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121.
L. Pyber 《Combinatorica》1996,16(4):521-525
By a well-known result of Nash-Williams if a graphG is not edge reconstructible, then for all
,|A||E(G)| mod 2 we have a permutation ofV(G) such thatE(G)E(G)=A. Here we construct infinitely many graphsG having this curious property and more than
edges.Research (partially) supported by Hungarian National Foundation for Scientific Research Grant No.T016389. 相似文献
122.
Set-valued mappings from a topological space into subsets of a Banach space which satisfy a restricted form of weak upper semi-continuity, have particularly noteworthy properties. We establish a selection theorem for certain set-valued mappings from a (-) unfavourable topological space into subsets of a Banach space and as a consequence derive the property that restricted weak upper semi-continuous set-valued mappings which satisfy a minimality condition, from a (-) unfavourable topological space into subsets of a Banach space are single-valued and norm upper semi-continuous at the points of a residual subset of their domain. 相似文献
123.
Inclusion-exclusion: Exact and approximate 总被引:1,自引:0,他引:1
It is often required to find the probability of the union of givenn eventsA
1
,...,A
n
. The answer is provided, of course, by the inclusion-exclusion formula: Pr(A
i
)=
i
–
i<j
Pr(A
i
A
j
)±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A
i
), from the above data with an additive error of exp
. In the present article we develop an expression that can be computed in polynomial time, that, given the sums |S|=j
Pr(
iS
A
i
) forj=1,...k, approximates Pr(A
i
) with an additive error of exp
. This error is optimal, up to the logarithmic factor implicit in the
notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v
l
m
C
i
is an instance of the general problem that had been extensively studied [7]. HereA
i
is the set of assignments that satisfyC
i
, and Pr(
iS
A
i
)=a
S
/2n where
iS
C
i
is satisfied bya
S
assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa
S
for, say, all cardinalities
. Quite surprisingly, already the numbersa
S
over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation. 相似文献
124.
Ryszard Rudnicki 《Integral Equations and Operator Theory》1996,24(3):320-327
A class of Markov operators appearing in biomathematics is investigated. It is proved that these operators are asymptotic stable inL
1, i.e. lim
n
P
n f=0 forfL
1 and f(x) dx=0. 相似文献
125.
Ayelet Lindenstrauss 《K-Theory》1996,10(3):239-265
Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x
n) and [x]/(x
n–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra. 相似文献
126.
David Applebaum 《Letters in Mathematical Physics》1993,28(3):231-237
The index of a Fredholm operator associated to a-summable Fredholm module is expressed in terms of the vacuum expectation value of a unitary operator-valued stochastic process which satisfies a stochastic differential equation with unbounded coefficients driven by fermion noise. 相似文献
127.
J. Czarnowska 《Periodica Mathematica Hungarica》1993,26(2):101-110
To 80th birthday of Paul Erds 相似文献
128.
W. K. Nicholson 《Periodica Mathematica Hungarica》1993,27(2):85-88
A ringR is called a leftPP-ring if every principal left ideal is projective, equivalently if the left annihilatorl(a) is generated by an idempotent for allaR. These rings seem first to have been discussed by Hattori [2] and examples include (von Neumann) regular rings and domains (possibly noncommutative). In this note we give a new characterization of leftPP-rings, use that to give an elementary proof of a result of Xue [4] characterizing triangularPP-rings, and then determine when the ringT
n
(R) of upper triangular matrices overR is a leftPP-ring. Throughout the paper all rings have a unity and all modules are unitary.This research was supported by NSERC Grant A8075 相似文献
129.
Riddhi Shah 《Monatshefte für Mathematik》1993,115(3):191-213
For any locally compact groupG, we show that any locally tight homomorphism from a real directed semigroup intoM
1
(G) (semigroup of probability measures onG) has a shift which extends to a continuous one-parameter semigroup. IfG is ap-adic algebraic group then the above holds even iff is not locally tight. These results are applied to give sufficient conditions for embeddability of some translate of limits of sequences of the form {v
n
kn
} and M
1
(G) such that ()=
M
, for somek>1 and AutG (cf. Theorems 2.1, 2.4, 3.7). 相似文献
130.
For a fixed setI of positive integers we consider the set of paths (p
o,...,p
k
) of arbitrary length satisfyingp
l
–p
l–1I forl=2,...,k andp
0=1,p
k
=n. Equipping it with the uniform distribution, the random path lengthT
n
is studied. Asymptotic expansions of the moments ofT
n
are derived and its asymptotic normality is proved. The step lengthsp
l
–p
l–1 are seen to follow asymptotically a restricted geometrical distribution. Analogous results are given for the free boundary case in which the values ofp
0 andp
k
are not specified. In the special caseI={m+1,m+2,...} (for some fixed m) we derive the exact distribution of a random m-gap subset of {1,...,n} and exhibit some connections to the theory of representations of natural numbers. A simple mechanism for generating a randomm-gap subset is also presented. 相似文献