This is a presentation I gave about what LaTeX can do some years ago. I've continued to update it (slightly) for other talks. As this is quite a large project with many files and packages, users on the Free plan may not be able to compile it successfully on Overleaf. If that's the case, feel free to grab the PDF here, and download the sources as a .zip for offline perusal/compilation!
The present work analyses designs of coaxial rotor systems in an attempt to maximize its performance in hover flight. The study is carried out with the software XROTOR and CROTOR. Influence of parameters such as tip radius, revolutions per minute, lift coefficient and number of blades have been studied. The optimization process has been carried out on two possible models of the drone DONuT. Both of them are designed to allowfor torque cancellation. In order to validate the designs, the optimized models have been 3-D printed to be tested in a test bench.
On the basis of the conclusions selectively gleaned from the history of ontological thought, it was assumed that the real geometry of the space of the Universe is the geometry of topologically fixed 3-dimensional hyper sphere. It claims that the understanding of metaphysical principles of space formation is important, resulting in the simplest mathematical approach to the calculation of actual astronomical distances. The comparisons of calculated lengths of trajectories of photons with the actual intergalactic distances reported by observers for different \(z\)-values are carried out using the selected assumptions. Photon mileage \(L_f = f (L_z, R_D)\) don't equal to the astronomical distance \(L_z\) detected by \(z\) value if \(R_D\) is the discrete quantum length of one of 4 space dimensions, associated with the curvature of space as a whole. The research concludes there is a good agreement between data obtained this way for star brightness with experimental data, when we speak about the hypothesis presupposing an accelerating growth of the Universe and abnormal brightness of supernovae; besides conclusions imply that adjustments to this hypothesis forward in the search of the values of brightness attenuation undetectable by today's tools are needed, otherwise, it could be talk about a possible expansion of our Universe in our era without accelerating.
V. A. Ivanov