Dead Men at War: The Ideological Battle Between Karl Marx and Adam Smith

This thesis’s foremost purpose is to illustrate the nature of the intellectual battle waged between Karl Marx and Adam Smith. A detailed summary of each philosopher’s respective ideology is given, as well as an explanation for how such ideologies arose. Furthermore, an illustration of how the writings of Marx and Smith impacted historical events is provided. Ultimately, this thesis seeks to explain the core differences between Marxism and the free market system, and why such differences exhibit a great need for the preservation of liberty

Spiral lead platen robotic end effector

A robotic end effector is disclosed which makes use of a rotating platen with spiral leads used to impact lateral motion to gripping fingers. Actuation is provided by the contact of rolling pins with the walls of the leads. The use of the disclosed method of actuation avoids jamming and provides excellent mechanical advantage while remaining light in weight and durable. The entire end effector is compact and easily adapted for attachment to robotic arms currently in use

Action-Angle variables for the Gel'fand-Dikii flows

Using the scattering transform for $n^{th}$ order linear scalar operators, the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side. Action-angle variables are then constructed. Using this, complete integrability is demonstrated in the strong sense. Real action-angle variables are constructed in the self-adjoint case

Factorization and the Dressing Method for the Gel'fand-Dikii Hierarch

The isospectral flows of an $n^{th}$ order linear scalar differential operator $L$ under the hypothesis that it possess a Baker-Akhiezer function were originally investigated by Segal and Wilson from the point of view of infinite dimensional Grassmanians, and the reduction of the KP hierarchy to the Gel'fand-Dikii hierarchy. The associated first order systems and their formal asymptotic solutions have a rich Lie algebraic structure which was investigated by Drinfeld and Sokolov. We investigate the matrix Riemann-Hilbert factorizations for these systems, and show that different factorizations lead respectively to the potential, modified, and ordinary Gel'fand-Dikii flows. Lie algebra decompositions (the Adler-Kostant-Symes method) are obtained for the modified and potential flows. For $n>3$ the appropriate factorization for the Gel'fand-Dikii flows is not a group factorization, as would be expected; yet a modification of the dressing method still works. A direct proof, based on a Fredholm determinant associated with the factorization problem, is given that the potentials are meromorphic in $x$ and in the time variables. Potentials with Baker-Akhiezer functions include the multisoliton and rational solutions, as well as potentials in the scattering class with compactly supported scattering data. The latter are dense in the scattering class

Double lead spiral platen parallel jaw end effector

The double lead spiral platen parallel jaw end effector is an extremely powerful, compact, and highly controllable end effector that represents a significant improvement in gripping force and efficiency over the LaRC Puma (LP) end effector. The spiral end effector is very simple in its design and has relatively few parts. The jaw openings are highly predictable and linear, making it an ideal candidate for remote control. The finger speed is within acceptable working limits and can be modified to meet the user needs; for instance, greater finger speed could be obtained by increasing the pitch of the spiral. The force relaxation is comparable to the other tested units. Optimization of the end effector design would involve a compromise of force and speed for a given application

Multipeakons and a theorem of Stieltjes

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.Comment: 6 page

Acoustic Scattering and the Extended Korteweg deVries hierarchy

The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scattering problem associated with the Camassa-Holm flows on the real line is solved explicitly for a special case, which is used to reduce a general class of such problems to scattering problems on finite intervals.Comment: 18 page

The application of pulse excitation to ground and flight vibration tests

A discussion of the relative merits of sinusoidal versus nonharmonic excitation for flight flutter testing is presented. It is concluded that the use of transient excitation is rapidly becoming a necessity. The application of small-scale rocket motors to the excitation of the aircraft is suggested. The design and development of rocket motors specifically for flight flutter testing is described. Methods of measuring and analyzing the transient response of the aircraft are discussed, and the techniques of theoretically predicting the structural response are described