Symplectic Microgeometry II: Generating functions

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur

Students Serve Refugees in Georgia

In a time in which travel is limited, Cedarville University students will be serving the nations who have come to the States this summer

New MBA Specialties will Prepare Graduates for High-demand Careers

Three new concentrations will be added to Cedarville University’s online Master of Business Administration (MBA) program, starting with the fall 2018 semester. The new concentrations include business analytics, cybersecurity, and innovation and entrepreneurship* (*pending approval of the Higher Learning Commission)

Assessment of effects on vegetation of degradation products from alternative fluorocarbons

Concern with the effects of fluorides on plants has been devoted to that resulting from dry deposition (mainly with reference to gaseous HF and secondarily with particulate forms). The occurrence of precipitation as rain or mist and the presence of dew or free water on the foliage has mainly been considered with respect to their effects on the accumulation of air-borne fluoride and not with fluoride in wet deposition. That is, precipitation has been viewed primarily with respect to its facilitation of the solution and subsequent absorption of deposits by the foliar tissues or its elution of deposited fluoride from foliage. Accordingly, our evaluation of inorganic fluoride from fluorocarbon degradation rests upon a comparison with what is known about the effects of industrial emissions and what could be considered the natural condition

Report of an exploratory study: Safety and liability considerations for photovoltaic modules/panels

An overview of legal issues as they apply to design, manufacture and use of photovoltaic module/array devices is provided and a methodology is suggested for use of the design stage of these products to minimize or eliminate perceived hazards. Questions are posed to stimulate consideration of this area

A Discrete Theory of Connections on Principal Bundles

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition, that takes into account the principal bundle structure, is introduced. Computational issues, such as the order of approximation, are also addressed. Discrete connections provide an intrinsic method for introducing coordinates on the reduced space for discrete mechanics, and provide the necessary discrete geometry to introduce more general discrete symmetry reduction. In addition, discrete analogues of the Levi-Civita connection, and its curvature, are introduced by using the machinery of discrete exterior calculus, and discrete connections.Comment: 38 pages, 11 figures. Fixed labels in figure

Hot-wire anemometry in hypersonic helium flow

Hot-wire anemometry techniques are described that have been developed and used for hypersonic-helium-flow studies. The short run time available dictated certain innovations in applying conventional hot-wire techniques. Some examples are given to show the application of the techniques used. Modifications to conventional equipment are described, including probe modifications and probe heating controls

Equilibrium Configuration of Black Holes and the Inverse Scattering Method

The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizon must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived.Comment: LaTeX, 14 pages, no figure