Equivalence of functional limit theorems for stationary point processes and their Palm distributions

Summary Let P be the distribution of a stationary point process on the real line and let P ⁰ be its Palm distribution. In this paper we consider two types of functional limit theorems, those in terms of the number of points of the point process in (0, t] and those in terms of the location of the nth point right of the origin. The former are most easily obtained under P and the latter under P ⁰. General conditions are presented that guarantee equivalence of either type of functional limit theorem under both probability measures, and under a third, P ₁, which plays a role in the proofs and is obtained from P by shifting the origin to the first point of the process on the right.In a brief final section the obtained results for either type of functional limit theorem are extended to equivalences between the two types by applying well-known results about processes drifting to infinity and the corresponding inverse processes.     

Experimental results on neutrino-electron scattering

A determination of sin² θ _w based on measurements of elastic scattering of muon-neutrinos and muon-anti-neutrinos on atomic electrons is described. These purely leptonic processes were studied using the CHARM calorimeter exposed to neutrino and antineutrino wide-band beams at the CERN super proton synchrotron. A total of 83±16 neutrino-electron and 112±21 antineutrino-electron events have been detected. From the measurement of the ratio of muon-neutrino and muon-antineutrino cross-sections a value of sin² θ _w =0.211±0.037 was obtained.     

A search for neutrino oscillations

We present here the final results of experiments searching for neutrino oscillations, carried out by the CHARM Collaboration. The data — taking took place in 1983. The first experiment was performed by exposing two detectors simultaneously to the CERN PS low energyv _µ beam. In the second experiment the full CHARM detector was exposed to the wide-band horn-focusedv _µ beam of the CERN SPS. Complete details of the experiments and data reduction are presented. No statistically significant signals for neutrino oscillations were observed. Our 90% CL limits in the appearance experiment (v _µ→v _e ) exclude Δm ²≧0.19 eV² for complete mixing (sin²2θ=1), and sin²2θ≧0.008 for the region Δm ²≧30 eV². These results, and the limits observed for (v _µ→v _x ) (disappearance of (v _µ), are in agreement with those of most other experiments but exclude part of the region previously reported as a possible indication ofv _µ→v _e oscillations.     

Properly efficient and efficient solutions for vector maximization problems in euclidean space

Recently Benson proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone K is any nontrivial, closed convex cone. We give an equivalent definition of his notion of proper efficiency. Our definition, by means of perturbation of the cone K, seems to offer another justification of Benson's choice above Borwein's extension of Geoffrion's concept. Our result enables one to prove some other theorems concerning properly efficient and efficient points. Among these is a connectedness result.     

Two kinds of normality in vector optimization

In this paper two kinds of normality in vector optimization are compared. Both notions generalize a concept due to Van Slyke and Wets and similar work of Rockafellar. Research partially supported by an N.S.E.R.C. Operating Grant.     

Radical cyclization of sugar-derived beta-(alkynyloxy)acrylates: synthesis of novel fused ethers

[formula: see text] Tributyltin radical mediated cyclization of carbohydrate-derived beta-(alkynyloxy)acrylates leading to highly functionalized cis- and trans-fused bicyclic ethers of various ring sizes is described. The efficacy of the radical cyclization is nicely illustrated in the iterative construction of a trans-fused tricyclic tetrahydropyran.