Are there Hilbert-style Pure Type Systems?

For many a natural deduction style logic there is a Hilbert-style logic that is equivalent to it in that it has the same theorems (i.e. valid judgements with empty contexts). For intuitionistic logic, the axioms of the equivalent Hilbert-style logic can be propositions which are also known as the types of the combinators I, K and S. Hilbert-style versions of illative combinatory logic have formulations with axioms that are actual type statements for I, K and S. As pure type systems (PTSs)are, in a sense, equivalent to systems of illative combinatory logic, it might be thought that Hilbert-style PTSs (HPTSs) could be based in a similar way. This paper shows that some PTSs have very trivial equivalent HPTSs, with only the axioms as theorems and that for many PTSs no equivalent HPTS can exist. Most commonly used PTSs belong to these two classes. For some PTSs however, including lambda* and the PTS at the basis of the proof assistant Coq, there is a nontrivial equivalent HPTS, with axioms that are type statements for I, K and S.Comment: Accepted in Logical Methods in Computer Scienc

The Superposition Principle of Waves Not Fulfilled under M. W. Evans' O(3) Hypothesis

In 1992 M.W. Evans proposed a so-called O(3) symmetry of electromagnetic fields by adding a constant longitudinal "ghost field" to the well-known transversal plane em waves. He considered this symmetry as a new law of electromagnetics. Later on, since 2002, this O(3) symmetry became the center of his Generally Covariant Unified Field Theory which he recently renamed as ECE Theory. One of the best-checked laws of electrodynamics is the principle of linear superposition of electromagnetic waves, manifesting itself in interference phenomena. Its mathematical equivalent is the representation of electric and magnetic fields as vectors. By considering the superposition of two phase-shifted waves we show that the superposition principle is incompatible with M.W. Evans' O(3) hypothesis.Comment: 5 pages, no figure

On a possibility to determine the S-factor of the hep process in experiments with thermal (cold) neutrons

The problem of the magnitude of the S--factor of the hep process $p + {^3\mathrm{He}} \to {^4\mathrm{He}} + e^+ + \nu_e$ is one of the most important unsolved problems in nuclear astrophysics. The magnitude of $S(hep)$ has also an important impact on the interpretation of the Super-Kamiokande solar neutrino results in terms of neutrino oscillations. We point out the possiblity to determine the major hadronic contribution to $S(hep)$ from the measurement of the total cross section of the process $n + {^3\mathrm{H}} \to {^4\mathrm{He}} + e^- + \bar{\nu}_e$ in experiments with high intensity beams of thermal or cold neutrons.Comment: 7 pages, revtex, no figures; note added; final version to be published in Astropart. Phy

Charge asymmetries of lepton transverse momenta in Drell-Yan processes at the LHC

Charged lepton transverse momenta in the Drell-Yan processes play an important role at the LHC in precision measurements of the Standard Model parameters, such as the W-boson mass and width, their charge asymmetries and sin^2(theta_W). Therefore, their distributions should be described as accurate as possible by the Monte Carlo event generators. In this paper we discuss the problem of matching the hard-process kinematics of the Monte Carlo generator WINHAC with the parton-shower kinematics of the PYTHIA 6.4 generator while interfacing these two programs. We show that improper assignment of the quark and antiquark effective momenta in the LO matrix element computations may affect considerably the predicted lepton transverse momenta and even completely reverse their charge asymmetries at the LHC. We propose two matching schemes in which the NLO QCD distributions of the leptonic kinematical variables can be well reproduced by the LO WINHAC generator.Comment: 18 pages, 8 figure

Optimization Techniques for the Power Beaming Analysis of Microwave Transmissions from a Space-Based Solar Power Satellite

In the 21st century, the development of technologies to produce carbon free power sources remains paramount. In this paper, we study an optimal power transmission strategy from a space-based satellite generation station to Earth using scalar diffraction theory. The resulting model is then solved via a spectral method that guarantees a compactly supposed profile from the transmitting antenna. Finally, the problem is then solved via a more general pseudo-spectral method using control theory