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1.
In this paper, we continue our investigation on “Extremal problems under dimension constraints” introduced [1]. The general problem we deal with in this paper can be formulated as follows. Let
be an affine plane of dimension k in
. Given
determine or estimate
.Here we consider and solve the problem in the special case where
is a hyperplane in
and the “forbidden set”
. The same problem is considered for the case, where
is a hyperplane passing through the origin, which surprisingly turns out to be more difficult. For this case we have only partial results.AMS Classification: 05C35, 05B30, 52C99 相似文献
2.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
3.
George M. Bergman 《Algebra Universalis》2005,53(2-3):357-395
Properties of several sorts of lattices of convex subsets of
are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of
and the lattice of all convex subsets of
The lattices of arbitrary, of open bounded, and of compact convex sets in
all satisfy the same identities, but the last of these is join-semidistributive, while for n > 1 the first two are not. The lattice of relatively convex subsets of a fixed set
satisfies some, but in general not all of the identities of the lattice of “genuine” convex subsets of
To the memory of Ivan RivalReceived April 22, 2003; accepted in final form February 16, 2005.This revised version was published online in August 2005 with a corrected cover date. 相似文献
4.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p. 相似文献
5.
Özgür Ceyhan 《Selecta Mathematica, New Series》2007,13(2):203-237
The moduli space parameterizes the isomorphism classes of S-pointed stable real curves of genus zero which are invariant under relabeling by the involution σ. This moduli space is stratified according to the degeneration types of σ-invariant curves. The degeneration types of σ-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex
generated by the fundamental classes of strata of . We show that the homology of is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of .
相似文献
6.
T. R. Riley 《Geometriae Dedicata》2005,113(1):215-229
We give a nondeterministic algorithm that expresses elements of
, for N ≥ 3, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We show that the nondeterministic time-complexity of the subtractive version of Euclid’s algorithm for finding the greatest common divisor of N ≥ 3 integers a1, ..., aN is at most a constant times
. This leads to an elementary proof that for N ≥ 3 the word metric in
is biLipschitz equivalent to the logarithm of the matrix norm – an instance of a theorem of Mozes, Lubotzky and Raghunathan. And we show constructively that there exists K>0 such that for all N ≥ 3 and primes p, the diameter of the Cayley graph of
with respect to the generating set
is at most
.Mathematics Subject Classification: 20F05 相似文献
7.
The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are
not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on .
Received: October, 2007. Accepted: February, 2008. 相似文献
8.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
for all
Here (g)a denotes the function x g(x)eax for
and
where R+ is the spectral radius of the shift S : f(x) f(x–1) on
while
is the spectral radius of the backward shift S–1 : f(x) (P+f)(x+1) on
Moreover, there exists a constant C, depending on , such that
for every a I. If R– < R+, we prove that there exists a bounded holomorphic function v on
such that for
the function va is the restriction of v on the line
Received: 18 May 2004 相似文献
9.
We establish a new 3G-Theorem for the Green’s function for the half space
We exploit this result to introduce a new class of potentials
that we characterize by means of the Gauss semigroup on
. Next, we define a subclass
of
and we study it. In particular, we prove that
properly contains the classical Kato class
. Finally, we study the existence of positive continuous solutions in
of the following nonlinear elliptic problem
where h is a Borel measurable function in
satisfying some appropriate conditions related to the class
.
Mathematics Subject Classification (1991): Primary: 34B27, 34B16, 34J65; Secondary: 35B50, 31B05 相似文献
10.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
11.
Jorge L. Arocha Javier Bracho Chaim Goodman-Strauss Luis Montejano 《Archiv der Mathematik》2006,86(2):185-192
We prove that affine configurations of 4 lines in
are topologically and combinatorially homeomorphic to affine configurations of 6 points in
Received: 14 July 2004; revised: 18 February 2005 相似文献
12.
In this paper we fix a set * of positive elements of the free group
(e. g. the set of finite words occurring in a Markov subshift) as well as n partial isometries on a Hilbert space H. Based on these we define a map S :
which we prove to be a partial representation of
on H under certain conditions studied by Matsumoto.*Supported by Capes. 相似文献
13.
Gioconda Moscariello Carlo Sbordone 《Journal of Fixed Point Theory and Applications》2007,1(2):337-350
Let
be a sequence of Borel measurable functions satisfying, for a function
the inequalities
and suppose
Then there exists a sequence of increasing homeomorphisms
converging to a homeomorphism
weakly in
and locally uniformly, such that
Dedicated to the memory of Jean Leray 相似文献
14.
Let M be a four-holed sphere and Γ the mapping class group of M fixing the boundary ∂M. The group Γ acts on
which is the space of completely reducible SL (2,
-gauge equivalence classes of flat SL
-connections on M with fixed holonomy
on ∂M. Let
and
be the compact component of the real points of
. These points correspond to SU(2)-representations or SL(2,
-representations. The Γ-action preserves
and we study the topological dynamics of the Γ-action on
and show that for a dense set of holonomy
, the Γ-orbits are dense in
. We also produce a class of representations
such that the Γ-orbit of [ρ] is finite in the compact component of
, but
is dense in SL(2,
.Mathematics Subject Classiffications (2000). 57M05, 54H20, 11D99 相似文献
15.
Joseph Zaks 《Journal of Geometry》2005,82(1-2):195-203
Benz proved that every mapping
that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping
that preserves the distances 1 and
is an isometry, provided d ≥ 5. 相似文献
16.
Piotr Kot 《Czechoslovak Mathematical Journal》2007,57(1):29-47
We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball
For a function u which is lower semi-continuous on
we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈
such that
. 相似文献
17.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
18.
Let Γ be an arithmetic lattice in an absolutely simple Lie group G with trivial centre. We prove that there exists an integer N ≥ 2, a subgroup Λ of finite index in Γ, and an action of Λ on
such that the pair (
) has property (T). If G has property (T), then so does
. If G is the adjoint group of Sp(n, 1), then
is a property (T) group satisfying the Baum–Connes conjecture. If Γ is an arithmetic lattice in SO(n, 1), then the associated von Neumann algebra
is a II1-factor in Popa’s class
. Elaborating on this result of Popa, we construct a countable family of pairwise nonstably isomorphic group II1-factors in the class
, all with trivial fundamental groups and with all L2-Betti numbers being zero.Mathematics Subject Classiffications (2000). 22E40, 22E47, 46L80, 37A20 相似文献
19.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
20.
Xianling Fan Shao-Gao Deng 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):255-271
We study the existence and multiplicity of positive solutions for the inhomogeneous Neumann boundary value problems involving
the p(x)-Laplacian of the form
where Ω is a bounded smooth domain in , and p(x) > 1 for with and φ ≢ 0 on ∂Ω. Using the sub-supersolution method and the variational method, under appropriate assumptions on f, we prove that, there exists λ* > 0 such that the problem has at least two positive solutions if λ = λ*, has at least one positive solution if λ = λ*, and has no positive solution if λ = λ*. To prove the result we establish a special strong comparison principle for the Neumann problems.
The research was supported by the National Natural Science Foundation of China 10371052,10671084). 相似文献