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

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

Building Middle-Level Mathematics Teachers\u27 Capacities as Teachers and Leaders: The Math in the Middle Institute Partnership

This article describes professional development for middle-level mathematics teachers offered through the Math in the Middle Institute Partnership, a National Science Foundation-funded project to build teachers’ capacities to improve mathematics learning for all students. An overview of the project, including descriptions of its goals and curriculum are provided. Detailed descriptions of two mathematics courses and one pedagogy course are offered. The mathematics courses included here are the introductory course to the Math in the Middle Institute, as well as one of the final math courses of the Institute in which participants apply mathematical knowledge and processes to real-world problems. The pedagogy course features curriculum that enables teachers to acquire an understanding of the nature and purpose of action research, and launches teachers into planning and implementing systematic inquiry in their own mathematics classrooms around topics of their choosing. The varied abilities of teachers, as well as growth in teachers’ mathematical and pedagogical capacities, are represented by several samples of student work provided within the article. In addition, mathematical and pedagogical products of student work are also provided through the project’s URL links. Improving teacher quality is identified as a national need in mathematics education and one many universities and schools across the country are working in partnership to try to address. This article describes a professional development project aimed at improving mathematics teaching and learning in the middle grades. An overview of the project, along with a close look at several of its course offerings, are presented highlighting mathematical and pedagogical goals, challenges, and accomplishments

Simultaneous planar growth of amorphous and crystalline Ni silicides

We report a solid-state interdiffusion reaction induced by rapid thermal annealing and vacuum furnace annealing in evaporated Ni/Si bilayers. Upon heat treatment of a Ni film overlaid on a film of amorphous Si evaporated from a graphite crucible, amorphous and crystalline silicide layers grow uniformly side by side as revealed by cross-sectional transmission electron microscopy and backscattering spectrometry. This phenomenon contrasts with the silicide formation behavior previously observed in the Ni-Si system, and constitutes an interesting counterpart of the solid-state interdiffusion-induced amorphization in Ni/Zr thin-film diffusion couples. Carbon impurity contained in the amorphous Si film stabilizes the amorphous phase. Kinetic and thermodynamic factors that account for the experimental findings are discussed

Creep studies on oriented thermoplastics

The enhancement of many of the mechanical properties of thermoplastics which may be achieved by orienting the molecules has been known for some time. It has been exploited in the production of textile fibres end oriented films. Molecular orientation also occurs during processes such as extrusion, moulding or forming. Here, unless carefully controlled, it may well cause a deterioration in the properties of the finished article. In view of this a systematic study on the anisotropy of the mechanical properties of thermoplastics, resulting from molecular orientation, is being carried out at present in these laboratories … [cont.]