Some Optimization Problems with Bulk-Service Queues

An optimal control problem for a single bulk-service queue is considered. Theorems that characterize the optimal control strategy in some circumstances are proved; they complement earlier results by Deb and Serfozo for a comparable problem. Most of the analysis uses direct probabilistic reasoning rather than specialized methods such as dynamic programming. Some illustrative examples are presented.     

On the existence of surface wave solutions in piezoelectric crystals an example of non-existence

According to general theory, a semi-infinite piezoelectric crystal with mechanically free surface and an adjoining medium with zero dielectric constant, may or may not allow a surface wave solution. Examples where surface wave solutions are not allowed, are not known, and one might think that solutions actually always exist. In the present paper this problem is put to rest by an explicit example of non-existence.     

Search for the ρρ enhancement near 1700 MeV/c in the reaction at 8.3 GeV/c

Results are presented from a search for a ρ⁰ρ⁰ enhancement in antiproton annihilations. A ρ⁰ρ⁰ resonance was recently observed in radiative ψ decays, and its existence has been supported by the results of an antiproton experiment at 5.7 GeV/c. No indication of this ρ⁰ρ⁰ enhancement is seen is our data, in direct contradiction with the earlier, lower statistics experiment.     

Measurement of charged-particle multiplicities in gluon and quark jets in pp collisions at square root of s = 1.8 TeV

We report the first largely model independent measurement of charged particle multiplicities in quark and gluon jets, Nq and Ng, produced at the Fermilab Tevatron in pp collisions with a center-of-mass energy of 1.8 TeV and recorded by the Collider Detector at Fermilab. The measurements are made for jets with average energies of 41 and 53 GeV by counting charged particle tracks in cones with opening angles of theta(c) = 0.28, 0.36, and 0.47 rad around the jet axis. The corresponding jet hardness Q = Ejet theta c varies in the range from 12 to 25 GeV. At Q = 19.2 GeV, the ratio of multiplicities r = Ng/Nq is found to be 1.64+/-0.17, where statistical and systematic uncertainties are added in quadrature. The results are in agreement with resummed perturbative QCD calculations.     

Search for [corrected] B0(s) --> mu+ mu- and B0(d) [corrected] --> mu + mu- decays in pp collisions with CDF II

We report on a search for B0(s) --> mu+ mu- and B0(d) --> mu + mu- decays in pp collisions at square root(s) = 1.96 TeV using 364 pb(-1) of data collected by the CDF II detector at the Fermilab Tevatron Collider. After applying all selection requirements, we observe no candidates inside the B0(s) or B0(d) mass windows. The resulting upper limits on the branching fractions are B(B0(s) --> mu+ mu-) < 1.5 x 10(-7) and B(B0(d) --> mu+ mu-) < 3.9 x 10(-8) at 90% confidence level.     

Search for long-lived doubly charged Higgs bosons in pp collisions at sqrt[s] = 1.96 TeV

We present a search for long-lived doubly charged Higgs bosons (H(+/- +/-)), with signatures of high ionization energy loss and muonlike penetration. We use 292 pb(-1) of data collected in pp collisions at sqrt[s] = 1.96 TeV by the CDF II detector at the Fermilab Tevatron. Observing no evidence of long-lived doubly charged particle production, we exclude H(+/- +/-)(L) and H(+/- +/-)(R) bosons with masses below 133 GeV/c(2) and 109 GeV/c(2), respectively. In the degenerate case we exclude H(+/- +/-) mass below 146 GeV/c(2). All limits are quoted at the 95% confidence level.     

Search for doubly charged Higgs bosons decaying to dileptons in pp collisions at square root of s=1.96 TeV

We present the results of a search for doubly charged Higgs bosons (H+/-+/-) decaying to dileptons (ll(')) using approximately 240 pb(-1) of pp collision data collected by the CDF II experiment at the Fermilab Tevatron. In our search region, given by same-sign ll(') mass m(ll('))>80 GeV/c(2) (100 GeV/c(2) for ee channel), we observe no evidence for H+/-+/- production. We set limits on sigma(pp -->H++H---->l(+)l('+)l(-)l('-)) as a function of the mass of the H+/-+/- and the chirality of its couplings. Assuming exclusive same-sign dilepton decays, we derive lower mass limits on H(+/-+/-)(L) of 133, 136, and 115 GeV/c(2) in the ee, mumu, and emu channels, respectively, and a lower mass limit of 113 GeV/c(2) on H(+/-+/-)(R) in the mumu channel, all at the 95% confidence level.     

The holomorphic flow of the Riemann zeta function

The flow of the Riemann zeta function, , is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica.

The phase diagrams suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures.

     

Motion and rotation of small glissile dislocation loops in stress fields

We derive here for the first time the equations that describe the combined motion and rotation of small prismatic dislocation loops in stress fields. When the applied torque is balanced by the self-torque of the loop, we show how the solution can be obtained for the loop orientation, and how this orientation affects the glide force on the loop.