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1.
A Borel derivative on the hyperspace 2
X
of a compactumX is a Borel monotone mapD: 2
X
→2
X
. The derivative determines a Cantor-Bendixson type rank δ:2X → ω1 ∪ {∞} . We show that ifA⊂2
X
is analytic andZ⊂A intersects stationary many layers δ−1({ξ}), then for almost all σ,F∩δ−1({ξ}) cannot be separated fromZ ∩∪
a<ξ
δ−1({a}) (and also fromZ ∩∪
a>ξ
δ−1({a}) by anyF
σ-set. Another main result involves a natural partial order on 2
X
related to the derivative. The results are obtained in a general framework of “resolvable ranks” introduced in the paper.
During our work on this paper the second author was a Visiting Professor at the Miami University, Ohio. This author would
like to express his gratitude to the Department of Mathematics and Statistics for the hospitality. 相似文献
2.
We explicitly solve the equation Ax
n
− By
n
= ±1 and, along the way, we obtain new results for a collection of equations Ax
n
− By
n
= z
m
with m ∈ {3, n}, where x, y, z, A, B, and n are unknown nonzero integers such that n ≥ 3, AB = p
α
q
β
with nonnegative integers α and β and with primes 2 ≤ p < q < 30. The proofs depend on a combination of several powerful methods, including the modular approach, recent lower bounds for
linear forms in logarithms, somewhat involved local considerations, and computational techniques for solving Thue equations
of low degree. 相似文献
3.
Imre Patyi 《Mathematische Annalen》2003,326(3):443-458
Let X be one of the Banach spaces c
0
, ℓ
p
, 1≤p<∞; Ω⊂X pseudoconvex open, a holomorphic Banach vector bundle with a Banach Lie group G
*
for structure group. We show that a suitable Runge-type approximation hypothesis on X, G
*
(which we also prove for G
*
a solvable Lie group) implies the vanishing of the sheaf cohomology groups H
q
(Ω, 𝒪
E
), q≥1, with coefficients in the sheaf of germs of holomorphic sections of E. Further, letting 𝒪Γ (𝒞Γ) be the sheaf of germs of holomorphic (continuous) sections of a Banach Lie group bundle Γ→Ω with Banach Lie groups G, G
*
for fiber group and structure group, we show that a suitable Runge-type approximation hypothesis on X, G, G
*
(which we prove again for G, G
*
solvable Lie groups) implies the injectivity (and for X=ℓ1 also the surjectivity) of the Grauert–Oka map H
1
(Ω, 𝒪Γ)→H
1
(Ω, 𝒞Γ) of multiplicative cohomology sets.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L20, 32L05, 46G20
RID="*"
ID="*" Kedves Laci Móhan kisfiamnak.
RID="*"
ID="*" To my dear little Son 相似文献
4.
D. V. Shirkov 《Theoretical and Mathematical Physics》1999,119(1):438-447
The structure of the QFT expansion is studied in the framework of a new “invariant analytic” version of the perturbative QCD.
Here, an invariant coupling constant α(Q
2
/Λ
2
) = β
1
αs(Q
2
)/(4π) becomes a Q
2
-analytic invariant function α
an
(Q2/Λ
2
) ≡A(x), which, by construction, is free of ghost singularities because it incorporates some nonperturbative structures. In the
framework of the “analyticized” perturbation theory, an expansion for an observable F, instead of powers of the analytic invariant
charge A(x), may contain specific functions An(x)=[an(x)]
an
, the “nth power of a(x) analyticized as a whole.” Functions A
n>2(x) for small Q2 ≤Λ
2
oscillate, which results in weak loop and scheme dependences. Because of the analyticity requirement, the perturbation series
for F(x) becomes an asymptotic expansion à la Erdélyi using a nonpower set {A
n
(x)}. The probable ambiguities of the invariant analyticization procedure and the possible inconsistency of some of its versions
with the renormalization group structure are also discussed.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 55–66, April, 1999. 相似文献
5.
Nir Ben David 《Israel Journal of Mathematics》2009,170(1):317-335
A finite group G is of central type (in the non-classical sense) if it admits a non-degenerate cohomology class [c] ∈ H
2(G, ℂ*) (G acts trivially on ℂ*). Groups of central type play a fundamental role in the classification of semisimple triangular complex
Hopf algebras and can be determined by their representation-theoretical properties.
Suppose that a finite group Q acts on an abelian group A so that there exists a bijective 1-cocycle π ∈ Z
1(Q,Ǎ), where Ǎ = Hom(A, ℂ*) is endowed with the diagonal Q-action. Under this assumption, Etingof and Gelaki gave an explicit formula for a non-degenerate 2-cocycle in Z
2(G, ℂ*), where G:= A × Q. Hence, the semidirect product G is of central type.
In this paper, we present a more general correspondence between bijective and non-degenerate cohomology classes. In particular,
given a bijective class [π] ∈ H
1(Q,Ǎ) as above, we construct non-degenerate classes [cπ] ∈ H
2(G,ℂ*) for certain extensions 1 → A → G → Q → 1 which are not necessarily split. We thus strictly extend the above family of
central type groups. 相似文献
6.
Principal eigenvalues,topological pressure,and stochastic stability of equilibrium states 总被引:2,自引:0,他引:2
Yuri Kifer 《Israel Journal of Mathematics》1990,70(1):1-47
Suppose thatL is a second order elliptic differential operator on a manifoldM, B is a vector field, andV is a continuous function. The paper studies by probabilistic and dynamical systems means the behavior asɛ → 0 of the principal eigenvalueλ
ε
(V) for the operatorL
ε
= ɛL + (B, ∇) +V considered on a compact manifold or in a bounded domain with zero boundary conditions. Under certain hyperbolicity conditions
on invariant sets of the dynamical system generated by the vector fieldB the limit asɛ → 0 of this principal eigenvalue turns out to be the topological pressure for some function. This gives a natural transition
asɛ → 0 from Donsker-Varadhan’s variational formula for principal eigenvalues to the variational principle for the topological
pressure and unifies previously separate results on random perturbations of dynamical systems.
This work was supported by US-Israel Binational Science Foundation. 相似文献
7.
We formulate, for regular μ>ω, a “forcing principle” Sμ which we show is equivalent to the existence of morasses, thus providing a new and systematic method for obtaining applications
of morasses. Various examples are given, notably that for infinitek, if 2
k
=k
+ and there exists a (k
+, 1)-morass, then there exists ak
++-super-Souslin tree: a normalk
++ tree characterized by a highly absolute “positive” property, and which has ak
++-Souslin subtree. As a consequence we show that CH+SHℵ
2⟹ℵ2 is (inaccessible)L.
This author thanks the US-Israel Binational Science Foundation for partial support of this research. 相似文献
8.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献
9.
Let Ω be a set of pairwise-disjoint polyhedral obstacles in R
3 with a total of n vertices, and let B be a ball in R
3. We show that the combinatorial complexity of the free configuration space F of B amid Ω:, i.e., (the closure of) the set of all placements of B at which B does not intersect any obstacle, is O(n
2+ε
), for any ε >0; the constant of proportionality depends on ε. This upper bound almost matches the known quadratic lower bound
on the maximum possible complexity of F . The special case in which Ω is a set of lines is studied separately. We also present a few extensions of this result, including
a randomized algorithm for computing the boundary of F whose expected running time is O(n
2+ε
).
Received July 6, 1999, and in revised form April 25, 2000. Online publication August 18, 2000. 相似文献
10.
Let (ρ λ ) λ∈Λ be a holomorphic family of representations of a finitely generated group G into PSL(2,ℂ), parameterized by a complex manifold Λ. We define a notion of bifurcation current in this context, that is, a positive closed current on Λ describing the bifurcations of this family of representations in a quantitative sense. It is the analogue of the bifurcation current introduced by DeMarco for holomorphic families of rational mappings on ℙ1. Our definition relies on the theory of random products of matrices, so it depends on the choice of a probability measure μ on G. 相似文献
11.
V. A. Ustimenko 《Journal of Mathematical Sciences》2007,140(3):461-471
The paper is devoted to the study of a linguistic dynamical system of dimension n ≥ 2 over an arbitrary commutative ring K,
i.e., a family F of nonlinear polynomial maps f
α : K
n
→ K
n
depending on “time” α ∈ {K − 0} such that f
α
−1 = f
−αM, the relation f
α1 (x) = f
α2 (x) for some x ∈ Kn implies α1 = α2, and each map f
α has no invariant points. The neighborhood {f
α (υ)∣α ∈ K − {0}} of an element v determines the graph Γ(F) of the dynamical system on the vertex set Kn. We refer to F as a linguistic dynamical system of rank d ≥ 1 if for each string a = (α1, υ, α2), s ≤ d, where αi + αi+1 is a nonzero divisor for i = 1, υ, d − 1, the vertices υ
a = f
α1 × ⋯ × f
αs
(υ) in the graph are connected by a unique path. For each commutative ring K and each even integer n ≠= 0 mod 3, there is a family of linguistic dynamical systems Ln(K) of rank d ≥ 1/3n. Let L(n, K) be the graph of the dynamical system Ln(q). If K = Fq, the graphs L(n, Fq) form a new family of graphs of large girth. The projective limit L(K) of L(n, K), n → ∞, is well defined for each commutative
ring K; in the case of an integral domain K, the graph L(K) is a forest. If K has zero divisors, then the girth of K drops
to 4. We introduce some other families of graphs of large girth related to the dynamical systems Ln(q) in the case of even q. The dynamical systems and related graphs can be used for the development of symmetric or asymmetric
cryptographic algorithms. These graphs allow us to establish the best known upper bounds on the minimal order of regular graphs
without cycles of length 4n, with odd n ≥ 3. Bibliography: 42 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 214–234. 相似文献
12.
Xiao Jie 《数学学报(英文版)》1994,10(2):192-201
LetD={z∈Σ:|z|<1} and ϕ be a normal function on [0,1). Forp∈(0,1) such a function ϕ is used to define a Bergman spaceA
p
(ϕ) onD with weight ϕ
p
(|·|)/(1-|·|2). In this paper, the dual space ofA
p
(ϕ) is given, four characteristics of Carleson measure onA
p
(ϕ) are obtained. Moreover, as an application, three sequence interpolation theorems inA
p
(ϕ) are derived.
Supported by the Doctoral Program Foundation of Institute of Higher Education, P.R. China. 相似文献
13.
Given the integer polyhedronP
t
:= conv{x ∈ℤ
n
:Ax⩽b}, whereA ∈ℤ
m × n
andb ∈ℤ
m
, aChvátal-Gomory (CG)cut is a valid inequality forP
1 of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ
+
m
such that λτA∈ℤ
n
. In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2}
m
. We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary
clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a
convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of
strong inequalities forP
1. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering
polytopes are briefly discussed. 相似文献
14.
Yonglin Cao 《Semigroup Forum》2011,82(1):121-130
We show that every finitely presented, cancellative and commutative ordered monoid is determined by a finitely generated and
cancellative pseudoorder on the monoid (ℕ
n
,+) for some positive integer n. Every cancellative pseudoorder on (ℕ
n
,+) is determined by a submonoid of the group (ℤ
n
,+), and we prove that the pseudoorder is finitely generated if and only if the submonoid is an affine monoid in ℤ
n
. 相似文献
15.
Saharon Shelah 《Central European Journal of Mathematics》2010,8(2):213-234
Our main theorem is about iterated forcing for making the continuum larger than ℵ2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing
ℵ1,ℵ2 by λ, λ
+ (starting with λ = λ
<λ
> ℵ1). Well, we demand absolute c.c.c. So we get, e.g. the continuum is λ
+ but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a “partial” countable support iteration but it is c.c.c. 相似文献
16.
We obtain the best approximation in L
1(ℝ), by entire functions of exponential type, for a class of even functions that includes e
−λ|x|, where λ>0, log |x| and |x|
α
, where −1<α<1. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded
degree. 相似文献
17.
Laura DeMarco 《Mathematische Annalen》2003,326(1):43-73
Let L(f)=∫log∥Df∥dμ
f
denote the Lyapunov exponent of a rational map, f:P
1→P
1
. In this paper, we show that for any holomorphic family of rational maps {f
λ
:λX} of degree d>1, T(f)=dd
c
L(f
λ
) defines a natural, positive (1,1)-current on X supported exactly on the bifurcation locus of the family. The proof is based on the following potential-theoretic formula
for the Lyapunov exponent:
Here F:C
2
→C
2
is a homogeneous polynomial lift of f; ; G
F
is the escape rate function of F; and capK
F
is the homogeneous capacity of the filled Julia set of F. We show, in particular, that the capacity of K
F
is given explicitly by the formula
where Res(F) is the resultant of the polynomial coordinate functions of F.
We introduce the homogeneous capacity of compact, circled and pseudoconvex sets K⊂C
2 and show that the Levi measure (determined by the geometry of ∂K) is the unique equilibrium measure. Such K⊂C
2 correspond to metrics of non-negative curvature on P
1, and we obtain a variational characterization of curvature.
Received: 28 November 2001 / Revised version: 2 April 2002 /
Published online: 10 February 2003 相似文献
18.
19.
This article gives the representations of two types of real functionals on L
∞(Ω, Ƒ) or L
∞(Ω, Ƒ, ℙ) in terms of Choquet integrals. These functionals are comonotonically subadditive and comonotonically convex, respectively. 相似文献
20.
We use a piecewise-linear, discontinuous Galerkin method for the time discretization of a fractional diffusion equation involving
a parameter in the range − 1 < α < 0. Our analysis shows that, for a time interval (0,T) and a spatial domain Ω, the error in L¥((0,T);L2(W))L_\infty\bigr((0,T);L_2(\Omega)\bigr) is of order k
2 + α
, where k denotes the maximum time step. Since derivatives of the solution may be singular at t = 0, our result requires the use of non-uniform time steps. In the limiting case α = 0 we recover the known O(k
2) convergence for the classical diffusion (heat) equation. We also consider a fully-discrete scheme that employs standard
(continuous) piecewise-linear finite elements in space, and show that the additional error is of order h
2log(1/k). Numerical experiments indicate that our O(k
2 + α
) error bound is pessimistic. In practice, we observe O(k
2) convergence even for α close to − 1. 相似文献