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1.
On graphs that can be oriented as diagrams of ordered sets   总被引:1,自引:0,他引:1  
Oliver Pretzel 《Order》1985,2(1):25-40
We study some equivalent and necessary conditions for a finite graph to be the covering graph of a (partially) ordered set. For each 1, M. Aigner and G. Prins have introduced a notion of a vertex colouring, here called -good colouring, such that a 1-good colouring is the usual concept and graphs that have a 2-good colouring are precisely covering graphs. We present some inequalities for the corresponding chromatic numbers , especially for x 2. There exist graphs that satisfy these inequalities for =2 but are not covering graphs. We show also that x 2 cannot be bounded by a function of x=x 1. A construction of Neetil and Rödl is used to show that x 2 is not bounded by a function of the girth.  相似文献   

2.
Stability analysis of numerical methods for delay differential equations   总被引:7,自引:0,他引:7  
Summary This paper deals with the stability analysis of step-by-step methods for the numerical solution of delay differential equations. We focus on the behaviour of such methods when they are applied to the linear testproblemU(t)=U(t)+U(t–) with >0 and , complex. A general theorem is presented which can be used to obtain complete characterizations of the stability regions of these methods.  相似文献   

3.
Extensions from H 1(P) into H 1() (where P ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded.  相似文献   

4.
Let Z n (n=0, l, ...) be an aperiodic critical Galton-Watson process and let 2 be the (possibly infinite) variance of Z 1. Let k (k=1, 2, ...) denote the stationary measure of the process. Kesten, Ney and Spritzer proved in 1966 that k 2/ 2 as k (*) under the additional assumption that EZ 1 2 log Z 1< (**) In the present paper, (*) is proved without the assumption (**). The proof uses complex function theory.  相似文献   

5.
Summary In each lattice point , of a rectangular net a numerical valueu is given. A bicubical and twice continuously differentiable function is constructed interpolating the valuesu . The method is known as «spline interpolation».  相似文献   

6.
(v k) 1 n , 1v kr, v1+...+vn r, p(;r) — =(x 1,v 1),...,(x n,v n), v 1+...+v n-r (r(;·)=1. , (*;t) [, ] (;t) x 1<... n v 1 ...,v n. (*;t) .  相似文献   

7.
. E , f(x)L p (T N ),P1,f(x)=0 E (E— N =[-, ]N) E , . , .

In closing the author thanks V. A. Il'in and . A. Alimov for their constant attention paid to the present work.  相似文献   

8.
Summary A nonlinear generalizationÊ z of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE z and a twoparametric methodE . It is shown how to applyE orE , to compute the valuef(zo) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE andE , are superior toÊ z . A compact recursive algorithm is given for computingE andE ,.  相似文献   

9.
[0,1], - H .

This paper was written during the author's scholarship at the State University of Odessa in the USSR.  相似文献   

10.
. (R) fg(y)h(x–y) dx dy f ^ (x)g ^ (y)h ^ (x–y)dx dy (f,g0) —:f×gf ^ ×g ^(f,g 0) f^ g^ f g -, X — . , - f 1f 2 , f 1 ^ ×gf 2×g 0g. .  相似文献   

11.
f — , . p n (f) f . , n+2 , fp n (f) . , n . , .
On the distribution of points of maximal deviation in complex ebyev approximation
  相似文献   

12.
[Zho2] {x n } , n 0 n .

Supported in part by an NSERC Postdoctoral Fellowship and a CRF grant of University of Alberta.  相似文献   

13.
Zusammenfassung Die zeitabhängige (instationäre) Lösung für die Zustandswahrscheinlichkeiten und für einige Kenngrößen von Warteschlangensystemen mit einer Bedienungsstation, unendlich vielen Warteplätzen, exponentiellem Zu- und Abgang und beliebigem Anfangszustand wird bestimmt. Die ZustandswahrscheinlichkeitenP v (), d. h. die Wahrscheinlichkeiten für Einheiten im System zur Zeit, ergeben sich als Integrale, in denen modifizierteSessel-Funktionen 1. Art auftreten. Der ErwartungswertL () und die VarianzV() der Zahl von Einheiten im System lassen sich als Integrale darstellen, in denen nur die ZustandswahrscheinlichkeitP 0() auftritt.Für<1 und erreichen die Systeme einen stationären Zustand (für den die Lösung bekannt ist); für1 und giltP v ()0 für alle, L(),V().Ist>1, dann wachsenL() undV() für große linear mit; ihre Asymptoten werden berechnet. Ist=1, dann wachsenL() und die Standardabweichung() für große mit ; einfache Näherungsformeln werden gefunden.
Summary The time dependent solution is determined for the state probabilities and for some characteristic values of queuing systems with a single server, an infinite number of waiting places, exponentially distributed inter-arrival and service times, and any initial state. The state probabilitiesP v (), i.e. the probabilities for units in the system at time, are given in the form of integrals in which modifiedBessel functions of the first kind occur. Integrating the state probalityP 0() over leads to the meanL() and the varianceV() of the number of units in the system.For<1 and the systems tend to a steady state (for which the solution is known); for1 and we haveP v ()0 for all, L(),V().If>1 asymptotic expansions for large are found givingL() andV() proportional to. If=1 simple approximate formulas for large are obtained givingL() and the standard deviation() proportional to .


Vorgel. v.:J. Nitsche.  相似文献   

14.
    
( « . III») - B p,q g(x) F p,q g(x) ( ) R n . --, . : , , , .  相似文献   

15.
16.
Summary Let P={P : } be an exponential family of probability distributions with the canonical parameter and consider the one to one mapping : P . It is shown that, under mild regularity assumptions, and –1 are continuous with respect to the Lévy metric in P and Euclidean metric in .  相似文献   

17.
Let R 3 be a bounded domain, 0$$ " align="middle" border="0"> , a family of extending subdomains, and =(x) a positive function in be a space of -solenoidal vector fields, 0$$ " align="middle" border="0"> , a family of subspaces, G orthogonal projectors in onto . A unitary transformation that diagonalizes the family of projectors {G} is constructed: it takes to the operator of multiplication by the independent variable. The isometry of this transformation is proved with the help of the operator Riccati equation for the NeumanntoDirichlet mapping. Bibliography: 8 titles.  相似文献   

18.
Letf be a periodic function on with period 1, piecewise continuously differentiable, satisfying . For an arbitrary sequence = ( i ) in [0,1) put and . If then n (f,) >c· logn holds for some positive constantc (depending onf only) and almost alln. In a certain sense the converse is also true: there is a class of functionsf with such that n (f,) =o (logn).Support has been received from Netherlands Organization for the Advancement of Pure Research (Z. W. O.).  相似文献   

19.
X(Y) f -:X(Y)={fM(×): fX(Y)=f(x,.)YX< . =(0, ), M (×) — , ×, X, Y, Z— . X(Y) Z(×).  相似文献   

20.
Zusammenfassung Die Methode der inneren Parallelen von Makai und Pólya wird hier auf das Randwertproblem (3) angewendet. Die sich ergebenden Schranken (11) und (11) für das FunktionalQ() enthalten als Grenzfälle die von Pólya [9] erhaltenen Schranken (2) und (1) für die Torsionssteifigkeit (Fall=0) bzw. für den Grundton einer Membran (Fall 1.
Summary We apply here the method of interior parallels of Makai and Pólya to the boundary value problem (3). The resulting bounds (11) and (11) for the functionalQ() contain as limit cases the bounds (2) and (1) obtained by Pólya [9] for torsional rigidity (case=0) and for the lowest eigenfrequency of a membrane (case 1).
  相似文献   

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