Finite frames are special collections of vectors utilized in Harmonic Analysis and Digital Signal Processing. In this thesis, geometric aspects and construction techniques are considered for the family of k-vector frames in Fn = Rn or Cn sharing a fixed frame operator (denoted Fk(E, Fn), where E is the Hermitian positive definite frame operator), and also the subfamily of this family obtained by fixing a list of vector lengths (denoted Fk µ(E, Fn), where µ is the list of lengths). The family Fk(E, Fn) is shown to be diffeomorphic to the Stiefel manifold Vn(Fk), and Fk µ(E, Fn) is shown to be a smooth manifold if the list of vector lengths µ satisfy certain conditions. Calculations for the dimensions of these manifolds are also performed. Finally, a new construction technique is detailed for frames in Fk(E, Fn) and Fk µ(E, Fn).

The objective of this thesis is to analyze the power harmonic distortion of a steel factory and to mitigate the distortion by passive filters. The mathematical harmonic model of the industrial power system is built according to the power system network and the substation load characteristics of the steel factory. The substation load is converted as equivalent impedance, the harmonic voltage and harmonic current, and the total harmonic distortion of bus voltages and currents are then derived by the harmonic load flow analysis with the actual harmonic current data of the converters, cycloconverters, and VVVF in the plant. Due to the dynamic load behavior the stochastic harmonic current generated by various components is varied with the operation modes of all plants. To investigate the harmonic distortion of the steel factory with statistics oriented manner, the stochastic harmonic load flow analysis is executed to find the 95% confidential interval of system harmonic distortion.By this way, the effectiveness of passive filters for mitigation of harmonic distortion can be evaluated more accurately as compared to the conventional harmonic load flow analysis.

In the region of the harmonic parameter analysis, we often use the Fast Fourier Transform (FFT) to get the character of the signal, but due to the limit conditions of the FFT, the analysis results will appear some error effects, these error effects are: Aliasing effect¡BLeakage effect and Picket-fence effect. When the error effects appear, we can not get the harmonic parameter accurate. For the purpose of getting accuracy harmonic parameters, In this paper proposes, we will introduce the analysis method of FFT and it's limit conditions, then will based on FFT to develop an accuracy formula to find the harmonic parameter fast and accurately. This method will be divided into three parts. First, we will discuss the effect of harmonic to spectrum. Second, we will discuss the parameter calculation with no interfere. Third, we will rid interfere of the harmonic for getting accuracy harmonic parameter. Finally, we will analysis the actual signal to prove the ability of this method, and raise the future research direction for the successor.

In this thesis, the dynamic responses of harmonic drive (H.D.) systems under different operating conditions are investigated. The numerical simulation and the experimental measurements of harmonic drive systems are included in this thesis. The effects of flexspline of harmonic drive, i.e., the torsional stiffness and the damping ratio on the response of corresponding system are studied .Lagrange¡¦s equation is employed to derive the equation of motion of the system. The system equation with a nonlinear torsional stiffness is solved by using the 6th order Runge-Kutta method. Comparison between numerical simulation results and experimental measured data indicate that the proposed harmonic drive model is accurate and feasible for simulating the dynamic response of a harmonic drive system.

Inaug.-diss.--Göttingen. / Vita.

Not available

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

A study of exceptional sets in a finite product of Brelot spaces is made. The principal results obtained are a convergence theorem for decreasing sequences of n-superharmonic functions and an extension theorem for positive n-superharmonic functions. Similar results are obtained for plurisuperharmonic functions.

No description available.