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1.
The method of differences is used to establish that every 2-regular multigraph onv– 10,2 (mod 3) points occurs as the neighbourhood graph of an element in a twofold triple system of orderv, with two exceptions: C2C3and C3C3.Dedicated to Professor Hanfried Lenz on the occasion of his seventieth birthday 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.
A. G. Areshkina 《Mathematical Notes》1998,64(2):154-158
On a measurable space (T, , ) we choose an additive measure: Z (Z is a Banach space) with the following property: for alle , we have
; this measure defines an indefinite integral over the measure onL
2
(T, ,). We prove that if {
n
(t)}
n
=1/
is an orthonormal basis inL
2 and
n
(e)=e
n
(t) d, then any additive measure: Z whose Radon-Nikodým derivatived/d belongs toL
2 is uniquely expandable in a series(e)=
n
=1/
n
n(e) that converges to(e) uniformly with respect toe can be differentiated term-by-term, and satisfies
n
=1/
n
/2
<. In the caseL
2[0,2],Z=, the Fourier series of a 2-periodic absolutely continuous functionF(t) such thatF'(t) L
2[0, 2] is superuniformly convergent toF(t).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 180–184, August, 1998. 相似文献
4.
Andrea Laforgia Martin E. Muldoon 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1988,39(2):267-271
Summary We show, among other things, that the positive zeros of a solution ofy
+x
y=0,y(0)=0 decrease to 1 as increases, 0.
To the memory of Milo Háik
This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino. 相似文献
Sommario Si dimostra, tra l'altro, che gli zeri positivi d'una soiuzione diy +x y=0,y(0)=0 decrescono al limite 1, quando cresce, 0.
To the memory of Milo Háik
This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino. 相似文献
5.
The unit sphere of Hilbert space, 2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of 2, (C
i
)
i=1
, and reals
i
0 so that a) each setC
i
has nonempty intersection with every infinite dimensional closed subspace of 2 and b) forij,xC, andyC
j
, |x, y|<min(i, j)
E. Odell was partially supported by NSF and TARP. Th. Schlumprecht was partially supported by NSF and LEQSF. 相似文献
6.
Many design objectives may be formulated as semi-infinite constraints. Examples in control design, for example, include hard constraints on time and frequency responses and robustness constraints. A useful algorithm for solving such inequalities is the outer approximations algorithm. One version of an outer approximations algorithm for solving an infinite set of inequalities(x, y) 0 for allyY proceeds by solving, at iterationi of the master algorithm, a finite set of inequalities ((x, y) 0 for allyY
i) to yieldx
i and then updatingY
i toY
i+1=Y
i
{yi
} wherey
i arg max {(x
i,y)¦y Y}. Since global optimization is computationally extremely expensive, it is desirable to reduce the number of such optimizations. We present, in this paper, a modified version of the outer approximations algorithm which achieves this objective.The research reported herein was sponsored by the National Science Foundation Grants ECS-9024944, ECS-8816168, the Air Force Office of Scientific Research Contract AFOSR-90-0068, and the NSERC of Canada under Grant OGPO-138352. 相似文献
7.
Dr. E. Phan-huy-Hao 《Mathematical Methods of Operations Research》1982,26(1):105-119
The problem (QPQR) considered here is: minimizeQ
1 (x) subject toQ
i (x) 0,i M
1 {2,...,m},x P R
n, whereQ
i (x), i M {1} M
1 are quadratic forms with positive semi-definite matrices, andP a compact nonempty polyhedron of Rn. Applications of (QPQR) and a new method to solve it are presented.Letu S={u R
m;u 0, u
i= l}be fixed;then the problem:iM minimize u
iQi (x (u)) overP, always has an optimal solutionx (u), which is either feasible, iM i.e.
u C1 {u S;Q
i (x (u)) 0,i M
1} or unfeasible, i.e. there exists ani M
1 withu C {u S; Qi(x(u)) 0}.Let us defineC
i Ci S
i withS
i {u S; u
i=0}, i M. A constructive method is used to prove that C
i is not empty and thatx (û) withiM û C
i characterizes an optimal solution to (QPQR). Quite attractive numerical results have been reached with this method.
An earlier version of this paper was written during the author's stay at the Institute for Operations Research, Swiss Federal Institute of Technology, Zürich. 相似文献
Zusammenfassung Die vorliegende Arbeit befaßt sich mit Anwendungen und einer neuen Lösungsmethode der folgenden Aufgabe (QPQR): man minimiere eine konvexe quadratische ZielfunktionQ i (x) unter Berücksichtigung konvexer quadratischer RestriktionenQ i (x) 0, iM 1 {2,...,m}, und/oder linearer Restriktionen.·Für ein festesu S {u R m;u 0, u i=1},M {1} M1 besitzt das Problem:iM minimiere die konvexe quadratische Zielfunktion u i Qi (x (u)) über dem durch die lineareniM Restriktionen von (QPQR) erzeugten, kompakten und nicht leeren PolyederP R n, immer eine Optimallösungx (u), die entweder zulässig ist: u C1 {u S;Q 1 (x (u)) 0,i M 1} oder unzulässig ist, d.h. es existiert eini M 1 mitu Ci {u S;Q i (x(u))0}.Es seien folgende MengenC i Ci S i definiert, mitS i {u S;u i=0}, i M. Es wird konstruktiv bewiesen, daß C i 0 undx (û) mitû C i eine Optimallösung voniM iM (QPQR) ist; damit ergibt sich eine Methode zur Lösung von (QPQR), die sich als sehr effizient erwiesen hat. Ein einfaches Beispiel ist angegeben, mit dem alle Schritte des Algorithmus und dessen Arbeitsweise graphisch dargestellt werden können.
An earlier version of this paper was written during the author's stay at the Institute for Operations Research, Swiss Federal Institute of Technology, Zürich. 相似文献
8.
Summary LetC be the symmetric cusp {(x, y)2:–x
yx
,x0} where >1. In this paper we decide whether or not reflecting Brownian motion inC has a semimartingale representation. Here the reflecting Brownian motion has directions of reflection that make constant angles with the unit inward normals to the boundary. Our results carry through for a wide class of asymmetric cusps too. 相似文献
9.
In this paper we show that over any field K of characteristic different from 2, the Maslov index gives rise to a 2-cocycle on the stable symplectic group with values in the Witt group. We also show that this cocycle admits a natural reduction to I
2(K) and that the induced natural homomorphism from K
2
Sp(K)I
2(K) is indeed the homomorphism given by the symplectic symbol {x, y} mapping to the Pfister form 1, -x 1, –y. 相似文献
10.
For the nth order nonlinear differential equation y
(n)(t)=f(y(t)), t [0,1], satisfying the multipoint conjugate boundary conditions, y
(j)(ai) = 0,1 i k, 0 j n
i
- 1, 0 =a
1 < a
2 < < a
k
= 1, and
i=1
k
n
i
=n, where f: [0, ) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone. 相似文献
11.
We present two convergence theorems for Hamilton-Jacobi equations and we apply them to the convergence of approximations and perturbations of optimal control problems and of two-players zero-sum differential games. One of our results is, for instance, the following. LetT andT
h be the minimal time functions to reach the origin of two control systemsy = f(y, a) andy = f
h
(y, a), both locally controllable in the origin, and letK be any compact set of points controllable to the origin. If f
h –f Ch, then |T(x) – T
h
(x)| C
K
h
, for all x K, where is the exponent of Hölder continuity ofT(x). 相似文献
12.
A finite distance spaceX, d d: X
2 is hypermetric (of negative type) if a
x
a
y
d(x, y) 0 for all integral sequences{a
x
x X} that sum to 1 (sum to 0).X, d is connected if the set {(x, y)d(x, y) = 1, x, y X} is the edge set for a connected graph onX, and graphical ifd is the path length distance for this graph. Then we proveThe first author was partially supported by NSF grant DMS 8600882. 相似文献
13.
On the Eigenvalues and Eigenfunctions of the Sturm--Liouville Operator with a Singular Potential 总被引:1,自引:0,他引:1
In this paper we consider the Sturm--Liouville operators generated by the differential expression -y+q(x)y and by Dirichlet boundary conditions on the closed interval [0,]. Here q(x) is a distribution of first order,, i.e., q(x)dx L
2[0,]. Asymptotic formulas for the eigenvalues and eigenfunctions of such operators which depend on the smoothness degree of q(x) are obtained. 相似文献
14.
Eli Katz 《Annali di Matematica Pura ed Applicata》1989,154(1):1-11
Summary We would like to monitor the homotopy type of the loop space of mapping cones (Y tf CX) for X and Y fixed and varying f. The effect of f on the homotopy type is reflected by the cooperation of the loop space of the mapping cone induced by the usual cooperation of the mapping cone Y tfCX Y tfCXX. Using the singular complex functor we move to the category of differential graded algebras. Motivated by the cooperation of the loop space of the mapping cone we define a free co-module. We find universal objects in this category and two classification theorems. 相似文献
15.
A typical result of the paper states that if X is a Banach space with a basis and for some 1pq, the spaces p and q are finitely block representable in every block subspace of X, then every block subspace of X admits a block quotient Z such that for every r[p,q], the space r is finitely block representable in Z. Results of a similar nature are also established for N
p-block-sequences and asymptotic spaces. 相似文献
16.
Carlos Gutierrez Marco-Antonio Teixeira 《Bulletin of the Brazilian Mathematical Society》1995,26(1):57-66
Let >0 andX be aC
1 vector field on the plane such that: (i) for allq2, Det(DX(q))>0; and (ii) for allp2, with p, Trace(D(X(p))<0. IfX has a singularity and
2 Trace(DX)dxdy is less than 0 (resp. greater or equal than 0), then the point at infinity of the Riemann sphere 2{} is a repellor (resp. an attractor) ofX. 相似文献
17.
Е. П. долженко 《Analysis Mathematica》1976,2(3):191-201
LetG be a domain inC
n
,EG, mes
E=0 for (r)=r
2n–1(r), where (r) is a nondecreasing non-negative function (r>0). Iff(z) is holomorphic inGE and (,f, GE)(), C=const, thenf(z) is holomorphic inG.The impossibility of the relaxation of the stipulations on () and(r) is also established.The statement above is a corollary to a more general result about the representation of a holomorphic function from a certain class in the form of an integral with respect to -measure, extended over the set of singular points of the function. 相似文献
18.
In-Suk Wee 《Probability Theory and Related Fields》1990,85(4):469-488
Summary Let {X
t
} be a 1 process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x
–L
1
(x), v{yy<–x}=x
–L
2
(x) whereL
1,L
2 are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf
a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University 相似文献
19.
Let (X
n
)
n 0 be a real random walk starting at 0, with centered increments bounded by a constant K. The main result of this study is: |P(S
n
n x)–P( sup0 u 1
B
u x)| C(n,K) n/n, where x 0, 2 is the variance of the increments, S
n
is the supremum at time n of the random walk, (B
u
,u 0) is a standard linear Brownian motion and C(n,K) is an explicit constant. We also prove that in the previous inequality S
n
can be replaced by the local score and sup0 u 1 B
u
by sup0 u 1|B
u
|. 相似文献
20.
Živorad Tomovski 《Analysis Mathematica》2003,29(2):165-170
In this paper equivalent classes of the classes M'
and S'
p
r, p >1, 0,r {0,1,2,...,[]} defined by Sheng [5] are obtained. Then it is shown that the classes of Fourier coefficients S
p, S'
p(case r==0) and S
p(), p>1, defined by . V. Stanojevi, V. B. Stanojevi Sheng and the author of the present note are identical. As a corollary of this result, the L
1-estimate for cosine series, obtained in [10], is refined. 相似文献