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111.
Suppose one is given two related generating functionsa(x) = a
n
x
n
andb(x) = b
n
x
n
, often it is of interest to determine the limiting behaviour of the quantitiesa
n
/b
n
We survey some earlier results of this nature and give some new ones 相似文献
112.
Summary We consider a walk from a stateA
1 to a stateA
n+1 in which the probability of remaining atA
i
isp
i
, and the probability of progressing fromA
i
toA
i+1 is 1 –p
i
. The probabilityW
nk
of reachingA
n+1 fromA
1 in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp
1,,p
n
. We determine the maximum value ofW
nk
and the (unique) choice (p
1,,p
n
) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday 相似文献
113.
Takayuki Hibi 《Order》1987,3(4):383-389
A finite poset Q is called integral over a field k if there exists an ASL (algebra with straightening laws) domain on Q{–} over k. We classify all trees (rank one connected posets without cycles) which are integral over an infinite field. 相似文献
114.
B. Barabás 《Periodica Mathematica Hungarica》1987,18(2):115-122
The properties of the empirical density function,f
n(x) = k/n(
j
+
–
j-1
+
) if
j-1
+
< x + where
j-1
+
and
j
+
are sample elements and there are exactlyk – 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a good estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions. 相似文献
115.
116.
In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD
k
((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker. 相似文献
117.
118.
This is one in a series of papers studying measures of information in the so-called mixed theory of information (i.e. considering the events as well as their probabilities) on the open domain (i.e. without empty sets and zero probabilities). In this paper we find all-recursive, 3-semisymmetric inset entropies on the open domain. We do this by solving the fundamental equation of inset information of degree () on the open domain.Dedicated to Professor János Aczél on his 60th birthday. 相似文献
119.
Peter Šemrl 《Aequationes Mathematicae》1986,31(1):184-190
LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX. 相似文献
120.
David Whitley 《Acta Appl Math》1986,5(3):279-311
We study the dynamics of a two-parameter family of noninvertible maps of the plane, derived from a model in population dynamics. We prove that, as one parameter varies with the other held fixed, the nonwandering set changes from the empty set to an unstable Cantor set on which the map is topologically equivalent to the shift endomorphism on two symbols. With the help of some numerical work, we trace the genealogies of the periodic points of the family of period 5, and describe their stability types and bifurcations. Among our results we find that the family has a fixed point which undergoes fold, flip and Hopf bifurcations, and that certain families of period five points are interconnected through a codimension-two cusp bifurcation. 相似文献