G(x, y, z)). However, a varietyV is said to satisfy a hyperidentity ∈, if whenever the operation symbols of ∈ are replaced by any choice of polynomials (appropriate
forV) of the same arity as the corresponding operation symbols of ∈, then the resulting identity holds inV in the usual sense. For example, if a varietyV of type <2,2> with operation symbols ∨ and ∧ satisfies the hyperidentity given above, then substituting the polynomial (x∨y)∨z
for the symbolG, and the polynomialx∧y forF, we see thatV must in particular satisfy the identity ((x∨y)∨z)∧((x∨y)∨z)=((x∨y)∨z). The set of all hyperidentities satisfied by a varietyV, will be denoted byH(V). We shall letH
m
(V) be the set of all hyperidentities hoiding inV with operation symbols of arity at mostm, andH
n
(V) will denote the set of all hyperidentities ofV with at mostn distinct variables. In this paper we shall show that ifV is a nontrivial variety of lattices or the variety of all semilattices, then for any integersm andn, there exists a hyperidentity ∈ such that ∈ holds inV, and ∈ is not a consequence ofH
m
(V)∪H
n
(V). From this it is deduced that the hyperidentities ofV are not finitely based, partly soling a problem of Taylor [7, Problem 3].
The research of the author was supported by NSERC of Canada.
Presented by W. Taylor. 相似文献
3.
Antonio Leaci 《manuscripta mathematica》1992,75(1):429-441
We prove the existence of a minimizing pair for the functionalG defined for every closed setK ⊂R
2 and for every functionu ∈C
1(ω/K) by
where ω is an open set inR
2, λ, μ>0,q≥1,g ∈L
q
(ω) ∩L
p
(ω) withp>2q andH
1 is the 1-dimensional Hausdorff measure. 相似文献
4.
Juan Luis Vázquez 《Israel Journal of Mathematics》1982,43(3):255-272
The semilinear perturbation of Poisson’s equation (E): −Δu+β(u)∋f, where β is a maximal monotone graph inR, has been investigated by Ph. Bénilan, H. Brézis and M. Crandall forf∈L
1(R
N
),N≧1, under the assumptions 0∈β(0) ifN≧3 and 0∈β(0) ∩ Int β(R) ifN=1,2. We discuss in this paper the solvability and well-posedness of (E) in terms of any maximal monotone graph β. In particular,
if β takes only positive values andN≧3 we prove that no solution exists; ifN=2 we give necessary and sufficient conditions on β andf for (E) to be solvable in a natural sense. 相似文献
5.
m , we associate with a finite monoid S
0 and m finite commutative monoids S
1
,...,S
m
, a product ◊
m
(S
m
, ..., S
1
, S
0
). We give a representation of the free objects in the pseudovariety ◊
m
(W
m
, ..., W
1, W
0) generated by these (m + 1) -ary products where S
1
∈W
i
for all 0 ≤i≤m . We then give, in particular, a criterion to determine when an identity holds in ◊
m
(J
1, ..., J
1, J
1) with the help of a version of the Ehrenfeucht-Fra?ssé game (J
1 denotes the pseudovariety of all semilattice monoids.). The union U
m > 0
◊
m
(J
1, ..., J
1, J
1) turns out to be the second level of the Straubing's dot-depth hierarchy of aperiodic monoids. 相似文献
6.
The varieties in the title are shown to be precisely the product varieties Gp*Ab(d) for some prime p and some positive integer d dividing p−1. Here Gp denotes the variety of all finite p-groups and Ab(d) the variety of all finite Abelian groups of exponent dividing d. It turns out that these are exactly those varieties H of supersolvable groups for which all finitely generated free pro-H groups are freely indexed in the sense of Lubotzky and van den Dries. Several alternative characterizations of these varieties
are presented. Some applications to formal language theory and finite monoid theory are also given. Among these is the determination
of all supersolvable solutions H to the equations PH = J*H and J*H = J H which is, to the present date, the most complete solution to a problem raised by Pin. Another consequence of our results
is that for each such variety H the monoid variety PH = J*H = J H has decidable membership.
The authors gratefully acknowledge the support of NSERC 相似文献
7.
LetR be a ring and σ an automorphism ofR. We prove the following results: (i)J(R
σ[x])={Σiri
x
i:r0∈I∩J(R]),
r
i∈I for alliε 1} whereI↪ {r∈R:rx ∈J(R
Σ[x])|s= (ii)J(R
σ<x>)=(J(R
σ<x>)∩R)σ<x>. As an application of the second result we prove that ifG is a solvable group such thatG andR, + have disjoint torsions thenJ(R)=0 impliesJ(R(G))=0. 相似文献
8.
Nonparametric analysis of doubly truncated data 总被引:1,自引:0,他引:1
Pao-sheng Shen 《Annals of the Institute of Statistical Mathematics》2010,62(5):835-853
One of the principal goals of the quasar investigations is to study luminosity evolution. A convenient one-parameter model
for luminosity says that the expected log luminosity, T*, increases linearly as θ
0· log(1 + Z*), and T*(θ
0) = T* − θ
0· log(1 + Z*) is independent of Z*, where Z* is the redshift of a quasar and θ
0 is the true value of evolution parameter. Due to experimental constraints, the distribution of T* is doubly truncated to an interval (U*, V*) depending on Z*, i.e., a quadruple (T*, Z*, U*, V*) is observable only when U* ≤ T* ≤ V*. Under the one-parameter model, T*(θ
0) is independent of (U*(θ
0), V*(θ
0)), where U*(θ
0) = U* − θ
0· log(1 + Z*) and V*(θ
0) = V* − θ
0· log(1 + Z*). Under this assumption, the nonparametric maximum likelihood estimate (NPMLE) of the hazard function of T*(θ
0) (denoted by ĥ) was developed by Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999). In this note, we present an alternative derivation
of ĥ. Besides, the NPMLE of distribution function of T*(θ
0), [^(F)]{\hat F} , will be derived through an inverse-probability-weighted (IPW) approach. Based on Theorem 3.1 of Van der Laan (1996), we
prove the consistency and asymptotic normality of the NPMLE [^(F)]{\hat F} under certain condition. For testing the null hypothesis Hq0: T*(q0) = T*-q0·log(1 + Z*){H_{\theta_0}: T^{\ast}(\theta_0) = T^{\ast}-\theta_0\cdot \log(1 + Z^{\ast})} is independent of Z*, (Efron and Petrosian in J Am Stat Assoc 94:824–834, 1999). proposed a truncated version of the Kendall’s tau statistic.
However, when T* is exponential distributed, the testing procedure is futile. To circumvent this difficulty, a modified testing procedure
is proposed. Simulations show that the proposed test works adequately for moderate sample size. 相似文献
9.
V. B. Lender 《Semigroup Forum》1993,47(1):373-380
If a semigroup varietyV contains the variety of commutative three-nilpotent semigroups, or if it is a variety of bands containing all semilattices,
then, for anyA∈V and any left cancellative monoidM, there is a semigroupS∈V such thatA is a retract ofS andM is isomorphic to the monoid of all injective endomorphisms ofS. 相似文献
10.
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
11.
For natural numbers r,s,q,m,n with s≥r≤q we determine all natural functions g: T
*(J
(r,s,q)(Y, R
1,1)0)*→R for any fibered manifold Y with m-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n with s≥r we determine all natural functions g: T
*(J
(r,s)
(Y, R)0)*→R for any Y as above. 相似文献
12.
San Ling 《Israel Journal of Mathematics》2000,116(1):117-123
For an abelian varietyA over ℚ
p
, the special fibre in the Néron model ofA over ℤ
p
is the extension of a finite group scheme over ℤ
p
, called the group of connected components, by the connected component of identity. WhenA is the Jacobian variety of an algebraic curve, its component group has been calculated in many cases. We determine in this
paper the component group of thep-new subvariety ofJ
0(M
p
), forM>1 a positive integer andp≥5 a prime not dividingM. Such a subvariety is not the Jacobian of any obvious curve, but it is not clear if it can ever be realised as the Jacobian
of a curve. 相似文献
13.
A subgroup H of a finite group G is called a TI-subgroup if H ∩ H
x
= 1 or H for any x ∈ G. In this short note, the finite groups all of whose nonabelian subgroups are TI-subgroups are classified. 相似文献
14.
We present a formula for the Fourier transforms of order statistics in ℝ
n
showing that all these Fourier transforms are equal up to a constant multiple outside the coordinate planes in ℝ
n
.
Fora
1≥...≥a
n≥0 andq>0, denote by ℓ
w,q
n
then-dimensional Lorentz space with the norm ‖(x
1,...,x
n)‖=(a
1(x
1
*
)
q
+...+a
n(x
n
*
)
q
)1/q
, where (x
1
*
,...,x
n
*
) is the non-increasing permutation of the numbers |x
1|,...,|x
n|. We use the above mentioned formula and the Fourier transform criterion of isometric embeddability of Banach spaces intoL
q [10] to prove that, forn≥3 andq≤1, the space ℓ
w,q
n
is isometric to a subspace ofL
q if and only if the numbersa
1,...,a
n form an arithmetic progression. Forq>1, all the numbersa
i must be equal so that ℓ
w,q
n
= ℓ
q
n
. Consequently, the Lorentz function spaceL
w,q(0, 1) is isometric to a subspace ofL
q if and only ifeither 0<q<∞ and the weightw is a constant function (so thatL
w,q=Lq),or q≤1 andw(t) is a decreasing linear function.
Finally, we relate our results to the theory of positive definite functions.
Both authors were supported in part by the NSF Workshop in Linear Analysis and Probability held at Texas A&M University in
August 1993. The work was done during the first author’s visit to Texas A&M University. 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.
Let F
q
be the finite field consisting of q = p
r
elements and yy an additive character of the field F
q
. Take an arbitrary multiplicative subgroup H of size |H| > q
C/(log log q) for some constant C > 0 not largely contained in any multiplicative shift of a subfield. We show that |Σ
h∈H
yy(h)| = o(|H|). This means that H is equidistributed in F
q
. 相似文献
17.
Andrés del Junco 《Israel Journal of Mathematics》1983,44(2):160-188
LetT
α be the translationx↦x+α (mod 1) of [0, 1), α irrational. LetT be the Lebesgue measure-preserving automorphism ofX=[0, 3/2) defined byTx = x + 1 forx∈[0, 1/2),Tx=T
α(x−1) forx∈[1,3/2) andTx = T
α
x forx∈[1/2, 1), i.e.T isT
α with a tower of height one built over [0, 1/2). If α is poorly approximable by rationals (there does not exist {p
n
/q
n
} with |α−p
n
/q
n
|=o(q
n
−2)) and λ is a measure onX
k
all of whose one-dimensional marginals are Lebesgue and which is ⊗
i − 1
k
T
1 invariant and ergodic (l>0) then λ is a product of off-diagonal measures. This property suffices for many purposes of counterexample construction.
A connection is established with the POD (proximal orbit dense) condition in topological dynamics.
Research supported in part by NSF contract MCS-8003038. 相似文献
18.
We prove a removal lemma for systems of linear equations over finite fields: let X
1, …, X
m
be subsets of the finite field F
q
and let A be a (k × m) matrix with coefficients in F
q
; if the linear system Ax = b has o(q
m−k
) solutions with x
i
∈ X
i
, then we can eliminate all these solutions by deleting o(q) elements from each X
i
. This extends a result of Green [Geometric and Functional Analysis 15 (2) (2005), 340–376] for a single linear equation in abelian groups to systems of linear equations. In particular, we also
obtain an analogous result for systems of equations over integers, a result conjectured by Green. Our proof uses the colored
version of the hypergraph Removal Lemma. 相似文献
19.
LetR be a ring and J its radical. DefineJ
1=∩Jn, J2=∩J
1
n
,…,… Jk=∩J
k−1
n
.... It is shown that in a ringR satisfying a polynomial identity and the ascending chain condition on ideals,J
k
=0 for some appropriatek.
The work of the first author was supported by an NSF grant at the University of Chicago. The work of the second author was
supported by an NSF grant at the University of California, San Diego. 相似文献
20.
J. B. Stephen 《Semigroup Forum》1992,44(1):255-270
There has recently been considerable interest in inverse monoids which are presented by generators and relations. In this
work the author employs graphical techniques to investigate the word problem for presentations of inverse monoids which generalize
the case in which all relations in a presentation are of the formw=w
2
. The work also investigates free objects in finitely based varieties of inverse semigroups, where the free objects have similar
presentations. A fundamental charecteristic of the monoids (semigroups) investigated is: ifF is a free inverse monoid andM=F/θ, then form∈F, theR-class ofmθ has no more elements than theR-class ofm. 相似文献