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I. The syzygetic pencil of cubics with a new geometrical development of its Hesse Group, G16 II. The complete Pappus hexagon ...Grove, Charles Clayton, January 1906 (has links)
Thesis (Ph.D.)--Johns Hopkins University. / Plate printed on both sides. Vita.
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The effects and detection of collinearity in an analysis of covarianceGiacomini, Jo Jane January 2011 (has links)
Typescript (photocopy). / Digitized by Kansas Correctional Industries
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Webová aplikace pro výuku osové afinity a středové kolineace / Web application for teaching of axial affinity and perspective collineationPlichtová, Petra January 2013 (has links)
This work is intended for high school and university students and their teachers who want to learn or improve their knowledge about affine transformations and perspective collineation. In this work the reader acquainted with the ideal elements, dividing ratio and cross ratio. The main part of the work is perspective collineation and affine transformations, their definitions, properties, specificity and finding other elements. This work also deals with the use of affine transformations and perspective collineation in descriptive geometry. The text is supplemented with illustrative images, applets and step-by-step images that are created with GeoGebra software. Keywords: affine transformations, perspective collineation, ideal elements, cuts of solids, dividing ratio, cross ratio
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Nonlinear mixing of two collinear Rayleigh wavesMorlock, Merlin B. 13 January 2014 (has links)
Nonlinear mixing of two collinear, initially monochromatic, Rayleigh waves propagating in the same direction in an isotropic, nonlinear elastic solid is investigated: analytically, by finite element method simulations and experimentally. In the analytical part, it is shown that only collinear mixing in the same direction
fulfills the phase matching condition based on Jones and Kobett 1963 for the resonant generation of the second harmonics, as well as the sum and difference frequency components
caused by the interaction of the two fundamental waves. Next, a coupled
system of ordinary differential equations is derived based on the Lagrange equations of the second kind for the varying amplitudes of the higher harmonic and combination
frequency components of the fundamentals waves. Numerical results of the evolution of the amplitudes of these frequency components over the propagation distance are provided for different ratios of the fundamental wave frequencies. It is shown that the energy transfer is larger for higher frequencies, and that the oscillation of the energy between the different frequency components depends on the amplitudes and frequencies of the fundamental waves. Furthermore, it is illustrated that the horizontal velocity component forms a shock wave while the vertical velocity component
forms a pulse in the case of low attenuation. This behavior is independent of the two fundamental frequencies and amplitudes that are mixed. The analytical model is then extended by implementing diffraction effects in the parabolic approximation.
To be able to quantify the acoustic nonlinearity parameter, β, general relations based on the plane wave assumption are derived. With these relations a β is expressed, that is analog to the β for longitudinal waves, in terms of the second harmonics and the sum and the difference frequencies. As a next step, frequency and amplitude ratios of the fundamental frequencies are identified, which provide a maximum amplitude of one of the second harmonics as well as the sum or difference frequency components
to enhance experimental results.
Subsequently, the results of the analytical model are compared to those of finite element method simulations. Two dimensional simulations for small propagation distances gave similar results for analytical and finite element simulations. Consquently.
this shows the validity of the analytical model for this setup. In order to demonstrate the feasibility of the mixing technique and of the models, experiments were conducted using a wedge transducer to excite mixed Rayleigh waves and an air-coupled transducer to detect the fundamentals, second harmonics and the sum frequency. Thus, these experiments yield more physical information compared to the case of using a single fundamental wave. Further experiments were conducted
that confirm the modeled dependence on the amplitudes of the generated waves. In conclusion, the results of this research show that it is possible to measure the acoustic nonlinearity parameter β to quantify material damage by mixing Rayleigh
waves on up to four ways.
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Cvičebnice Mongeova promítání / Workbook of Monge projectionPajerová, Nikola January 2016 (has links)
In this thesis there can be found various examples from Monge projection. The theory is summarized in the beginning, which is important of understanding the projection and for solving the examples. There are also examples of solving axial affinity and central collineation. Then there is a chapter about the projection of all types of angular and rotational solids, which are solved at the secondary schools. Then follows a chapter, where the sections of these solids are constructed. In the last chapter, there are solved intersection of solids from each type. Powered by TCPDF (www.tcpdf.org)
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