The Cesàro operator on the Bergman space $ A^{2} (\mathbb{D}) $

The Cesàro operator is shown to be subdecomposable on the Bergman spaces A^p (\mathbbD) A^{p} (\mathbb{D}) for p \geqq 2 p \geqq 2 , extending a result of [12] to the case that p < 4. For A² (\mathbbD) A^{2} (\mathbb{D}) , we show that Cesàro operator is in fact subscalar, but in contrast to the situation in the Hardy space, C |_A² C |_{A^2} fails to be hyponormal.     

Proper-Time Classical Electrodynamics

We construct a generalization of Maxwell's equations associated with the proper-time of the source which accounts for radiation reaction without any assumptions concerning the nature of the source. The theory leads to a new invariance group, related to the Lorentz group, which leaves the proper-time of the source fixed for all observers.     

Canonical Proper-Time Formulation of Relativistic Particle Dynamics. II

Our purpose in this paper is to provide theframework for a generalization of classical mechanicsand electrodynamics, including Maxwell's theory, whichis simple, technically correct, and requires noadditional work for the quantum case. We first show thatthere are two other definitions of proper-time, eachhaving equal status with the Minkowski definition. Weuse the first definition, called the proper-velocity definition, to construct a transformationtheory which fixes the proper-time of a given physicalsystem for all observers. This leads to a new invariancegroup and a generalization of Maxwell's equations left covariant under the action of this group.The second definition, called the canonical variablesdefinition, has the unique property that it isindependent of the number of particles. This definition leads to a general theory of directlyinteracting relativistic particles. We obtain theLorentz force for one particle (using its proper-time),and the Lorentz force for the total system (using theglobal proper-time). Use of the global proper-time tocompute the force on one particle gives the Lorentzforce plus a dissipative term corresponding to thereaction of this particle back on the cause of itsacceleration (Newton's third law). The wave equation derivedfrom Maxwell's equations has an additional term, firstorder in the proper-time. This term arisesinstantaneously with acceleration. This shows explicitly that the longsought origin of radiationreaction is inertial resistance to changes in particlemotion. The field equations carry intrinsic informationabout the velocity and acceleration of the particles in the system. It follows that our theory isnot invariant under time reversal, so that the existenceof radiation introduces an arrow for the (proper-time ofthe) system.     

The reaction of the hydroxyl radical with acetylene

The reaction of OH with acetylene was studied in a discharge flow system at room temperature. OH was generated by the reaction of atomic hydrogen with NO₂ and was monitored throughout the reaction using ESR spectroscopy. Mass-spectrometric analysis of the reaction products yielded the following results: (1) less than 3 molecules of OH were consumed, and less than 2 molecules of H₂O were formed for every molecule of acetylene that reacted; (2) CO was identified as the major carbon-containing product; (3) NO, formed in the generation of OH, reacted with a reaction intermediate to give among other products N₂O. These observations placed severe limitations on the choice of a reaction mechanism. A mechanism containing the reaction OH + C₂H₂ → HC₂O + H₂ better accounted for the experimental results than one involving the abstraction reaction OH + C₂H₂ → C₂H + H₂O. The rate constant for the initial reaction was measured as 1.9 ± 0.6 × 10^?13 cm³ molecule^?1 sec^?1.     

Surface plasmons propagating parallel to the grooves of a large amplitude grating

The dispersion relation is obtained for a surface plasmon propagating parallel to the grooves of a large amplitude grating. Two variants of the Rayleigh method arc used: the first requires the evaluation of the zeros of a determinant; the second yields the dispersion relation in terms of the solution of a matrix eigenvalue problem. The dispersion relations are solved numerically for a sinusoidal and for a symmetric sawtooth grating profile, yielding in each case an infinity of discrete branches.     

Freeze-out conditions in ultrarelativistic heavy-ion collisions

We present recent results on single particle transverse momentum distributions of pions, kaons and protons, measured in CERN Experiment NA44, of 200 AGeV/c S+S and 158 AGeV/c Pb+Pb central collisions. By comparing these data with thermal and transport models, freeze-out parameters like the temperatureT _fo and the chemical potentials (μ _q ,μ _s ) are extracted and discussed.     

The ionic conductivity of rapidly quenched tungstate and molybdate glasses containing lithium halides

Rapidly quenched lithium tungstate and molybdate glasses containing up to 20 mole% lithium chloride and bromide additives have been prepared. The additives are found to give a small increase (up to a factor of two at room temperature) in the lithium ion conductivity of the glass which can be understood in terms of models developed for network forming glasses.