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1.
Denote by
the class of all triangle-free
graphs on n vertices and
m edges. Our main result is
the following sharp threshold, which answers the question for
which densities a typical triangle-free graph is bipartite. Fix
> 0 and let
. If
n/2 m (1 – ) t
3, then almost
all graphs in
are not bipartite, whereas if
m (1 + )t
3, then almost
all of them are bipartite. For m (1 + )t
3, this allows
us to determine asymptotically the number of graphs in
. We also obtain corresponding
results for C
-free graphs, for any
cycle C
of fixed odd length.
Forschergruppe Algorithmen, Struktur, Zufall
supported by Deutsche Forschungsgemeinschaft grant FOR
413/1-1 相似文献
2.
Thomas Stehling 《Combinatorica》1992,12(4):475-479
We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
. 相似文献
3.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
4.
Hermann Hähl 《Geometriae Dedicata》1995,58(2):213-226
As a contribution to a classification of all sixteen-dimensional translation planes whose collineation group
has dimension at least 38, this paper deals with the case that
contains a subgroup (locally) isomorphic to SU2Spin5. Under various further assumptions, it is shown that such a plane satisfying dim
38 is necessarily isomorphic to the classical plane over the octonions.The complete classification will reveal that these further assumptions may in fact be omitted, except for the case that
even contains a subgroup isomorphic to Spin7. The latter planes have been explicitly determined in previous papers.
Meinem verehrten Lehrer Helmut Salzmann zum 65. Geburtstag 相似文献
5.
Ton Daorong 《数学学报(英文版)》1990,6(1):47-56
In this paper we discuss the completions (,
) of a commutativel-groupG with respect to the intrinsic topologies . We give some conditions under which
is the intrinsic topology of the same type on as
and give the relations between these completions. 相似文献
6.
Abdelhafed Elkhadiri 《Bulletin of the Brazilian Mathematical Society》2000,31(1):45-71
Let be an open subset of
n
and
be a subalgebra of the algebra of analytic functions on . We suppose that
satisfies some weak conditions of noetherianity such that we can construct a finite stratification for each ideal of
. We also suppose that
satifies global £ojasiewicz's inequalities. We prove the following: Let
andf C
on
flat on ; if for eacha the Taylor's serie off ata, T
a
f, is in the ideal generated byT
a
f
1,...,T
a
f
p
in the ring of formal power series, then there exist
1,...,
p
,C
on
flat on such that
. This result extends the classic Hormander's theorem of division (for a polynomial) or the £ojasiewicz-Malgrange theorem in the local analytic case.Reherches menées dans le cadre du Programme d'Appui à la Recherche Scientifique (PARS MI 33) 相似文献
7.
V. M. Badkov 《Mathematical Notes》1973,13(5):453-459
For the polynomials {pn(t)}
0
, orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t)
v=1
m
, we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1)
2)
and 3)
with the conditions that
on [–1, 1] and (H,)–1 L2(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973. 相似文献
8.
Two finite real sequences (a
1,...,a
k
) and (b
1,...,b
k
) are cross-monotone if each is nondecreasing anda
i+1–a
i
b
i+1–b
i
for alli. A sequence (1,...,
n
) of nondecreasing reals is in class CM(k) if it has disjointk-term subsequences that are cross-monotone. The paper shows thatf(k), the smallestn such that every nondecreasing (1,...,
n
) is in CM(k), is bounded between aboutk
2/4 andk
2/2. It also shows thatg(k), the smallestn for which all (1,...,
n
) are in CM(k)and eithera
k
b
1 orb
k
a
1, equalsk(k–1)+2, and thath(k), the smallestn for which all (1,...,
n
) are in CM(k)and eithera
1b
1...a
k
b
k
orb
1a
1...b
k
a
k
, equals 2(k–1)2+2.The results forf andg rely on new theorems for regular patterns in (0, 1)-matrices that are of interest in their own right. An example is: Every upper-triangulark
2×k
2 (0, 1)-matrix has eitherk 1's in consecutive columns, each below its predecessor, ork 0's in consecutive rows, each to the right of its predecessor, and the same conclusion is false whenk
2 is replaced byk
2–1. 相似文献
9.
A probability measurep on the set of matchings in a graph (or, more generally 2-bounded hypergraph) ishard-core if for some : [0,), the probabilityp(M) ofM is proportional to
. We show that such distributions enjoy substantial approximate stochastic independence properties. This is based on showing that, withM chosen according to the hard-core distributionp, MP () the matching polytope of , and >0, if the vector ofmarginals, (Pr(AM):A an edge of ), is in (1–) MP (), then the weights (A) are bounded by someA(). This eventually implies, for example, that under the same assumption, with fixed,
as the distance betweenA, B tends to infinity.Thought to be of independent interest, our results have already been applied in the resolutions of several questions involving asymptotic behaviour of graphs and hypergraphs (see [14, 16], [11]–[13]).Supported in part by NSFThis work forms part of the author's doctoral dissertation [16]; see also [17]. The author gratefully acknowledges NSERC for partial support in the form of a 1967 Science and Engineering Scholarship. 相似文献
10.
In this paper we are concerned with the summability of the geometric series
by matrix methods. We prove the following theorem: Suppose Mo:={z:|z|<1}, M1, M2, is a collection of countably many Lebesgue measureable, disjoint sets. For k=1,2, let fk be a prescribed function, analytic on
. Then there exists a triangular matrix
, such that the V-transform {n(z)} of the geometric series has the following properties: {n(z)} converges compactly to
on Mo; for k=1,2, there are sets Bk, such that
has Lebesgue-measure zero and n(z)fk(z) for zBk; if
there is a set B*, such that B*M* has Lebesgue-measure zero and {n(z)} diverges for zB*. 相似文献
11.
Let be a finite-dimensional hereditary algebra over a finite field k,
() and
() be, respectively, the Hall algebra and the composition algebra of ,
be the isomorphism classes of finite dimensional -modules and I the isomorphism classes of simple -modules. We define and , in
, to be the right and left derivations of
() respectively. By using these derivations and the action of the braid group on the set of exceptional sequences of -mod, we provide an effective algorithm of calculating the root vectors of real Schur roots. This means that we get an inductive method to express u as the combinations of elements ui in the Hall algebra, where i I and in
is any exceptional -module. Because of the canonical isomorphism between the Drinfeld–Jimbo quantum group and the generic composition algebra, our algorithm is applicable directly to quantum groups. In particular, all the root vectors are obtained in this way in the finite type cases. 相似文献
12.
Summary We investigate the asymptotic behaviour of
n
(n),n where
n
(x) denotes the Laguerre polynomial of degreen. Our results give a partial answer to the conjecture
n
(n)>1 forn>6, made in 1984 by van Iseghem. We also show the connection between this conjecture and the continued fraction approximants of
.Work sponsored by the Consiglio Nazionale delle Ricerche and by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica of Italy 相似文献
13.
V. V. Makeev 《Journal of Mathematical Sciences》2002,110(4):2774-2775
Let A1,...,An be points in
, let
be a fixed point, let p be a positive integer, and let 1,...,n be positive real numbers. If the
does not depend on the position of M on a sphere with center O, then one says that the point system {A1,...,An} has an invariant of degree p with weight system {,...,n}. It is proved that for arbitrary positive integers d and N there exists a finite point system
having invariants of degrees p=1,...,N with common positive weight system {1,...,n}. Bibliography: 2 titles. 相似文献
14.
Hansmartin Zeuner 《Journal of Theoretical Probability》1994,7(2):225-245
Let (X
n:n) be i.i.d. with finite variance and values in a hypergroupK:=+ or and
j=1
n
X
j
be the randomized sum of these random variables. It is shown that the processes
converge in distribution to a Gaussian process in the caseK=+, that the processes
converge towards a Bessel process on + in the case of polynomial growth of the hypergroupK=+ or , and that in the case of exponential growth
converges towards a Brownian motion asn. 相似文献
15.
Luca Brandolini 《Annali di Matematica Pura ed Applicata》1990,156(1):231-242
Summary Let D denote the interior of a piecewise regular curve of R2 having a point with Gauss curvature different from zero. We show that the Lebesgue constants L
D
relative to D behave like 1/2 as . 相似文献
16.
An integer partition {1,2,...,
v
} is said to be graphical if there exists a graph with degree sequence
i
. We give some results corcerning the problem of deciding whether or not almost all partitions of even integer are non-graphical. We also give asymptotic estimates for the number of partitions with given rank. 相似文献
17.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
18.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
19.
Let :=. The following are known: two -sets of power are isomorphic. Let >0. Two ordered divisible Abelian groups that are -sets of power are isomorphic, two real closed fields that are -sets of power are isomorphic. The following is shown: (1) there exist 2 nonisomorphic ordered Abelian groups (respectively ordered fields) that are -sets of power ; (2) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) of power all having the same order type; (3) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) that are -sets having the same order type. 相似文献
20.
In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices
for which
for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity
such that its Fourier series is -divergent everywhere for any
. 相似文献