Adaptive Synchronization of Interconnected Linear Systems

In this paper we introduce the concept of an adaptive synchronizationcontroller. Synchronization is modelled as an adaptive trackingproblem for families of interconnected linear systems. Stabilizationand tracking results are obtained for minimum-phase systems.     

Multiplicativity of the Smith Normal Form

New conditions are derived which are sufficient to make the Smith Normal Form a Multiplicative matrix function.     

Critical point inequalities and scaling limits

A refined and extended version of the Buckingham-Gunton inequality relating various pairs of critical exponents is shown to be valid for a large class of statistical mechanical models. If this inequality is an equality (in the refined sense) and one of the critical exponents has a non-Gaussian value, then any scaling limit must be non-Gaussian. This result clarifies the relationship between the nontriviality or triviality of the scaling limit for ordinary critical points in four dimensions (or tricritical points in three dimensions) and the existence of logarithmic factors in the asymptotics which define the two critical exponents.Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation Grant MCS 77-20683     

A measurement of the transverse momenta of partons,and of jet fragmentation as a function of √s in p-p collisions

A large solid-angle apparatus consisting of a superconducting solenoid magnet, cylindrical drift chambers and two arrays of lead-glass counters was used to examine particles associated with a high transverse momentum trigger in p-p collisions with three √s values at the CERN ISR. The trigger was given by energy deposition in lead-glass arrays centred at 90°. The trigger transverse momentum range covered was 3 < $\text{p}{}_{\mathrm{<mtext>T\; trig</mtext>}}\text{< 11}\text{GeV}\text{c}$. Results are given for p_out for both individual charged particles, and also for the sum of charged particle momenta in the hemisphere opposite to the trigger. Mean values are then deduced for the parton transverse momentum k_T, and for the jet fragmentation momentum j_T.     

Black holes without singularities

The conventional interpretation of the Hawking-Penrose singularity theorems is that gravitational collapse, signified by the presence of a closed trapped surface, generally leads to the formation of a singularity. Consideration is given here to an alternative interpretation according to which collapse scenarios may give rise, not to singularities, but to chronology violation instead. An example is given of a singularity-free, chronology-violating space-time with a (non-achronal) closed trapped surface. In a large class of singularity-free space-times, the presence of a closed trapped surface, achronal or not, necessitates a violation of chronology. Moreover, all closed trapped surfaces and chronology violations are confined to black holes; weak cosmic censorship must hold in the sense that the region of the space-time visible from infinity is globally hyperbolic.Expanded version of essay given Honorable Mention in the 1986 Gravity Foundation Award.