On the Summability and Generalized Sum of a Series of Legendre Polynomials

The results obtained in this paper are as follows. (A) The series of Legendre polynomials ΣnpXn(x), where p is a positive integer, is summable (H, p) for -1\u3c x \u3c 1, and summable (H, p +1) for - 1 ≤ x \u3c 1

Search for composite and exotic fermions at LEP 2

A search for unstable heavy fermions with the DELPHI detector at LEP is reported. Sequential and non-canonical leptons, as well as excited leptons and quarks, are considered. The data analysed correspond to an integrated luminosity of about 48 pb^{-1} at an e^+e^- centre-of-mass energy of 183 GeV and about 20 pb^{-1} equally shared between the centre-of-mass energies of 172 GeV and 161 GeV. The search for pair-produced new leptons establishes 95% confidence level mass limits in the region between 70 GeV/c^2 and 90 GeV/c^2, depending on the channel. The search for singly produced excited leptons and quarks establishes upper limits on the ratio of the coupling of the excited fermio

Search for lightest neutralino and stau pair production in light gravitino scenarios with stau NLSP

Promptly decaying lightest neutralinos and long-lived staus are searched for in the context of light gravitino scenarios. It is assumed that the stau is the next to lightest supersymmetric particle (NLSP) and that the lightest neutralino is the next to NLSP (NNLSP). Data collected with the Delphi detector at centre-of-mass energies from 161 to 183 \GeV are analysed. No evidence of the production of these particles is found. Hence, lower mass limits for both kinds of particles are set at 95% C.L.. The mass of gaugino-like neutralinos is found to be greater than 71.5 GeV/c^2. In the search for long-lived stau, masses less than 70.0 to 77.5 \GeVcc are excluded for gravitino masses from 10 to 150 \eVcc . Combining this search with the searches for stable heavy leptons and Minimal Supersymmetric Standard Model staus a lower limit of 68.5 \GeVcc may be set for the stau mas

Molecular dynamics simulations and drug discovery

This review discusses the many roles atomistic computer simulations of macromolecular (for example, protein) receptors and their associated small-molecule ligands can play in drug discovery, including the identification of cryptic or allosteric binding sites, the enhancement of traditional virtual-screening methodologies, and the direct prediction of small-molecule binding energies. The limitations of current simulation methodologies, including the high computational costs and approximations of molecular forces required, are also discussed. With constant improvements in both computer power and algorithm design, the future of computer-aided drug design is promising; molecular dynamics simulations are likely to play an increasingly important role

Measurement of inclusive π0\pi^{0} production in hadronic Z0Z^{0} decays

An analysis is presented of inclusive \pi^0 production in Z^0 decays measured with the DELPHI detector. At low energies, \pi^0 decays are reconstructed by \linebreak using pairs of converted photons and combinations of converted photons and photons reconstructed in the barrel electromagnetic calorimeter (HPC). At high energies (up to x_p = 2 \cdot p_{\pi}/\sqrt{s} = 0.75) the excellent granularity of the HPC is exploited to search for two-photon substructures in single showers. The inclusive differential cross section is measured as a function of energy for {q\overline q} and {b \bar b} events. The number of \pi^0's per hadronic Z^0 event is N(\pi^0)/ Z_{had}^0 = 9.2 \pm 0.2 \mbox{(stat)} \pm 1.0 \mbox{(syst)} and for {b \bar b}~events the number of \pi^0's is {\mathrm N(\pi^0)/ b \overline b} = 10.1 \pm 0.4 \mbox{(stat)} \pm 1.1 \mbox{(syst)} . The ratio of the number of \pi^0's in b \overline b events to hadronic Z^0 events is less affected by the systematic errors and is found to be 1.09 \pm 0.05 \pm 0.01. The measured \pi^0 cross sections are compared with the predictions of different parton shower models. For hadronic events, the peak position in the \mathrm \xi_p = \ln(1/x_p) distribution is \xi_p^{\star} = 3.90^{+0.24}_{-0.14}. The average number of \pi^0's from the decay of primary \mathrm B hadrons is found to be {\mathrm N} (B \rightarrow \pi^0 \, X)/\mbox{B hadron} = 2.78 \pm 0.15 \mbox{(stat)} \pm 0.60 \mbox{(syst)}

Search for new phenomena using single photon events in the DELPHI detector at LEP

Data are presented on the reaction \epem~\into~\gamma + no other detected particle at center-of-mass energies, \sqs = 89.48 GeV, 91.26 GeV and 93.08 GeV. The cross section for this reaction is related directly to the number of light neutrino generations which couple to the \zz boson, and to several other phenomena such as excited neutrinos, the production of an invisible `X' particle, a possible magnetic moment of the tau neutrino, and neutral monojets. Based on the observed number of single photon events, the number of light neutrinos which couple to the \zz is measured to be N_\nu = 3.15 \pm 0.34. No evidence is found for anomalous production of energetic single photons, and upper limits at the 95\% confidence level are determined for excited neutrino production (BR < 4-9 \times 10^{-6}), production of an invisible `X' particle (\sigma < 0.1 pb), and the magnetic moment of the tau neutrino (< 5.2 \times 10^{-6} \mu_B). No event with the topology of a neutral monojet is found, and this corresponds to the limit \sigma < 0.044/\epsilon pb at the 95\% confidence level, where \epsilon is the unknown overall monojet detection efficiency

Measurement of the Bd0^{0}_{d} oscillation frequency using kaons, leptons and jet charge

A measurement of the mass difference, \Delta m_d, between the two physical \mbox{B}^0_d states has been obtained from the analysis of the impact parameter distribution of a lepton emitted at large transverse momentum (p_t) relative to the jet axis and from the analysis of the flight distance distribution of secondary vertices tagged by either a high p_t lepton or an identified kaon. In the opposite hemisphere of the event, the charge of the initial quark has been evaluated using a high p_t lepton, a charged kaon or the mean jet charge. With 1.7 million hadronic Z^0 decays recorded by DELPHI between 1991 and 1993, \Delta m_d is found to be: \Delta m_d = 0.531^{+0.050}_{-0.046} ~(stat.) \pm 0.078 ~(syst.) ~ {\mathrm{ps}}^{-1} \,