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81.
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
82.
Milan Práger 《Applications of Mathematics》2003,48(3):225-236
Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered. 相似文献
83.
The Aitken's 2-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's 2-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of 2-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method. 相似文献
84.
The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX
On the real line and of
On the half-line are studied. Assuming that the inhomogeneityf (resp.g) belongs to a given homogeneous subspace ofBUC(X) (resp.BUC(
+;X)) it is shown that given bounded solutionsu (resp.v) belong also to provided the spectra of these equations are countable. The results are applied to an equation of scalar type which is of importance in applications like viscoelasticity. 相似文献
85.
86.
Der Präsident des Kongresses F. H. Müller 《Rheologica Acta》1961,1(4-6):331-331
Ohne Zusammenfassung 相似文献
87.
Delphine Declerck 《Tetrahedron letters》2009,50(19):2171-1809
We have developed an expedient method for the synthesis of 2-aminocyclopropyl pyrrolidines from carbohydrate-derived α-aminonitriles involving up to five or six steps, the key step being the titanium-mediated aminocyclopropanation on the aminonitrile moiety, followed by cleavage of the protecting groups. 相似文献
88.
Summary. Total positivity is an important concept which has been studied by Gantmacher, Karlin and Schoenberg. In section 1, new properties
of totally positive functions are given. The concept of totally monotonic families of sequences (TMFS), by mean of positivity
of some determinant, is defined and studied.
Applications to extrapolation algorithms are given.
Received October 22, 1997 / Revised version received April 14, 1998 / Published online August 19, 1999 相似文献
89.
90.
Heinz Prüfer 《Mathematische Zeitschrift》1923,17(1):35-61
Ohne Zusammenfassung 相似文献