1,172 research outputs found
Differential constraints compatible with linearized equations
Differential constraints compatible with the linearized equations of partial
differential equations are examined. Recursion operators are obtained by
integrating the differential constraints
On the variational noncommutative Poisson geometry
We outline the notions and concepts of the calculus of variational
multivectors within the Poisson formalism over the spaces of infinite jets of
mappings from commutative (non)graded smooth manifolds to the factors of
noncommutative associative algebras over the equivalence under cyclic
permutations of the letters in the associative words. We state the basic
properties of the variational Schouten bracket and derive an interesting
criterion for (non)commutative differential operators to be Hamiltonian (and
thus determine the (non)commutative Poisson structures). We place the
noncommutative jet-bundle construction at hand in the context of the quantum
string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries'
(July 18-23, 2011; JINR Dubna, Russia), 4 page
Estate of Fortier v. City of Lewiston: Is Maine\u27s Tort Claims Act Unintelligible?
In Estate of Fortier v. City of Lewiston, the Maine Supreme Judicial Court, sitting as the Law Court, was asked to decide if the City of Lewiston was âusingâ an aircraft under the Maine Tort Claims Act (MTCA) when it chartered a plane from Twin Cities Air Services (Twin Cities) as part of an Air Force Junior Reserve Officer Training Corp (AFJROTC) exercise. Tragically, the pilot and three AFJROTC cadets from Lewiston High School lost their lives when the plane crashed into Barker Mountain shortly after take-off. The families of the students brought suit against Lewiston, in part, alleging negligence on behalf of the high schoolâs Senior Aerospace Instructor, who was responsible for coordinating the chartered flight as part of the AFJROTC program. A slim majority held that, under the courtâs rules of statutory construction, and in the interest of narrowly construing exceptions to immunity under the MTCA, the statutory exception for âuseâ only applied when the governmental entity had some measure of direct control over the vehicle that was being used. Because the aircraft was under the direct control of Twin Citiesâ pilot, Lewiston was not âusingâ the plane as defined by the MTCA and was thus immune from suit. The dissent would not have equated âuseâ to âoperation,â as it believed the majority did, but instead would have used a broader, plain meaning definition of âuse.â When Lewiston chartered the plane as part of its AFJROTC program, this âuseâ qualified as an exception to the MTCA, allowing the lawsuit to go forward
Jet Bundles in Quantum Field Theory: The BRST-BV method
The geometric interpretation of the Batalin-Vilkovisky antibracket as the
Schouten bracket of functional multivectors is examined in detail. The
identification is achieved by the process of repeated contraction of even
functional multivectors with fermionic functional 1-forms. The classical master
equation may then be considered as a generalisation of the Jacobi identity for
Poisson brackets, and the cohomology of a nilpotent even functional multivector
is identified with the BRST cohomology. As an example, the BRST-BV formulation
of gauge fixing in theories with gauge symmetries is reformulated in the jet
bundle formalism. (Hopefully this version will be TeXable)Comment: 26 page
Rational Approximate Symmetries of KdV Equation
We construct one-parameter deformation of the Dorfman Hamiltonian operator
for the Riemann hierarchy using the quasi-Miura transformation from topological
field theory. In this way, one can get the approximately rational symmetries of
KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure
Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane
We present a new vorticity-raising transformation for the second integrable
complexification of the sine-Gordon equation on the plane. The new
transformation is a product of four Schlesinger maps of the Painlev\'{e}-V to
itself, and allows a more efficient construction of the -vortex solution
than the previously reported transformation comprising a product of maps.Comment: Part of a talk given at a conference on "Nonlinear Physics. Theory
and Experiment", Gallipoli (Lecce), June-July 2004. To appear in a topical
issue of "Theoretical and Mathematical Physics". 7 pages, 1 figur
Hypoid gear vehicle axle efficiency
© 2016 Elsevier Ltd. All rights reserved.In this paper, a study of a hypoid gear vehicle axle is presented. Using a custom rig, load-independent losses have been accurately measured and the effect of viscosity on spin loss has been quantified. Solution methods for the calculation of component losses are presented and combined into a complete thermally coupled transient model for the estimation of axle efficiency. An analysis of hypoid gear kinematics reveals a simplification, commonly adopted by other researchers, regarding the velocity of the point of contact in hypoid gears, to be in error. As a result, the calculation of lubrication parameters has been improved. Finally, experimental measurements are compared to the generated simulation results for a number of operating scenarios and satisfactory correlation is observed
On a Order Reduction Theorem in the Lagrangian Formalism
We provide a new proof of a important theorem in the Lagrangian formalism
about necessary and sufficient conditions for a second-order variational system
of equations to follow from a first-order Lagrangian.Comment: 9 pages, LATEX, no figures; appear in Il Nuovo Cimento
Bi-Hamiltonian structures for integrable systems on regular time scales
A construction of the bi-Hamiltonian structures for integrable systems on
regular time scales is presented. The trace functional on an algebra of
-pseudo-differential operators, valid on an arbitrary regular time
scale, is introduced. The linear Poisson tensors and the related Hamiltonians
are derived. The quadratic Poisson tensors is given by the use of the recursion
operators of the Lax hierarchies. The theory is illustrated by
-differential counterparts of Ablowitz-Kaup-Newell-Segur and Kaup-Broer
hierarchies.Comment: 18 page
Conditional symmetry and spectrum of the one-dimensional Schr\"odinger equation
We develop an algebraic approach to studying the spectral properties of the
stationary Schr\"odinger equation in one dimension based on its high order
conditional symmetries. This approach makes it possible to obtain in explicit
form representations of the Schr\"odinger operator by matrices for
any and, thus, to reduce a spectral problem to a purely
algebraic one of finding eigenvalues of constant matrices. The
connection to so called quasi exactly solvable models is discussed. It is
established, in particular, that the case, when conditional symmetries reduce
to high order Lie symmetries, corresponds to exactly solvable Schr\"odinger
equations. A symmetry classification of Sch\"odinger equation admitting
non-trivial high order Lie symmetries is carried out, which yields a hierarchy
of exactly solvable Schr\"odinger equations. Exact solutions of these are
constructed in explicit form. Possible applications of the technique developed
to multi-dimensional linear and one-dimensional nonlinear Schr\"odinger
equations is briefly discussed.Comment: LaTeX-file, 31 pages, to appear in J.Math.Phys., v.37, N7, 199
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