Integrability of second-order Lagrangians admitting a first-order Hamiltonian formalism

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) necessary and sufficient conditions for the Poincaré–Cartan form of a second-order Lagrangian on an arbitrary fibred manifold p : E → N to be projectable onto J 1 E are explicitly determined; ii) for each of such Lagrangians, a first-order Hamiltonian formalism is developed and a new notion of regularity is introduced; iii) the variational problems of this class defined by regular Lagrangians areprovedtobeinvolutive

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Direct molecular level measurements of the electrostatic properties of a protein surface

In this work, we used direct measurements with the surface force apparatus to determine the pH-dependent electrostatic charge density of a single binding face of streptavidin. Mean field calculations have been used with considerable success to model electrostatic potential fields near protein surfaces, but these models and their inherent assumptions have not been tested directly at the molecular level. Using the force apparatus and immobilized, oriented monolayers of streptavidin, we measured a pI of 5–5.5 for the biotin-binding face of the protein. This differs from the pI of 6.3 for the soluble protein and confirms that we probed the local electrostatic features of the macromolecule. With finite difference solutions of the linearized Poisson–Boltzmann equation, we then calculated the pH-dependent charge densities adjacent to the same face of the protein. These calculated values agreed quantitatively with those obtained by direct force measurements. Although our study focuses on the pH-dependence of surface electrostatics, this direct approach to probing the electrostatic features of proteins is applicable to investigations of any perturbations that alter the charge distribution of the surfaces of immobilized molecules.

On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

On the origin of the order Artiodactyla.

The first known members of the order Artiodactyla appeared suddenly throughout the Holarctic region at the beginning of the Eocene. They are characterized by distinctive cursorial skeletal specializations. Owing to their abrupt appearance and the lack of transitional forms, the origin of the order is problematic. Descent from a "condylarth," specifically the arctocyonid Chriacus, has been suggested based on dental resemblances, but until now postcranial anatomy seemed to preclude close relationship between Arctocyonidae and Artiodactyla. A middle Paleocene specimen of a small arctocyonid (?Chriacus) reported here is much more similar to the oldest artiodactyl, Diacodexis, in the derived condition of the hindlimb, reviving the possibility that Artiodactyla evolved from an arctocyonid.

An Analysis of U.S. Air Force Policy and Installation CO2 Emissions to Determine Best Practices for the Implementation of Executive Order 13514

United States Air Force (USAF) energy policy is a measured but aggressive response to federal energy policy guidance. Previous USAF efforts, like those of the federal government, focused primarily on energy intensity reduction, cost, and BTU savings, and in certain cases have resulted in facility greenhouse gas (GHG) emission reductions. The USAF now faces the challenge of integrating GHG reduction goals and inventory requirements set forth in Executive Order 13514. Using USAF reported energy consumption data, facility GHG emission estimates have been synthesized to identify trends and elucidate existing energy best practices to be applied as part of overarching USAF GHG mitigation efforts and to highlight areas of possible concern for the integration of EO 13514 into operational USAF policy.

Cardipeltis; an early Devonian agnathan of the order Heterostraci / Robert H. Denison.

v.16:no.4(1966)

Die Gestaltung der Globalität. Schlüsselwörter der sozialen Ordnung (II) = The design of the global order: the keywords of social order. ZEI Discussion Paper C215, 2013

No abstract.

Die proto-konstitutionelle Etablierung der europäischen Innenpolitik, Rückblick und Ausblick auf Bedingungen föderaler Ordnung in Europa = The proto-constitutional establishment of European domestic policy. Review and outlook on conditions of federal order in Europe. ZEI Discussion Paper C225, 2014

ZEI Director Prof. Ludger Kühnhardt recalls the leading ideas of federalism as territorial equivalent for political pluralism. Celebrating the 80th anniversary of Bonn historian and political scientist Prof. Dr. Hans-Peter Schwarz, he reflects on the emerging EU domestic policies in ZEI Discussion Paper C 225.

Investigation of the flow over simple bodies at Mach numbers of the order of 20 /

"It is shown that adequate means are available for calculating inviscid direct and induced pressures on simple axisymmetric bodies at zero angle of attack. The extent to which viscous effects can alter these predictions is indicated. It is also shown that inviscid induced pressures can significantly affect the stability of blunt, two-dimensional flat wings at low angles of attack. However, at high angles of attack, the inviscid induced pressure effects are negligible."

Development of a passenger vehicle finite element model.

Transportation Department, Washington, D.C.