Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give explicit definitions for some functions that are not computable and grow faster than any computable function. He put forward the problem of computing the values of these functions on numbers 1, 2, 3, . . .. More and more powerful computers have made possible the computation of lower bounds for these values. ...

In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/I queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/I, R/G/I queues, where R is the class of distributions with rational Laplace tran...

Using 22.7M BB events recorded by the BaBar detector, the inclusive branching ratios for the production of J/ψ , ψ(2S) and χc in B decays are presented. Combining the charmonium state with a K± , K, K∗± , K∗0 or π, B decays are reconstructed exclusively and their branching fractions are determined. A preliminary study is also presented for the B → ηcK decay mode.

Introduction. The db complex is well defined on any smooth CR manifold M, and once a metric is fixed, so is the complex Laplace-Beltrami operator Db on forms of type (p, q). For compact M without boundary, the bb cohomology of M may be studied via Ub [6], and thus local smoothness of solutions to Dbu = ƒ is important. In its own right, Ub is a prototype of doubly characteristic operators. Under...

A high luminosity storage ring operating at center-of-mass energies in the range 3 5 GeV would allow high-statistics studies of the T lepton. To take full advantage of the large data samples, the systematic errors must be greatly reduced compared to those for existing 7 measurements. The size of uncertainties on current measurements and the desired precision of future measurements of T properti...

Recent results on Heavy Flavours and CP violation are presented. After a short introduction a taste of K and D results is given. In a third part results on |V td | and |V ts | are summaryzed including BB mixing results and B d radiative decays. A summary of |V cb | and |V ub | measurements is presented in the fourth part. In the next section CP violation measurements in the B d sector are shown...

CLEO has made a number of important new B measurements over the past two years. I report here a new measurement of the inclusive branching fraction B(B ! X``) using lepton tags which has very small model uncertainties and provides the best upper limit yet for the fraction of non-BB decays of the (4S). New values for V cb and B(b ! c ! `) which result from this analysis are also reported. A numb...

It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally quasi-convex groups for which the analogue to the Grothendieck theorem does not hold. By means of...

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We present a search for the radiative leptonic decays B → eνeγ and B → μνμγ using data collected by the BABAR detector at the PEP-II B factory. We fully reconstruct the hadronic decay of one of the B mesons in Υ (4S) → BB and then search for evidence of the signal decay within the rest of the event. This method provides clean kinematic information on the signal’s missing energy and high momentu...