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1.
Let K be a field and
a non-trivial valuation ring of K withm as its maximal ideal. Denote by
and
the rings of polynomials f∈K[X] and rational functions f∈K(X) resp. such that
. We prove that for one variable X we have
if and only if the completion of (K,
) is locally compact or algebraically closed. In the second case—i.e. if K is dense in the algebraic closure of (K,
)—we even get
for any number of variables X=(X1,...,Xn).
This work contains parts of the second author's thesis [Ri] written under the supervision of the first author. 相似文献
2.
Summary Let
a plane angle of opening α∈(π, 2π). LetP
D andP
N the Dirichlet and Neumann problems associated to the Poisson equation in
. ForP
D andP
N it is proved non existence of solution in L
p
(
) whenp=2/(1±π/α). In other words, the ranges of elliptic operators naturally associated toP
D andP
N are not-closed in L
p
(
) forp=2/(1±π/α).
Sunto Sia } un angolo piano di apertura α∈(π, 2π). SianoP D eP N i problemi di Dirichlet e di Neumann associati all'equazione di Poisson in . PerP D eP N si prova non esistenza di soluzioni in L p ( ) quandop=2/(1±π/α). Vale a dire i ranges degli operatori ellittici naturalmente associati aP D eP N sono non-chiusi in π--AgBrα K L p ( ) perp=2/(1±π/α).相似文献
3.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
4.
A powerful tool for studying the growth of analytic and harmonic functions is Hall's Lemma, which states that there is a constantC>0 so that the harmonic measure of a subsetE of the closed unit disk
evaluated at 0 satisfies
whereE
rad is the radial projection ofE onto
. FitzGerald, Rodin and Warschawski proved that ifE is a continuum in
whose radial projection has length at most π then (*) is true withC=1, and they asked how large the length, |E
rad|, can be in order for their result to be valid. We prove that (*) holds withC=1 for every continuum
satisfying
and θc cannot be replaced by a larger number. Fuchs asked for the largest constantC so that (*) holds for allE. We show that for every continuum
, (*) holds withC=C
2π≅.977126698498665669…, whereC
2π is the harmonic measure of the two long sides of a 3∶1 rectangle evaluated at the center. There are Jordan curves for which
equality holds in (*) withC=C
2π.
The authors are supported in part by NSF grants DMS-9302823 and DMS-9401027, and while at MSRI by NSF grant DMS-9022140. 相似文献
5.
We study the boundary-value problemu
tt
-u
xx
=g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of, and-periodic functions (q and s are natural numbers). We obtain the results only for sets of periods, and which characterize the classes of π-, 2π -, and 4π-periodic functions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 281–284, February, 1999. 相似文献
6.
7.
Gerhard Edelmann 《manuscripta mathematica》1994,82(1):393-406
Let
be a 3-dimensional submanifold of ℙ5 of degree 12. This article gives, up to one case, a complete classification of the deformation classes of those 3-folds.
The main tools used are methods already applied in the classification of degrees 9 to 11 and adjunction theoretic results.
We show here how the 2nd reduction of
can be applied to analyse the birational structure of
or even exclude the existence of
. 相似文献
8.
A. T. Gainov 《Algebra and Logic》1996,35(2):67-79
Special monocomposition algebras introduced in [1] are studied. Using their properties, we prove that any nondegenerate monocomposition
algebra
,dim
≥ 3, with unity contains no proper ideal of dimension ≤8. This implies that if 3≤dim
≤ 9, then
is a central simple algebra.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 125–144, March–April, 1996. 相似文献
9.
According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of
-modules, theresidue complex
. These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex
is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes,
and
, which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical
dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms. 相似文献
10.
We define a cohomological invariantE(G, S, M) whereG is a group,S is a non empty family of (not necessarily distinct) subgroups of infinite index inG andM is a
-module (
is the field of two elements). In this paper we are interested in the special case where the family of subgroups consists
of just one subgroup, andM is the
-module
. The invariant
will be denoted byE(G, S). We study the relations of this invariant with other endse(G), e(G, S) ande(G,S)), and some results are obtained in the case whereG andS have certain properties of duality. 相似文献
11.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献
12.
The paper is concerned with the sharpness of some well-known estimates in universal linear-invariant families
of regular functions. It is shown that the estimate of | arg ƒ′(z)|,z ∈ Δ = {z: |z| < 1} obtained by Pommerenke in 1964 is sharp; the extremal function is found. A lower estimate for the Schwarzian derivative
in
is obtained. For
, a sharp estimate of order of the function ƒr(z)=ƒ(rz)/r withr ∈ (0, 1) is found; this estimate is applied to solve other problems.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 665–672, May, 1998. 相似文献
13.
A necessary and sufficient condition for regularity of the
-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto
-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.
The first author partially supported by NSF Grant DMS-8701038 相似文献
14.
1.IntroductionLetfibeaplanedomainwithsmoothboundaryonandWm,p(fl)betheusualSobolevspaceonnwithnormWhenp=2,pisusuallyomitted.WeshalldenotetheusualinnerproductinL'(fl)orLa(O)'by','),andinL'(ofl)by't').Weshallusethesamenotationstoindicatethedualltiesbetw... 相似文献
15.
An upper bound and a lower bound for α0 are given such that
for
for α≤α0, whereB is a nonnegative matrix and satisfies that for any positive constant β,βI+B is a power invariant zero pattern matrix.
This project is supported by Science and Art Foundation of Central South University of Technology. 相似文献
16.
Consider the nonparametric regression model
, whereg is an unknown function to be estimated on [0, 1],
are the fixed design points in the interval [0, 1] and
is a triangular array of row iid random variables having median zero. The nearest neighbor median estimator
is taken as the estimator of the unknown functiong(x). Median cross validation (mev) criterion is employed to select the smoothing parameterh. Leth
π
*
be the smoothing parameter chosen by mev criterion. Under mild regularity conditions, the upper and lower bounds ofh
π
*
, the rate of convergence and the weak consistency of the median cross-validated estimate
are obtained.
Project supported by the National Natural Science Foundation of China and the Doctoral Foundation of Education of China. 相似文献
17.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
18.
The exit measures of super-Brownian motions with branching mechanism
from a bounded smooth domain D in ℝd+1 are known to be absolutely continuous with respect to the surface area on ϑD if
whereas in the case
they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely
continuous states for alld≥1.
Project supported by the National Natural Science Foundation of China (Grant No. 16931063). 相似文献
19.
Andrew J. Sommese 《Milan Journal of Mathematics》1997,67(1):49-75
Let
be an algebraic submanifold of complex projective space ℙ
N
. Assume thatn:=dim
and let
denote the restriction of the hyperplane section bundle
to
. The meromorphic map
associated to
fork≥1 ties together the pluricanonical maps of the surface sections of
. Known results show that the behavior of
is far better than one would expect from experience with the pluricanonical mappings of algebraic surfaces. In this article
we discuss the known results on the structure of the mappings
and describe the open problems.
Conferenza tenuta il 5 giugno 1997 相似文献
20.
R. Carroll 《Journal of Nonlinear Science》1994,4(1):519-544
Summary We use the SDiff(2) framework of Takasaki and Takebe and the (L, M) program (L is the Lax operator andMω=ωλ) to show that
=semiclassical limit ofM is
, where (
) are action angle variables in the Gibbons-Kodama theory of Hamilton-Jacobi type for dispersionless KP. We also show
is the semiclassical limit ofWxW
−1 (W is the gauge operator), whereG=WxW
−1 is a quantity studied by the author in an earlier paper in connection with symmetries. We give then a semiclassical version
of the Jevicki-Yoneya action principle for 2D gravity, where again
arises in calculations, and this yields directly the Landau-Ginsburg equation that corresponds to the semiclassical limit
of an integrated string equation. For KdV we also show how inverse scattering data are connected to Hamiltonians for dispersionless
KdV. We also discuss Hirota bilinear formulas relative to the dispersionless hierarchies and establish various limiting formulas. 相似文献