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 “using” 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 school’s Senior Aerospace Instructor, who was responsible for coordinating the chartered flight as part of the AFJROTC program. A slim majority held that, under the court’s rules of statutory construction, and in the interest of narrowly construing exceptions to immunity under the MTCA, the statutory exception for “use” 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 Cities’ pilot, Lewiston was not “using” the plane as defined by the MTCA and was thus immune from suit. The dissent would not have equated “use” to “operation,” as it believed the majority did, but instead would have used a broader, plain meaning definition of “use.” When Lewiston chartered the plane as part of its AFJROTC program, this “use” 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 $n$-vortex solution than the previously reported transformation comprising a product of $2n$ 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

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

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

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 $\delta$-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 $\Delta$-differential counterparts of Ablowitz-Kaup-Newell-Segur and Kaup-Broer hierarchies.Comment: 18 page