1,770,890 research outputs found
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
Ellipsoidal optical reflectors reproduced by electroforming
An accurately dimensioned convex ellipsoidal surface, which will become a master after polishing, is fabricated from 316L stainless steel. When polishing of the master is completed, it is suspended in a modified watt bath for electroforming of nickel reflectors
Conforming polisher for aspheric surface of revolution Patent
Conforming polisher for aspheric surfaces of revolution with inflatable tub
Fixed-Base Simulator Studies of the Ability of the Human Pilot to Provide Energy Management Along Abort and Deep-Space Entry Trajectories
A simulation study has been made to determine a pilot's ability to control a low L/D vehicle to a desired point on the earth with initial conditions ranging from parabolic orbits to abort conditions along the boost phase of a deep-space mission. The program was conducted to develop procedures which would allow the pilot to perform the energy management functions required while avoiding the high deceleration or skipout region and to determine the information display required to aid the pilot in flying these procedures. The abort conditions studied extend from a region of relatively high flight-path angles at suborbital velocities while leaving the atmosphere to a region between orbital and near-escape velocity outside the atmosphere. The conditions studied included guidance from suborbital and superorbital aborts as well as guidance following return from a deepspace mission. In this paper, the role of the human pilot?s ability to combine safe return abort procedures with guidance procedures has been investigated. The range capability from various abort and entry conditions is also presented
Role of Self-Interaction Effects in the Geometry Optimization of Small Metal Clusters
By combining the Self-Interaction Correction (SIC) with pseudopotential
perturbation theory, the role of self-interaction errors inherent to the Local
Density Approximation (LDA) to Density Functional Theory is estimated in the
determination of ground state and low energy isomeric structures of small
metallic clusters. Its application to neutral sodium clusters with 8 and 20
atoms shows that the SIC provides sizeable effects in Na_8, leading to a
different ordering of the low lying isomeric states compared with ab-initio LDA
predictions, whereas for Na_20, the SIC effects are less pronounced, such that
a quantitative agreement is achieved between the present method and ab-initio
LDA calculations.Comment: RevTeX, 4 pages, 1 figure available from [email protected]
A Bohmian approach to quantum fractals
A quantum fractal is a wavefunction with a real and an imaginary part
continuous everywhere, but differentiable nowhere. This lack of
differentiability has been used as an argument to deny the general validity of
Bohmian mechanics (and other trajectory--based approaches) in providing a
complete interpretation of quantum mechanics. Here, this assertion is overcome
by means of a formal extension of Bohmian mechanics based on a limiting
approach. Within this novel formulation, the particle dynamics is always
satisfactorily described by a well defined equation of motion. In particular,
in the case of guidance under quantum fractals, the corresponding trajectories
will also be fractal.Comment: 19 pages, 3 figures (revised version
The Tulczyjew triple for classical fields
The geometrical structure known as the Tulczyjew triple has proved to be very
useful in describing mechanical systems, even those with singular Lagrangians
or subject to constraints. Starting from basic concepts of variational
calculus, we construct the Tulczyjew triple for first-order Field Theory. The
important feature of our approach is that we do not postulate {\it ad hoc} the
ingredients of the theory, but obtain them as unavoidable consequences of the
variational calculus. This picture of Field Theory is covariant and complete,
containing not only the Lagrangian formalism and Euler-Lagrange equations but
also the phase space, the phase dynamics and the Hamiltonian formalism. Since
the configuration space turns out to be an affine bundle, we have to use affine
geometry, in particular the notion of the affine duality. In our formulation,
the two maps and which constitute the Tulczyjew triple are
morphisms of double structures of affine-vector bundles. We discuss also the
Legendre transformation, i.e. the transition between the Lagrangian and the
Hamiltonian formulation of the first-order field theor
Imaging the Radio Photospheres of Mira Variables
We have used the VLA at 43 GHz to image the radio continuum emission from o
Ceti, R Leo, and W Hya and to precisely locate their SiO maser emission with
respect to the star. The radio continuum emission region for all three stars
has a diameter close to 5.6 AU. These diameters are similar to those measured
at infrared wavelengths in bands containing strong molecular opacity and about
twice those measured in line-free regions of the infrared spectrum. Thus, the
radio photosphere and the infrared molecular layer appear to be coextensive.
The 43 GHz continuum emission is consistent with temperatures near 1600 K and
opacity from H-minus free-free interactions. While the continuum image of o
Ceti appears nearly circular, both R Leo and W Hya display significant
elongations. The SiO masers for all three stars show partial rings with
diameters close to 8 AU.Comment: 14 pages; 3 figure
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
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