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Swiveling Lathe Jaw Concept for Holding Irregular Pieces
Clamp holds irregularly shaped pieces in lathe chuck without damage and eliminates excessive time in selecting optimum mounting. Interchangeable jaws ride in standard jaw slots but swivel so that the jaw face bears evenly against the workpiece regardless of contour. The jaws can be used on both engine and turret lathes
Parallel integer relation detection: techniques and applications
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Supersymmetric Quantum Mechanics and Painlev\'e IV Equation
As it has been proven, the determination of general one-dimensional
Schr\"odinger Hamiltonians having third-order differential ladder operators
requires to solve the Painlev\'e IV equation. In this work, it will be shown
that some specific subsets of the higher-order supersymmetric partners of the
harmonic oscillator possess third-order differential ladder operators. This
allows us to introduce a simple technique for generating solutions of the
Painlev\'e IV equation. Finally, we classify these solutions into three
relevant hierarchies.Comment: Proceedings of the Workshop 'Supersymmetric Quantum Mechanics and
Spectral Design' (July 18-30, 2010, Benasque, Spain
Complex solutions to Painleve IV equation through supersymmetric quantum mechanics
In this work, supersymmetric quantum mechanics will be used to obtain complex
solutions to Painleve IV equation with real parameters. We will also focus on
the properties of the associated Hamiltonians, i.e. the algebraic structure,
the eigenfunctions and the energy spectra.Comment: 5 pages, 3 figures. Talk given at the Advanced Summer School 2011,
Cinvestav (Mexico City), July 201
Supersymmetric quantum mechanics and Painleve equations
In these lecture notes we shall study first the supersymmetric quantum
mechanics (SUSY QM), specially when applied to the harmonic and radial
oscillators. In addition, we will define the polynomial Heisenberg algebras
(PHA), and we will study the general systems ruled by them: for zero and first
order we obtain the harmonic and radial oscillators, respectively; for second
and third order PHA the potential is determined by solutions to Painleve IV
(PIV) and Painleve V (PV) equations. Taking advantage of this connection, later
on we will find solutions to PIV and PV equations expressed in terms of
confluent hypergeometric functions. Furthermore, we will classify them into
several solution hierarchies, according to the specific special functions they
are connected with.Comment: 38 pages, 20 figures. Lecture presented at the XLIII Latin American
School of Physics: ELAF 2013 in Mexico Cit
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