共查询到20条相似文献,搜索用时 484 毫秒
1.
This paper is devoted to the study of dominant operators with an emphasis on their spectral properties. In particular the equation (T–)f() x (T a dominant or hyponormal operator on the Hilbert space ,x andf a function from the open setU to ) is investigated in an effort to discover necessary and/or sufficient conditions for the analyticity off.Supported in part by the National Science Foundation. 相似文献
2.
A general minimax theorem 总被引:2,自引:0,他引:2
Prof. Dr. A. Irle 《Mathematical Methods of Operations Research》1985,29(7):229-247
This paper is concerned with minimax theorems for two-person zero-sum games (X, Y, f) with payofff and as main result the minimax equality inf supf (x, y)=sup inff (x, y) is obtained under a new condition onf. This condition is based on the concept of averaging functions, i.e. real-valued functions defined on some subset of the plane with min {x, y}< (x, y)x, y} forx y and (x, x)=x. After establishing some simple facts on averaging functions, we prove a minimax theorem for payoffsf with the following property: Forf there exist averaging functions and such that for any x1, x2 X, > 0 there exists x0 X withf (x0, y) >
f (x1,y),f (x2,y))– for ally Y, and for any y1, y2 Y, > 0 there exists y0 Y withf (x, y0) (f (x, y1),f (x, y2))+. This result contains as a special case the Fan-König result for concave-convex-like payoffs in a general version, when we take linear averaging with (x, y)=x+(1–)y, (x, y)=x+(1–)y, 0 <, < 1.Then a class of hide-and-seek games is introduced, and we derive conditions for applying the minimax result of this paper.
Zusammenfassung In dieser Arbeit werden Minimaxsätze für Zwei-Personen-Nullsummenspiele (X, Y,f) mit Auszahlungsfunktionf behandelt, und als Hauptresultat wird die Gültigkeit der Minimaxgleichung inf supf (x, y)=sup inff (x, y) unter einer neuen Bedingung an f nachgewiesen. Diese Bedingung basiert auf dem Konzept mittelnder Funktionen, d.h. reellwertiger Funktionen, welche auf einer Teilmenge der Ebene definiert sind und dort der Eigenschaft min {x, y} < < (x, y)相似文献x, y} fürx y, (x, x)=x, genügen. Nach der Herleitung einiger einfacher Aussagen über mittelnde Funktionen beweisen wir einen Minimaxsatz für Auszahlungsfunktionenf mit folgender Eigenschaft: Zuf existieren mittelnde Funktionen und, so daß zu beliebigen x1, x2 X, > 0 mindestens ein x0 X existiert mitf (x0,y) (f (x 1,y),f (x2,y)) – für alley Y und zu beliebigen y1, y2 Y, > 0 mindestens ein y0 Y existiert mitf (x, y0) (f (x, y1),f (x, y 2))+ für allex X. Dieses Resultat enthält als Spezialfall den Fan-König'schen Minimaxsatz für konkav-konvev-ähnliche Auszahlungsfunktionen in einer allgemeinen Version, wenn wir lineare Mittelung mit (x, y)=x+(1–)y, (x, y)= x+(1–)y, 0 <, < 1, betrachten.Es wird eine Klasse von Suchspielen eingeführt, welche mit dem vorstehenden Resultat behandelt werden können.
3.
Mark Skandera 《Journal of Algebraic Combinatorics》2004,20(2):195-211
Let
I,I be the minor of a matrix which corresponds to row set I and column set I. We give a characterization of the inequalities of the form
I,I
K,K
J,J
L,L
which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson. 相似文献
4.
Héctor H. Cuenya 《Analysis Mathematica》2000,26(3):175-186
Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M
the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M
be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier. 相似文献
5.
С. А. Пичугов 《Analysis Mathematica》1991,17(1):21-33
LetA and be two arbitrary sets in the real spaceL
p, 1p<. Sufficient conditions are obtained for their strict separability by a hyperplane, in terms of the distance between the setsd(A,B)
p=inf{x-yp,xA,yB} and their diametersd(A)
p, d(B)p, whered(A)
p=sup{x-yp; x,yA}. In particular, it is proved that if in an infinite-demensional spaceL
p we haved
r(A,B)p>2–r+1(dr(A)p+dr(B)p), r=min{p, p(p–1)–1}, then there is a hyperplane which separatesA andB. On the other hand, the conditiond
r(A,B)p=2–r+1(dr(A)p+dr(B)p) does not guarantee strict separability. Earlier these results where obtained by V. L. Dol'nikov for the case of Euclidean spaces. 相似文献
6.
Lian-Xi Ku 《Southeast Asian Bulletin of Mathematics》2000,24(3):375-382
In this note, we prove that, for Robins boundary value problem, a unique solution exists if fx(t, x, x), fx(t, x, x), (t), and (t) are continuous, and fx -(t), fx -(t), 4(t) 2 + 2(t) ++ 2(t), and 4(t) 2 + 2(t) + 2(t).AMS Subject Classification (2000) 34B15 相似文献
7.
A. M. Kagan 《Journal of Mathematical Sciences》1986,34(2):1482-1487
Summary Denote by
k
a class of familiesP={P} of distributions on the line R1 depending on a general scalar parameter , being an interval of R1, and such that the moments µ1()=xdP
,...,µ2k
()=x
2k
dP
are finite, 1 (), ..., k (), k+1 () ...,
k
() exist and are continuous, with 1 () 0, and
j
+1 ()= 1 ()
j
() +[2() -1()2]
j
()/ 1 (), J=2, ..., k. Let 1=¯x=x
1 + ... +x
n/n, 2=x
1
2 + ... +x
n
2/n, ...,
k
=(x
1
k
+ ... +x
n
k/n denote the sample moments constructed for a sample x1, ..., xn from a population with distribution Pg. We prove that the estimator of the parameter by the method of moments determined from the equation 1= 1() and depending on the observations x1, ..., xn only via the sample mean ¯x is asymptotically admissible (and optimal) in the class
k
of the estimators determined by the estimator equations of the form 0 () + 1 () 1 + ... +
k
()
k
=0 if and only ifP
k
.The asymptotic admissibility (respectively, optimality) means that the variance of the limit, as n (normal) distribution of an estimator normalized in a standard way is less than the same characteristic for any estimator in the class under consideration for at least one 9 (respectively, for every ).The scales arise of classes
1
2... of parametric families and of classes 1 2 ... of estimators related so that the asymptotic admissibility of an estimator by the method of moments in the class
k
is equivalent to the membership of the familyP in the class
k
.The intersection consists only of the families of distributions with densities of the form h(x) exp {C0() + C1() x } when for the latter the problem of moments is definite, that is, there is no other family with the same moments 1 (), 2 (), ...Such scales in the problem of estimating the location parameter were predicted by Linnik about 20 years ago and were constructed by the author in [1] (see also [2, 3]) in exact, not asymptotic, formulation.Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, pp. 41–47, 1981. 相似文献
8.
On the distribution of square-full and cube-full integers 总被引:1,自引:0,他引:1
Jie Wu 《Monatshefte für Mathematik》1998,126(4):353-367
LetN
r
(x) be the number ofr-full integers x and let
r
(x) be the error term in the asymptotic formula forN
r
(x). Under Riemann's hypothesis, we prove the estimates 2(x)x1/7+, 3(x)x97/804+(>0), which improve those of Cao and Nowak. We also investigate the distribution ofr-full andl-free numbers in short intervals (r=2,3). Our results sharpen Krätzel's estimates. 相似文献
9.
Tomasz Rolski 《Probability Theory and Related Fields》1990,84(1):27-37
Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A
* and the Palm version A
0 corresponding to A
*. Let (T
i
,i) be the inter-point distance sequence in A and (T
i
0
,i) in A
0. We prove that forj, the sequence (T
i+j,i) converges in distribution to (T
i
0
,i). If the intensity function is periodic then the convergence is in variation. 相似文献
10.
We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (1, ...,
n
) = 1(1) + ... +
n
(
n
), where
i
(
i
) are ordinary moduli of continuity that depend on one variable. In the case where
i
(
i
) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L
2 for (1, ...,
n
) = 1(1) + ... +
n
(
n
); (ii) in the integral metric L
p (p 1) for (1, ...,
n
) = c
11 + ... + c
n
n
; (iii) in the integral metric L
(2, ..., 2, 2r) (r = 2, 3, ...) for (1, ...,
n
) = 1(1) + ... +
n – 1(
n – 1) + c
n
n
. 相似文献
11.
Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfyingX
n+1
=f(X
n
)+(X
n
)
n+1
, wheref, are measurable, {
n
} are i.i.d. with a (common) positive density,E|
n
|>. In the special casef(x)/x has limits, , asx– andx+, respectively, it is shown that <1, <1, <1 is sufficient for geometric ergodicity, and that <-1, 1, 1 is necessary for recurrence. 相似文献
12.
Summary Let (xini, y
i
be a sequence of independent identically distributed random variables, where x
i
R
p
and y
i
R, and let R
p
be an unknown vector such that y
i
=x
i
+u
i
(*), where u
i
is independent of x
i
and has distribution function F(u/), where >0 is an unknown parameter. This paper deals with a general class of M-estimates of regression and scale, (
*,*), defined as solutions of the system:
, where r= (y
i
–x
i
1*/)*, with R
p
×RR and RR. This class contains estimators of (, ) proposed by Huber, Mallows and Krasker and Welsch. The consistency and asymptotic normality of the general M-estimators are proved assuming general regularity conditions on and and assuming the joint distribution of (x
i
, y
i
) to fulfill the model (*) only approximately. 相似文献
13.
Erik Valtonen 《manuscripta mathematica》1989,63(1):45-68
LetR be a commutative ring with 1 andM anR-module. If:M
R
MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR
M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR
M; in particular, we are interested in some homological properties ofR
M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR
M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM
*, where the isomorphism is given by the adjoint of. 相似文献
14.
Wolfgang Reichel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):822-838
We consider the equation
(pu)-qu+wu
= f
in (0,1) subject to homogenous boundary conditions at
x = 0
and
x = 1, e.g.,
u(0)
= u(1) = 0. Let
1
be the first eigenvalue of the corresponding Sturm-Liouville problem. If
f 0
but
0 then it is known that there exists
> 0 (independent on
f) such that for
(1,
1 + ]
any solution
u
must be negative. This so-called
uniform anti-maximum principle
(UAMP)
goes back to Clément, Peletier [4]. In this paper we
establish the sharp values of
for which (UAMP) holds. The same phenomenon, including sharp values of
, can be shown for the radially symmetric
p-Laplacian on balls and annuli in
n
provided
1 n <
p. The results are illustrated by
explicitly computed examples. 相似文献
15.
The two point boundary problemy'-a(x)y–b(x)y=-f(x), o<x<1,y(0)=y(1)=0, is first solved approximately by the standard Galerkin method, (Y, ) + (aY+bY, )=(f, ),
1
0
(r, ), for a function Y
1
0
(r, ), the space ofC
1-piecewise--degree-polynomials vanishing atx=0 andx=1 and having knots at {x
0
,x
1
, ...,x
M
}=. ThenY is projected locally into a polynomial of higher degree by means of one of several projections. It is then shown that higher-order convergence results locally, provided thaty is locally smooth and is quasi-uniform.This research was supported in part by the National Science Foundation. 相似文献
16.
Given a setX and subsetsX
1,...,X
m, we consider the problem of finding a graphG with vertex setX and the minimum number of edges such that fori=1,...,m, the subgraphG
i; induced byX
i is connected. Suppose that for any pointsx
1,...,x
X, there are at mostX
i 's containing the set {x1,...,x
}. In the paper, we show that the problem is polynomial-time solvable for ( 2, 2) and is NP-hard for (3,=1), (=l,6), and (2,3).Support in part by the NSF under grant CCR-9208913 and CCR-8920505.Part work was done while this author was visiting at DIMACS and on leave from Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing. 相似文献
17.
R. A. Doney 《Probability Theory and Related Fields》1989,81(2):239-246
Summary Let
x
denote the time at which a random walk with finite positive mean first passes into (x, ), wherex0. This paper establishes the asymptotic behaviour of Pr {
x
>n} asn for fixedx in two cases. In the first case the left hand tail of the step-distribution is regularly varying, and in the second the step-distribution satisfies a one-sided Cramér type condition. As a corollary, it follows that in the first case
Pr {
x
>n}/Pr{
0
>n} coincides with the limit of the same quantity for recurrent random walk satisfying Spitzer's condition, but in the second case the limit is more complicated. 相似文献
18.
We investigate the asymptotic behaviour of the summatory functions of z(n, ), k(n, ) z
(n) and k(n, ) z
(n). 相似文献
19.
Horst Elmar Winkelnkemper 《Annals of Global Analysis and Geometry》1992,10(3):209-218
Let
t
be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M
n
, whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d
t
and, for each x M, we define a smooth real function
x
(t) : (1 +
i
(t)), where the i(t) are the eigenvalues of AA
T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t
, restricted to v at the point x
-t M
n.Among other things, we prove the
Theorem (Theorem II, below). Assume v is also volume preserving and that
x
'
(t) 0 for all x M and real t; then, if
x
t
: M M is weakly missng for some t, it is necessary that vx 0 at all x M. 相似文献
20.
N. M. Ivochkina 《Journal of Mathematical Sciences》1984,26(6):2349-2359
One proves that a priori boundedness of the norm
of the solution of the problem det(Uxx)=f(x,u,ux)>>0,u¦=0. The magnitudes of the exponents,() depends on whether the arguments u p occur or not in f (x,u,p).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 74–90, 1983. 相似文献