18,599 research outputs found
The Dynairship
A feasibility analysis for the construction and use of a combination airplane-airship named 'Dynairship' is undertaken. Payload capacities, fuel consumption, and the structural design of the craft are discussed and compared to a conventional commercial aircraft (a Boeing 747). Cost estimates of construction and operation of the craft are also discussed. The various uses of the craft are examined (i.e, in police work, materials handling, and ocean surveillance), and aerodynamic configurations and photographs are shown
Models of q-algebra representations: q-integral transforms and "addition theorems''
In his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation identities for Bessel functions and Laguerre polynomials associated with the addition theorems for these matrix elements. He also studied matrix elements of the pseudo-Euclidean and pseudo-oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the Cartan subalgebras of these Lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for Bessel functions and for confluent hypergeometric functions. Here we work out q analogs of these results in which the usual exponential function mapping from the Lie algebra to the Lie group is replaced by the q-exponential mappings Eq and eq. This study of representations of the Euclidean quantum algebra and the q-oscillator algebra (not a quantum algebra) leads to summation, integral transform, and q-integral transform identities for q analogs of the Bessel and confluent hypergeometric functions, extending the results of Vilenkin for the q=1 case
Complete sets of functions for perturbations of RobertsonâWalker cosmologies and spin 1 equations in RobertsonâWalker-type space-times
Crucial to a knowledge of the perturbations of RobertsonâWalker cosmological models are complete sets of functions with which to expand such perturbations. For the open RobertsonâWalker cosmology an answer to this question is given. In addition some observations concerning explicit solution by separation of variables of wave equations for spin 1 in a Riemannian space having an infinitesimal line element of which the RobertsonâWalker models are a special case are made
The relativistically invariant expansion of a scalar function on imaginary Lobachevski space
Using the previous analysis of Gel'fand and Graev a new relativistically invariant expansion of a scalar function on three-dimensional imaginary Lobachevski space L3(I) is given. The coordinate system used corresponds to the horospherical reduction SO(3,1) E2 SO(2) and covers all of L3(I)
Series solutions for the Dirac equation in KerrâNewman space-time
The Dirac equation is solved for an electron in a KerrâNewman geometry using an adaptation of the procedure of Chandrasekhar. The corresponding eigenfunctions obtained can be represented as series of Jacobi polynomials. The spectrum of eigenvalues can be calculated using continued fraction techniques. Representations for the eigenvalues and eigenfunctions are obtained for various ranges of the parameters appearing in the KerrâNewman metric. Some comments concerning the bag model of nucleons are made
Complete sets of functions for perturbations of Robertson Walker cosmologies
Crucial to a knowledge of the perturbations of Robertson Walker cosmological models is a knowledge of complete sets of functions with which to expand such perturbations. For the open Robertson Walker cosmology, this question will be completely answered. In addition, some observations will be made concerning explicit solution by separation of variables of wave equations for spin s in a Riemannan space having an infinitesmal line element of which the Robertson Walker models are a special case
Jacobi elliptic coordinates, functions of Heun and Lame type and the Niven transform
Lame and Heun functions arise via separation of the Laplace equation in general Jacobi ellipsoidal or conical coordinates. In contrast to hypergeometric functions that also arise via variable separation in the Laplace equation, Lame and Heun functions have received relatively little attention, since they are rather intractable. Nonetheless functions of Heun type do have remarkable properties, as was pointed out in the classical book \Modern Analysis" by Whittaker and Watson who devoted an entire chapter to the subject. Unfortunately the beautiful identities appearing in this chapter have received little notice, probably because the methods of proof seemed obscure. In this paper we apply the modern operator characterization of variable separation and exploit the conformal symmetry of the Laplace equation to obtain product identities for Heun type functions. We interpret the Niven transform as an intertwining operator under the action of the conformal group. We give simple operator derivations of some of the basic formulas presented by Whittaker and Watson and then show how to generalize their results to more complicated situations and to higher dimensions
Laplace equations, conformal superintegrability and B\^ocher contractions
Quantum superintegrable systems are solvable eigenvalue problems. Their
solvability is due to symmetry, but the symmetry is often "hidden". The
symmetry generators of 2nd order superintegrable systems in 2 dimensions close
under commutation to define quadratic algebras, a generalization of Lie
algebras. Distinct systems and their algebras are related by geometric limits,
induced by generalized In\"on\"u-Wigner Lie algebra contractions of the
symmetry algebras of the underlying spaces. These have physical/geometric
implications, such as the Askey scheme for hypergeometric orthogonal
polynomials. The systems can be best understood by transforming them to Laplace
conformally superintegrable systems and using ideas introduced in the 1894
thesis of B\^ocher to study separable solutions of the wave equation. The
contractions can be subsumed into contractions of the conformal algebra
to itself. Here we announce main findings, with detailed
classifications in papers under preparation.Comment: 10 pages, 2 figure
Observations on the Consistency of Federal Procurement Policies With Other Governmental Policies
Integrability, StÀckel spaces, and rational potentials
For a variety of classical mechanical systems embeddable into flat space with Cartesian coordinates {xi} and for which the HamiltonâJacobi equation can be solved via separation of variables in a particular curvalinear system {uj}, we answer the following question. When is the separable potential function v expressible as a polynomial (or as a rational function) in the defining coordinates {xi}? Many examples are given
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