共查询到20条相似文献,搜索用时 15 毫秒
1.
If R is a smooth semi-local algebra of geometric type over an infinite field, we prove that the Milnor K-group K
M
n
(R) surjects onto the higher Chow group CH
n
(R , n) for all n≥0. Our proof shows moreover that there is an algorithmic way to represent any admissible cycle in CH
n
(R , n) modulo equivalence as a linear combination of “symbolic elements” defined as graphs of units in R. As a byproduct we get a new and entirely geometric proof of results of Gabber, Kato and Rost, related to the Gersten resolution
for the Milnor K-sheaf. Furthermore it is also shown that in the semi-local PID case we have, under some mild assumptions, an isomorphism.
Some applications are also given.
Oblatum 17-XII-1998 & 1-X-2001?Published online: 18 January 2002 相似文献
2.
M. Laurent 《Journal of Mathematical Sciences》2012,180(5):592-598
Let Γ = Z
A + Z
n
⊂ R
n
be a dense subgroup of rank n + 1 and let [^(w)] \hat{w} (A) denote the exponent of uniform simultaneous rational approximation to the generating point A. For any real number v ≥
[^(w)] \hat{w} (A), the Hausdorff dimension of the set B
v
of points in R
n
that are v-approximable with respect to Γ is shown to be equal to 1/v. 相似文献
3.
Stephen H. Hechler 《Israel Journal of Mathematics》1973,15(4):384-395
For any topological spaceT, S. Mrówka has defined Exp (T) to be the smallest cardinal κ (if any such cardinals exist) such thatT can be embedded as a closed subset of the productN
κ of κ copies ofN (the discrete space of cardinality ℵ0). We prove that forQ, the space of the rationals with the inherited topology, Exp (Q) is equal to a certain covering number, and we show that by modifying some earlier work of ours it can be seen that it is
consistent with the usual axioms of set theory including the choice that this number equal any uncountable regular cardinal
less than or equal to 2ℵ
0. Mrówka has also defined and studied the class ℳ={κ: Exp (N
κ)=κ} whereN
κ is the discrete space of cardinality κ. It is known that the first cardinal not in ℳ must not only be inaccessible but cannot
even belong to any of the first ω Mahlo classes. However, it is not known whether every cardinal below 2ℵ
0 is contained in ℳ. We prove that if there exists a maximal family of almost-disjoint subsets ofN of cardinality κ, then κ∈ℳ, and we then use earlier work to prove that if it is consistent that there exist cardinals which
are not in the first ω Mahlo classes, then it is consistent that there exist such cardinals below 2ℵ
0 and that ℳ nevertheless contain all cardinals no greater than 2ℵ
0. Finally, we consider the relationship between ℳ and certain “large cardinals”, and we prove, for example, that if μ is any
normal measure on a measurable cardinal, then μ(ℳ)=0. 相似文献
4.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(3):443-460
We consider a family of open discrete mappings
f:D ?[`(\mathbb Rn)] f:D \to \overline {{{\mathbb R}^n}} that distort, in a special way, the p-modulus of a family of curves that connect the plates of a spherical condenser in a domain D in
\mathbb Rn {{\mathbb R}^n} ; p > n-1; p < n; and bypass a set of positive p-capacity. We establish that this family is normal if a certain real-valued function that controls the considered distortion
of the family of curves has finite mean oscillation at every point or only logarithmic singularities of order not higher than
n - 1: We show that, under these conditions, an isolated singularity x
0 ∈ D of a mapping
f:D\{ x0 } ?[`(\mathbb Rn)] f:D\backslash \left\{ {{x_0}} \right\} \to \overline {{{\mathbb R}^n}} is removable, and, moreover, the extended mapping is open and discrete. As applications, we obtain analogs of the known Liouville
and Sokhotskii–Weierstrass theorems. 相似文献
5.
Eric M. Rains 《Probability Theory and Related Fields》1998,112(3):411-423
Using the machinery of zonal polynomials, we examine the limiting behavior of random symmetric matrices invariant under conjugation
by orthogonal matrices as the dimension tends to infinity. In particular, we give sufficient conditions for the distribution
of a fixed submatrix to tend to a normal distribution. We also consider the problem of when the sequence of partial sums of
the diagonal elements tends to a Brownian motion. Using these results, we show that if O
n
is a uniform random n×n orthogonal matrix, then for any fixed k>0, the sequence of partial sums of the diagonal of O
k
n
tends to a Brownian motion as n→∞.
Received: 3 February 1998 / Revised version: 11 June 1998 相似文献
6.
S. A. Shakhova 《Algebra and Logic》2006,45(4):277-285
Let ℳ be any quasivariety of Abelian groups, Lq(ℳ) be a subquasivariety lattice of ℳ, dom
G
ℳ
be the dominion of a subgroup H of a group G in ℳ, and G/dom
G
ℳ
(H) be a finitely generated group. It is known that the set L(G, H, ℳ) = {dom
G
N
(H)| N ∈ Lq(ℳ)} forms a lattice w.r.t. set-theoretic inclusion. We look at the structure of dom
G
ℳ
(H). It is proved that the lattice L(G,H,ℳ) is semidistributive and necessary and sufficient conditions are specified for
its being distributive.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 484–499, July–August, 2006. 相似文献
7.
Nathanaël Enriquez Jacques Franchi Yves Le Jan 《Probability Theory and Related Fields》2001,119(2):213-255
Let ℳ be a geometrically finite hyperbolic surface with infinite volume, having at least one cusp. We obtain the limit law
under the Patterson-Sullivan measure on T
1ℳ of the windings of the geodesics of ℳ around the cusps. This limit law is stable with parameter 2δ− 1, where δ is the Hausdorff
dimension of the limit set of the subgroup Γ of M?bius isometries associated with ℳ. The normalization is t
−1/(2δ−1), for geodesics of length t. Our method relies on a precise comparison between geodesics and diffusion paths, for which we need to approach the Patterson-Sullivan
measure mentioned above by measures that are regular along the stable leaves.
Received: 8 October 1999 / Revised version: 2 June 2000 / Published online: 21 December 2000 相似文献
8.
Roberto Tauraso 《Monatshefte für Mathematik》1999,120(1):151-157
It is proven that the sets of periods for expanding maps on n-dimensional flat manifolds are uniformly cofinite, i.e. there is a positive integer m 0, which depends only on n, such that for any integer , for any n-dimensional flat manifold ℳ and for any expanding map F on ℳ, there exists a periodic point of F whose least period is exactly m. 相似文献
9.
S. B. Damelin 《Monatshefte für Mathematik》2003,4(1):111-131
For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L
p
(0 < p ⩽ ∞) norm of a weighted polynomial, P
n
w
n
, deg P
n
⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L
p
infinite–finite range inequalities. 相似文献
10.
We present some exponential inequalities for positively associated unbounded random variables. By these inequalities, we obtain
the rate of convergence n
−1/2
β
n
log 3/2
n in which β
n
can be particularly taken as (log log n)1/σ
with any σ>2 for the case of geometrically decreasing covariances, which is faster than the corresponding one n
−1/2(log log n)1/2log 2
n obtained by Xing, Yang, and Liu in J. Inequal. Appl., doi: (2008) for the case mentioned above, and derive the convergence rate n
−1/2
β
n
log 1/2
n for the above β
n
under the given covariance function, which improves the relevant one n
−1/2(log log n)1/2log n obtained by Yang and Chen in Sci. China, Ser. A 49(1), 78–85 (2006) for associated uniformly bounded random variables. In addition, some moment inequalities are given to prove the main results,
which extend and improve some known results. 相似文献
11.
Antonio J. Lozano Juan A. Mesa Frank Plastria 《Journal of Mathematical Modelling and Algorithms》2010,9(1):1-17
A line is sought in the plane which minimizes the sum of the k largest (Euclidean) weighted distances from n given points. This problem generalizes the known straight-line center and median problems and, as far as the authors are
aware, has not been tackled up to now. By way of geometric duality it is shown that such a line may always be found which
either passes through two of the given points or lying at equal weighted distance from three of these. This allows construction
of an algorithm to find all t-centrum lines for 1 ≤ t ≤ k in O((k + logn)n
3). Finally it is shown that both, the characterization of an optimal line and the algorithm, can be extended to any smooth
norm. 相似文献
12.
Roberto Tauraso 《Monatshefte für Mathematik》1999,128(2):151-157
It is proven that the sets of periods for expanding maps on n-dimensional flat manifolds are uniformly cofinite, i.e. there is a positive integer m
0, which depends only on n, such that for any integer , for any n-dimensional flat manifold ℳ and for any expanding map F on ℳ, there exists a periodic point of F whose least period is exactly m.
(Received 10 April 1998; in revised form 20 January 1999) 相似文献
13.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2012,63(8):1298-1305
The paper is devoted to the investigation of topological properties of space mappings. It is shown that orientation-preserving
mappings
f:D ?[`(\mathbbRn)] f:D \to \overline {{\mathbb{R}^n}} in a domain
D ì \mathbbRn D \subset {\mathbb{R}^n} , n ≥ 2; which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f (D), e.g., if Q has finite mean oscillation at an arbitrary point y
0 ∈ f (D). 相似文献
14.
Wolfgang Adamski 《Israel Journal of Mathematics》1989,65(1):79-95
Let (X,A) be a measureable space andT:X →X a measurable mapping. Consider a family ℳ of probability measures onA which satisfies certain closure conditions. IfA
0⊂A is a convergence class for ℳ such that, for everyA ∈A
0, the sequence ((1/n) Σ
i
=0/n−1
1
A
∘T
i) converges in distribution (with respect to some probability measurev ∈ ℳ), then there exists aT-invariant element in ℳ. In particular, for the special case of a topological spaceX and a continuous mappingT, sufficient conditions for the existence ofT-invariant Borel probability measures with additional regularity properties are obtained. 相似文献
15.
We introduce a sharp trace Tr
#
ℳ and a sharp determinant Det
#
(1−z ℳ) for an algebra of operators ℳ acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the
discrete spectrum of ℳ. The relationship with weighted zeta functions of interval maps and Milnor–Thurston kneading determinants is explained. This
yields a result on convergence of the discrete spectrum of approximated operators.
Oblatum 8-V-1995 & IX-1995 相似文献
16.
We say that X=[xij]i,j=1nX=[x_{ij}]_{i,j=1}^n is symmetric centrosymmetric if x
ij
= x
ji
and x
n − j + 1,n − i + 1, 1 ≤ i,j ≤ n. In this paper we present an efficient algorithm for minimizing ||AXA
T
− B|| where ||·|| is the Frobenius norm, A ∈ ℝ
m×n
, B ∈ ℝ
m×m
and X ∈ ℝ
n×n
is symmetric centrosymmetric with a specified central submatrix [x
ij
]
p ≤ i,j ≤ n − p
. Our algorithm produces a suitable X such that AXA
T
= B in finitely many steps, if such an X exists. We show that the algorithm is stable any case, and we give results of numerical
experiments that support this claim. 相似文献
17.
S. B. Damelin 《Monatshefte für Mathematik》2003,138(2):111-131
For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L
p
(0 < p ⩽ ∞) norm of a weighted polynomial, P
n
w
n
, deg P
n
⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L
p
infinite–finite range inequalities.
Received April 4, 2001; in final form June 21, 2002 相似文献
18.
Fernando Schwartz 《Annales Henri Poincare》2011,12(1):67-76
We consider asymptotically flat Riemannian manifolds with non-negative scalar curvature that are conformal to
\mathbbRn\ W, n 3 3{\mathbb{R}^{n}{\setminus} \Omega, n\ge 3}, and so that their boundary is a minimal hypersurface. (Here,
W ì \mathbbRn{\Omega\subset \mathbb{R}^{n}} is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by
\frac12(V/bn)(n-2)/n{\frac{1}{2}\left(V/\beta_{n}\right)^{(n-2)/n}}, where V is the Euclidean volume of Ω and β
n
is the volume of the Euclidean unit n-ball. This gives a partial proof to a conjecture of Bray and Iga (Commun. Anal. Geom. 10:999–1016, 2002). Surprisingly, we do not require the boundary to be outermost. 相似文献
19.
We prove real Paley-Wiener type theorems for the Dunkl transform ℱ
D
on the space
of tempered distributions. Let T∈S′(ℝ
d
) and Δ
κ
the Dunkl Laplacian operator. First, we establish that the support of ℱ
D
(T) is included in the Euclidean ball
, M>0, if and only if for all R>M we have lim
n→+∞
R
−2n
Δ
κ
n
T=0 in S′(ℝ
d
). Second, we prove that the support of ℱ
D
(T) is included in ℝ
d
∖B(0,M), M>0, if and only if for all R<M, we have lim
n→+∞
R
2n
ℱ
D
−1(‖y‖−2n
ℱ
D
(T))=0 in S′(ℝ
d
). Finally, we study real Paley-Wiener theorems associated with
-slowly increasing function.
相似文献
20.
In this paper we consider operators acting on a subspace ℳ of the space L
2 (ℝm; ℂm) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace
ℳ is defined as the orthogonal sum of spaces ℳs,k of specific Clifford basis functions of L
2(ℝm; ℂm).
Every Clifford endomorphism of ℳ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic
operators are characterized in terms of commutation relations and they transform a space ℳs,k into a similar space ℳs′,k′. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ℳ is known.
Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is
studied in detail. 相似文献