To a large extent mathematical transforms are applied on a signal to uncover information that is concealed, and the capability of such transforms is valuable for signal processing. One such transforms widely used in this area, is the conventional Fourier Transform (FT), which decomposes a stationary signal into different frequency components. However, a major drawback of the conventional transform is that it does not easily render itself to the analysis of non-stationary signals such as a frequency modulated (FM) or amplitude modulated (AM) signal. The different frequency components of complex signals cannot be easily distinguished and separated from one another using the conventional FT. So in this thesis an innovative mathematical transform, Fractional Fourier Transform (FRFT), has been considered, which is more suitable to process non-stationary signals such as FM signals and has the capability not only of distinguishing different frequency components of a multi-component signal but also separating them in a proper domain, different than the traditional time or frequency domain. The discrete-time FRFT (DFRFT) developed along with its derivatives, such as Multi-angle-DFRFT (MA-DFRFT), Slanted Spectrum and Spectrogram Based on Slanted Spectrum (SBSS) are tools belonging to the same FRFT family, and they could provide an effective approach to identify unknown signals and distinguish the different frequency components contained therein. Both artificial stationary and FM signals have been researched using the DFRFT and some derivative tools from the same family. Moreover, to accomplish a contrast with the traditional tools such as FFT and STFT, performance comparisons are shown to support the DFRFT as an effective tool in multi-component chirp signal analysis. The DFRFT taken at the optimum transform order on a single-component FM signal has provided higher degree of signal energy concentration compared to FFT results; and the Slanted Spectrum taken along the slant line obtained from the MA-DFRFT demonstration has shown much better discrimination between different frequency components of a multi-component FM signal. As a practical application of these tools, the motor current signal has been analyzed using the DFRFT and other tools from FRFT family to detect the presence of a motor bearing fault and obtain the fault signature frequency. The conclusion drawn about the applicability of DFRFT and other derivative tools on AM signals with very slowly varying FM phenomena was not encouraging. Tools from the FRFT family appear more effective on FM signals, whereas AM signals are more effectively analyzed using traditional methods like spectrogram or its derivatives. Such methods are able to identify the signature frequency of faults while using less computational time and memory.

This research compares the leakage and rotordynamic characteristics of a slanted-tooth labyrinth seal to a conventional straight-tooth labyrinth. Detailed results comparing the rotordynamic coefficients and leakage parameters of a slanted-tooth see-through labyrinth seal and a straight-tooth see-through labyrinth seal are presented. The straight-tooth labyrinth seal used in this research was originally tested by Arthur Picardo. The slanted-tooth labyrinth seal was designed and fabricated to be identical to the straight-tooth labyrinth seal in terms of pitch, depth, and the number of teeth. The angle of inclination of the teeth in the slanted-tooth labyrinth seal was chosen to be 65° from the normal axis. The seals were tested at an inlet pressure of 70 bar-a (1015 psi-a), pressure ratios of 0.4, 0.5, and 0.6, rotor speeds of 10,200, 15,350, and 20,200 rpm, and a radial clearance of 0.2 mm (8 mils). The experiments were carried out at zero, medium, and high inlet preswirl ratios. The experimental results show only minute differences in the rotordynamic coefficients between the two seals. But, the slanted-tooth labyrinth seal leaked approximately 10% less than the straight-tooth labyrinth seal. A study of prediction versus experimental data was done. XLlaby was used for prediction. XLlaby was developed for a straight-tooth labyrinth seal design and did not do a good job in predicting the rotordynamic coefficients and the leakage rate.

Most of the tall buildings that are built today have a straight and vertical shape, because vertical buildings are more stable and easily built than slanted ones. In the case of vertical building, bending moments in the base only exists from horizontal loads such as wind and seismic loads, but in slanted buildings there will also be bending moments from dead and live loads. In addition, transportation inside the building is also a challenge when it comes to slanted buildings. However, a new elevator system that ThyssenKrupp has developed will solve that problem. This new elevator has an ability to move in all direction both vertically and horizontally. The new structural system, Tube Mega Frame (TMF), has been studied and proved to have better efficiency than the central core with outriggers. Moving the bearing structure to the perimeter of the building, gives smaller overturning moment and better stability due to longer lever arm from the center. This thesis focuses on applying the Tube Mega Frame system to a slanted building which has a tripod structure. Different types of TMFs were used to compare the efficiency of the buildings performance. The TMF contains perimeter frame and mega columns with different binding systems such as belt walls and bracings. A pre-study has been carried out in order to see the overall behavior of the tripod shape. Different heights and inclinations have been analyzed with stick models. The analysis has been performed in the finite element software SAP2000 and deflections due to dead load was compared. The buildings with least deflection considering maximum height and maximum inclination was chosen for further model analysis in finite element software ETABS. Furthermore, a short study of different bracings system has been performed for the lateral loads and it concluded that X-bracing have better performance. The main study of this thesis focused on the two building models of 450 m with 7° inclination and 270 and 15° inclination. For each model, five different TMF systems were applied and analyzed. The TMF includes perimeter frame, perimeter frame with belt wall, mega columns, mega columns with belt wall and mega columns with bracings. Deformations due to wind load, seismic load and modal vibration has been compared. It concluded that the least deformation is achieved by the TMF mega columns with bracings for both models with two different heights. The periods of the building are comparatively lower than other systems. The deflection from TMF mega columns with belt walls did not differ much from the TMF mega columns with bracings. For the 270 m high building, the top story displacement was remarkably small because of the three legs, making it stiffer and stable. Even with the p delta effect, there were only millimeters of difference in top story displacement. TMF perimeter frame had a lower deflection than with belt wall, which should have been exact opposite. The reason was while making the total volume of buildings equal, the addition of belt walls led to thinner columns in the perimeter and lower stiffness.

L'objet d'étude de ce mémoire est la géométrie des courbes holomorphes entières à valeurs dans le complémentaire d'hypersurfaces génériques de l'espace projectif complexe. Les conjectures célèbres de Kobayashi et de Green-Griffiths énoncent que pour de telles hypersurfaces, de grand degré, les images de ces courbes entières doivent satisfaire certaines contraintes algébriques. En adaptant les techniques de jets développées notamment par Bloch, Green-Griffiths, Demailly, Siu, Diverio-Merker-Rousseau, pour les courbes à valeurs dans une hypersurface projective (cas dit compact), nous obtenons la dégénérescence algébrique des courbes entières f : ℂ→Pⁿ∖Xd (cas dit logarithmique), pour les hypersurfaces génériques Xd de Pⁿ de degré d ≥ (5n)² nⁿ. Comme dans le cas compact, notre preuve repose essentiellement sur l'élimination algébrique de toutes les dérivées dans des équations différentielles qui sont vérifiées par toute courbe entière non constante. L'existence de telles équations différentielles est obtenue grâce aux inégalités de Morse holomorphes et à une variante simplifiée d'une formule de résidus originalement élaborée par Bérczi à partir de la formule de localisation équivariante d'Atiyah-Bott. La borne effective d ≥ (5n)² nⁿ est obtenue par réduction radicale d'un calcul de résidus itérés de très grande ampleur. Ensuite, la déformation de ces équations différentielles par dérivation le long de champs de vecteurs obliques, dont l'existence est ici généralisée et clarifiée, nous permet d'engendrer suffisamment de nouvelles équations pour réaliser l'élimination algébrique finale évoquée ci-dessus. / The topic of this memoir is the geometry of holomorphic entire curves with values in the complement of generic hypersurfaces of the complex projective space. The well-known conjectures of Kobayashi and of Green-Griffiths assert that for such hypersurfaces, having large degree, the images of these curves shall fulfill algebraic constraints. By adapting the jet techniques developed notably by Bloch, Green-Griffiths, Demailly, Siu, Diverio-Merker-Rousseau, in the case of curves with values in projective hypersurfaces (so-called compact case), we obtain the algebraic degeneracy of entire curves f : ℂ→Pⁿ∖Xd (so called logarithmic case), for generic hypersurfaces Xd in Pⁿ of degree d ≥ (5n)² nⁿ. As in the compact case, our proof essentially relies on the algebraic elimination of all derivatives in differential equations that are satisfied by every nonconstant entire curve. The existence of such differential equations is obtained thanks to the holomorphic Morse inequalities and a simplified variant of a residue formula firstly developed by Bérczi from the Atiyah-Bott equivariant localization formula. The effective lower bound d ≥ (5n)² nⁿ is obtained by radically simplifying a huge iterated residue computation. Next, the deformation of these differential equations by derivation along slanted vector fields, the existence of which is here generalized and clarified, allows us to generate sufficiently many new differential equations in order to realize the final algebraic elimination mentioned above.