148 research outputs found
Formulas for Continued Fractions. An Automated Guess and Prove Approach
We describe a simple method that produces automatically closed forms for the
coefficients of continued fractions expansions of a large number of special
functions. The function is specified by a non-linear differential equation and
initial conditions. This is used to generate the first few coefficients and
from there a conjectured formula. This formula is then proved automatically
thanks to a linear recurrence satisfied by some remainder terms. Extensive
experiments show that this simple approach and its straightforward
generalization to difference and -difference equations capture a large part
of the formulas in the literature on continued fractions.Comment: Maple worksheet attache
Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras
This is a continuation of our "Lecture on Kac--Moody Lie algebras of the
arithmetic type" \cite{25}.
We consider hyperbolic (i.e. signature ) integral symmetric bilinear
form (i.e. hyperbolic lattice), reflection group
, fundamental polyhedron \Cal M of and an acceptable
(corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors
orthogonal to faces of \Cal M (simple roots). One can construct the
corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth
g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by .
We show that \goth g has good behavior of imaginary roots, its denominator
formula is defined in a natural domain and has good automorphic properties if
and only if \goth g has so called {\it restricted arithmetic type}. We show
that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth
g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth
g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus,
Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a
natural class to study.
Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the
best automorphic properties for the denominator function if they have {\it a
lattice Weyl vector }. Lorentzian Kac--Moody Lie algebras of the
restricted arithmetic type with generalized lattice Weyl vector are
called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on
results and ideas. 31 pages, no figures. AMSTe
Observation of weak neutral current neutrino production of
Observation of \jpsi production by neutrinos in the calorimeter of the CHORUS detector exposed to the CERN SPS wide-band \numu beam is reported. A spectrum-averaged cross-section = (6.3 3.0) is obtained for 20 GeV 200 GeV. The data are compared with the theoretical model based on the QCD Z-gluon fusion mechanism
Experimental search for muonic photons
We report new limits on the production of muonic photons in the CERN neutrino beam. The results are based on the analysis of neutrino production of dimuons in the CHARM II detector. A CL limit on the coupling constant of muonic photons, is derived for a muon neutrino mass in the range eV. This improves the limit obtained from a precision measurement of the anomalous magnetic moment of the muon by a factor from 8 to 4
Leading-order QCD Analysis of Neutrino-Induced Dimuon Events
The results of a leading-order QCD analysis of neutrino-induced charm production are presented. They are based on a sample of 4111 \numu- and 871 \anumu-induced opposite-sign dimuon events with , , observed in the CHARM~II detector exposed to the CERN wideband neutrino and antineutrino beams. The analysis yields the value of \linebreak the charm quark mass and the Cabibbo--Kobayashi--Maskawa matrix element . The strange quark content of the nucleon is found to be suppressed with respect to non-strange sea quarks by a factor
Measurements of the leptonic branching fractions of the
Data collected with the DELPHI detector from 1993 to 1995 combined with previous DELPHI results for data from 1991 and 1992 yield the branching fractions B({\tau \rightarrow \mbox{\rm e} \nu \bar{\nu}}) = (17.877 \pm 0.109_{stat} \pm 0.110_{sys} )\% and
The CHORUS neutrino oscillation search experiment
The CHORUS experiment has successfully finished run I (320~000 recorded \numu\ CC in 94/95) and performed half of run II (225~000 \numu\ CC in 96). The analysis chain was exercised on a small data sample for the muonic \tdecay\ search using for the first time fully automatic emulsion scanning. This pilot analysis, resulting in a limit \sintth \leq 3 \cdot 10^{-2}, confirms that the CHORUS proposal sensitivity (\sintth \leq 3 \cdot 10^{-4}) is within reach in two years
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