24,681 research outputs found
Restricting SLE(8/3) to an annulus
We study the probability that chordal in the unit disk
from to 1 avoids the disk of radius centered at zero. We find
the initial/boundary-value problem satisfied by this probability as a function
of and , and show that asymptotically as tends to one this
probability decays like with for . We
also give a representation of this probability as a functional of a Legendre
process.Comment: 28 pages, corrected proof of asymptotic dependenc
Chilodonella cyprini (Moroff, 1902) [Translation from: Izv.gos.nauchno-issled.Inst.ozer.i rech.ryb.kh-va 49 25-28, 1959]
The ciliated protozoan Chilodonella cyprini is described. Chilodon parasitizes the body, gills and fins of fishes. The infusoria produce irritation of the integument and strengthened mucous secretion. The sparse knowledsge of the ecology of chilodon is summarised and some advice on the struggle against cholodoniasis in carp given
Random incidence matrices: moments of the spectral density
We study numerically and analytically the spectrum of incidence matrices of
random labeled graphs on N vertices : any pair of vertices is connected by an
edge with probability p. We give two algorithms to compute the moments of the
eigenvalue distribution as explicit polynomials in N and p. For large N and
fixed p the spectrum contains a large eigenvalue at Np and a semi-circle of
"small" eigenvalues. For large N and fixed average connectivity pN (dilute or
sparse random matrices limit), we show that the spectrum always contains a
discrete component. An anomaly in the spectrum near eigenvalue 0 for
connectivity close to e=2.72... is observed. We develop recursion relations to
compute the moments as explicit polynomials in pN. Their growth is slow enough
so that they determine the spectrum. The extension of our methods to the
Laplacian matrix is given in Appendix.
Keywords: random graphs, random matrices, sparse matrices, incidence matrices
spectrum, momentsComment: 39 pages, 9 figures, Latex2e, [v2: ref. added, Sect. 4 modified
Core percolation in random graphs: a critical phenomena analysis
We study both numerically and analytically what happens to a random graph of
average connectivity "alpha" when its leaves and their neighbors are removed
iteratively up to the point when no leaf remains. The remnant is made of
isolated vertices plus an induced subgraph we call the "core". In the
thermodynamic limit of an infinite random graph, we compute analytically the
dynamics of leaf removal, the number of isolated vertices and the number of
vertices and edges in the core. We show that a second order phase transition
occurs at "alpha = e = 2.718...": below the transition, the core is small but
above the transition, it occupies a finite fraction of the initial graph. The
finite size scaling properties are then studied numerically in detail in the
critical region, and we propose a consistent set of critical exponents, which
does not coincide with the set of standard percolation exponents for this
model. We clarify several aspects in combinatorial optimization and spectral
properties of the adjacency matrix of random graphs.
Key words: random graphs, leaf removal, core percolation, critical exponents,
combinatorial optimization, finite size scaling, Monte-Carlo.Comment: 15 pages, 9 figures (color eps) [v2: published text with a new Title
and addition of an appendix, a ref. and a fig.
QCD-Factorization of inclusive B decays and |Vub|
Recent progress in the theoretical description of inclusive B to X_u l nu
decays in the shape-function region is reported. Finite moments of the shape
function are related to HQET parameters. Event fractions for several
experimental cuts are presented, with a particular emphasis on the hadronic
variable P+. The aim of this talk is to introduce the P+ spectrum, to compare
it to the hadronic invariant mass spectrum and the charged-lepton energy
spectrum, and to study the prospect of evaluating |Vub| in the presence of a
large background from B to X_c decays.Comment: 8 pages, 7 figures, uses espcrc2.sty (included). Talk presented at
the Sixth International Conference on Hyperons, Charm and Beauty Hadrons,
IIT, Chicago, June 27--July 3 200
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