Projection estimates for harmonic measure

Stochastic proofs of the Beurling projection theorem and the Hall projection theorem for harmonic measure are given. Somed-dimensional versions (for alld>1) which follow from this     

Derivatives and reactions of glutaconaldehyde—IX : Substitution reactions in the glutaconaldehyde anion. assignment of structure of a free glutaconaldehyde

Substitution in the glutaconaldehyde anion takes place at C 2 or 4, demonstrated by deuterium exchange and by preparation of the mono- and dichloro or bromo and the monoiodo glutaconaldehyde sodium salts and their respective enol esters. The stable 2-iodoglutaconaldehyde was suggested to have the all-trans structure of 2-iodo-5-hydroxy-trans-2, trans-4-pentadienal. The preparations from the monochloro and bromo glutaconaldehyde anions of 3-halogenopyridines and thiopene-2-carboxaldehyde have been reinvestigated.     

Conformally invariant differential equations and projective geometry

We combine harmonic analysis on certain pseudo-Riemannian symmetric spaces with results on conformally invariant linear and non-linear differential equations. This gives in many cases part of the decomposition of certain representations of the conformal group of a manifold when restricted to the isometry group.     

The rotating disk: Reply to Grünbaum and Janis

Using the time orthogonal spatial line element, which characterizes the spatial geometry inside a given reference frame in a coordinate-invariant way, the condition for uniform rotating motion without tangential strain is deduced. The results are the same as those previously found by Grunbaum and Janis using another method, and shows that my earlier criticism of their work is not valid.     

Algorithms over partially ordered sets

We here study some problems concerned with the computational analysis of finite partially ordered sets. We begin (in § 1) by showing that the matrix representation of a binary relationR may always be taken in triangular form ifR is a partial ordering. We consider (in § 2) the chain structure in partially ordered sets, answer the combinatorial question of how many maximal chains might exist in a partially ordered set withn elements, and we give an algorithm for enumerating all maximal chains. We give (in § 3) algorithms which decide whether a partially ordered set is a (lower or upper) semi-lattice, and whether a lattice has distributive, modular, and Boolean properties. Finally (in § 4) we give Algol realizations of the various algorithms.     

Neutron star matter superfluidity and superconductivity

The possibility of superfluidity or superconductivity in neutron or proton subsystems in the nuclear-matter region in neutron stars is investigated. The energy gap and corresponding critical temperature and critical magnetic field is calculated or estimated as function of density or Fermi momentum. In the calculations are used reaction matrix elements calculated earlier by means of Brueckner theory by the author. The final results indicate that neutron superfluidity, corresponding specifically toS-state pairing, may exist in a low-density shell in the nuclear-matter region of a neutron star. There is probably anisotropic neutron superfluidity, corresponding to the³ P ₂ or the singletD state, for higher densities. Superfluidity or superconductivity, corresponding toS-state pairing for the proton subsystem, is quite likely in most of the nuclear-matter region. The expected temperatures and magnetic fields in neutron stars seem to be well below the estimated critical temperatures or critical magnetic fields corresponding to the calculated values of the energy gap. However, similar methods have earlier predicted a much too high critical temperature for liquid³He.     

Induced representations and a new proof of the imprimitivity theorem

We present a brief and elementary proof of the Imprimitivity Theorem for an arbitrary locally compact group.     

The Coulomb correction to electron pair production by intermediate-energy photons

The Coulomb correction to the total cross section for intermediate-energy pair production is evaluated in terms of a high-energy-expansion formula, with the Davies-Bethe-Maximon correction as the leading term, followed by terms proportional to k^?1ln²k, k^?1lnk, k^?1 etc., the coefficients of which are determined by fitting to the Øverb?-Mork-Olsen exact low-energy results. The formula is estimated to be accurate within a few tenths of a per cent for photon energies between 3.5 m_ec² and infinity.     

Relativistic description of Marinov's modification of the Harress experiment

It is shown that Marinov's modification of the Harress experiment does not provide a means of giving an experimental decision between the theory of space-time absoluteness and the special theory of relativity     

Electron Wavefunctions and Densities for Atoms

With a special 'Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, sup _y∈B(x,R) |∇ψ (y)| ≤C(R) sup_y∈B(x,2R) |ψ (y)| and obtain for the spherically averaged electron density, p(r), that p"(0) exists and is non-negative.