共查询到10条相似文献,搜索用时 140 毫秒
1.
Prog. Dr. Erhard Heinz 《manuscripta mathematica》1979,28(1-3):81-88
Let T be the domain in N defined by the inequalities O < 1 < ... < N < +. Put N+k = /2(1+k) (k=1,2,3), N+4=1+2, and denote byF() the set of functions x=x(u,v)=(x1(u,v),...,xp(u,v)), (p2) of class
, where B is the unit disk u2+v2<1, which maps the circular arcs k={w=ei:k<<K+1} (k=1,..., N+3) into the straight lines containing the edges ak, ak+1 (aN+4=a1) of a polygon IRp. Then we show that the function ()=
inf
xF()
D(x) is analytic in T. This generalizes and sharpens an unproved result of I. Marx and M. Shiffman (see [4]).
Hans Lewy und Charles B. Morrey gewidmet 相似文献
Hans Lewy und Charles B. Morrey gewidmet 相似文献
2.
Liu Huimei 《Annals of the Institute of Statistical Mathematics》2000,52(1):15-27
Let Xhave a multivariate, p-dimensional normal distribution (p 2) with unknown mean and known, nonsingular covariance . Consider testing H
0 : b
i 0, for some i = 1,..., k, and b
i 0, for some i = 1,..., k, versus H
1 : b
i < 0, for all i = 1,..., k, or b
i
< 0, for all i = 1,..., k, where b
1,..., b
k
, k 2, are known vectors that define the hypotheses and suppose that for each i = 1,..., k there is an j {1,..., k} (j will depend on i) such that b
i b
j 0. For any 0 < < 1/2. We construct a test that has the same size as the likelihood ratio test (LRT) and is uniformly more powerful than the LRT. The proposed test is an intersection-union test. We apply the result to compare linear regression functions. 相似文献
3.
Rod Gow 《Geometriae Dedicata》1997,64(3):283-295
Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers
k
V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies 2 = 0 and (
k
V)
k–1
V We prove that (
k
V)= ker
k–1
V except when k=m+2. In the exceptional case, (
m+2
V) has codimension 2m in ker
m
V and we show that the quotient module ker
m
V/
m+2
V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in
m
V and multiplicity 0 in all other components of V. 相似文献
4.
Toivo Leiger 《manuscripta mathematica》1984,45(3):293-307
Let A and B be normal matrices. In :={x=(xk) ¦ xk} we define the order relation A by xA0:<=>
k=0
n
ankxk0 (n ). Let T be a row-finite matrix. A is called T-section-positive, if ktmkxke(k) A0 (m ) for xA0 (see [5]). We study the relation between T-sectional positivity and T-sectional boundedness. An (A,B)-summability factor sequence =(k) is called positive, if (kxk)B0 for each xcA with xA0. For B-section-positive matrices A we give a functional analytic characterization of positive (A,B)-summability factor sequences.
Die Arbeit entstand während eines vom DAAD unterstützten Forschungsaufenthalts an der Fernuniversität-Gesamthochschule Hagen 相似文献
Die Arbeit entstand während eines vom DAAD unterstützten Forschungsaufenthalts an der Fernuniversität-Gesamthochschule Hagen 相似文献
5.
Jürg T. Marti 《Numerische Mathematik》1990,57(1):51-62
Summary The inverse Sturm-Liouville problem is the problem of finding a good approximation of a potential functionq such that the eigenvalue problem (*)–y
+qy=y holds on (0, ) fory(0)=y()=0 and a set of given eigenvalues . Since this problem has to be solved numerically by discretization and since the higher discrete eigenvalues strongly deviate from the corresponding Sturm-Liouville eigenvalues , asymptotic corrections for the 's serve to get better estimates forq. Let
k
(1kn) be the first eigenvalues of (*), let
k
be the corresponding discrete eigenvalues obtained by the finite element method for (*) and let
k
k
for the special caseq=0. Then, starting from an asymptotic correction technique proposed by Paine, de Hoog and Anderssen, new estimates for the errors
of the corrected discrete eigenvalues
are obtained and confirm and improve the knownO(kh
2)(h:=/(n+1)) behaviour. The estimates are based on new Sobolev inequalities and on Fourier analysis and it is shown that
for 4+c
2
k(n+1)/2, wherec
1 andc
2 are constants depending onq which tend to 0 for vanishingq. 相似文献
6.
Robert Roussarie 《Bulletin of the Brazilian Mathematical Society》1998,29(2):229-251
LetH be a germ of holomorphic diffeomorphism at 0 . Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze
2i
)=HS(z) (1). IfH
is an unfolding of diffeomorphisms depending on (,0), withH
0=Id, one introduces its ideal
. It is the ideal generated by the germs of coefficients (a
i
(), 0) at 0
k
, whereH
(z)–z=a
i
()z
i
. Then one can find a parameter solutionS
(z) of (1) which has at each pointz
0 belonging to the domain of definition ofS
0, an expansion in seriesS
(z)=z+b
i
()(z–z
0)
i
with
, for alli.This result may be applied to the bifurcation theory of vector fields of the plane. LetX
be an unfolding of analytic vector fields at 0 2 such that this point is a hyperbolic saddle point for each . LetH
(z) be the holonomy map ofX
at the saddle point and
its associated ideal of coefficients. A consequence of the above result is that one can find analytic intervals , , transversal to the separatrices of the saddle point, such that the difference between the transition mapD
(z) and the identity is divisible in the ideal
. Finally, suppose thatX
is an unfolding of a saddle connection for a vector fieldX
0, with a return map equal to identity. It follows from the above result that the Bautin ideal of the unfolding, defined as the ideal of coefficients of the difference between the return map and the identity at any regular pointz, can also be computed at the singular pointz=0. From this last observation it follows easily that the cyclicity of the unfoldingX
, is finite and can be computed explicity in terms of the Bautin ideal.Dedicated to the memory of R. Mañé 相似文献
7.
Tor Helleseth Torleiv Kløve Vladimir I. Levenshtein 《Designs, Codes and Cryptography》2003,28(3):265-282
An ordered orthogonal array OOA(, k, n) is a binary 2
k
× n matrix with the property that for each complete -set of columns, each possible -tuple occurs in exactly 2
k– rows of those columns (for definition of a complete -set, see below). Constructions of OOA(, k, n) for = 4 and = 5 are given. 相似文献
8.
We investigate the multidimensional equations
j=1
q
Aj(x)y(x+e
j
)=f(x),e
j
n wherex n andA
j
: n Hom(
p
,
m
),f : n m are given maps. Sufficient conditions for smooth and analytic solvability for anyf C
k
,k are found.Research partially supported by the Israel Ministry of ScienceAMS classification 39B Functional equations 相似文献
9.
Let M
n =X1+...+Xn be a martingale with bounded differences Xm=Mm-Mm-1 such that {|Xm| m}=1 with some nonnegative m. Write 2=
1
2
+ ... +
n
2
. We prove the inequalities {M
nx}c(1-(x/)), {M
n x} 1- c(1- (-x/)) with a constant
. The result yields sharp inequalities in some models related to the measure concentration phenomena. 相似文献
10.
Summary We consider a (possibly) vector-valued function u: RN, Rn, minimizing the integral
, 2-2/(n*1)<p<2, whereD
i
u=u/x
i
or some more general functional retaining the same behaviour, we prove higher integrability for Du: D1 u,..., Dn–1 u Lp/(p-1) and Dnu L2; this result allows us to get existence of second weak derivatives: D(D1 u),...,D(Dn–1u)L2 and D(Dn u) L
p.This work has been supported by MURST and GNAFA-CNR. 相似文献