Ob integrirovanii differentsialov soderzhashchikh kubicheskiĭ koren.

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Facilitating Realistic and Efficient Applications of Ab Initio Electronic Dynamics for Polyatomic Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Converged quantum calculations of HO2 bound states and resonances for J=6 and 10

Bound and resonance states of HO2 are calculated quantum mechanically using both the Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization method for nonzero total angular momentum J=6 and 10, using a parallel computing strategy. For bound states, agreement between the two methods is quite satisfactory; for resonances, while the energies are in good agreement, the widths are in general agreement. The quantum nonzero-J specific unimolecular dissociation rates for HO2 are also calculated. (C) 2004 American Institute of Physics.

Iterative quantum computations of HO2 bound states and resonances for J=4 and 5

Bound and resonance states of HO2 have been calculated by both the complex Lanczos homogeneous filter diagonalisation (LHFD) method(1,2) and the real Chebyshev filter diagonalisation method(3,4) for non-zero total angular momentum J = 4 and 5. For bound states, the agreement between the two methods is quite satisfactory; for resonances while the energies are in good agreement, the widths are only in general agreement. The relative performances of the two iterative FD methods have also been discussed in terms of efficiency as well as convergence behaviour for such a computationally challenging problem. A helicity quantum number Ohm assignment (within the helicity conserving approximation) is performed and the results indicate that Coriolis coupling becomes more important as J increases and the helicity conserving approximation is not a good one for the HO2 resonance states.

Recent developments in the quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Recent progresses for non-zero total angular momentum J calculations of resonances including parallel computing models are also included and future directions in this field are discussed.

A wideband array antenna with beam-steering capability using real valued weights

This article presents an array antenna with beam-steering capability in azimuth over a wide frequency band using real-valued weighting coefficients that can be realized in practice by amplifiers or attenuators. The described beamforming scheme relies on a 2D (instead of 1D) array structure in order to make sure that there are enough degrees of freedom to realize a given radiation pattern in both the angular and frequency domains. In the presented approach, weights are determined using an inverse discrete Fourier transform (IDFT) technique by neglecting the mutual coupling between array elements. Because of the presence of mutual coupling, the actual array produces a radiation pattern with increased side-lobe levels. In order to counter this effect, the design aims to realize the initial radiation pattern with a lower side-lobe level. This strategy is demonstrated in the design example of 4 X 4 element array. (C) 2005 Wiley Periodicals. Inc.

Planar electromagnetic bandgap structures

This article presents various novel and conventional planar electromagnetic bandgap (EBG)-assisted transmission lines. Both microstrip lines and coplanar waveguides (CPWs) are designed with circular, rectangular, annular, plus-sign and fractal-patterned EBGs and dumbbell-shaped defected ground structure (DGS). The dispersion characteristics and the slow-wave factors of the design are investigated. (c) 2006 Wiley Periodicals, Inc.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

El problema de Lagrange en cartografía

Esta Tesis trata sobre las proyecciones de Lagrange, que son proyecciones conformes del elipsoide de revolución sobre el plano, que transforman los meridianos y paralelos en arcos circulares, y que analizamos y revisamos, con especial cuidado en las fuentes originales (Lambert, Lagrange, Bonnet, Chebyshev, etc.) Como herramienta auxiliar, introducimos en cartografía la función caracter ística de una proyección conforme: m = jf0(z)j{u100000}1, z = + iq, fundamentados en que las curvaturas de las imágenes de los meridianos y paralelos son, según J. L. Lagrange (1779): 1 = {u100000}m y 2 = mq, respectivamente (el subíndice indica derivada parcial). Parametrizamos el elipsoide mediante la longitud geodésica o geográ ca y la latitud isométrica q. Una proyección conforme es de Lagrange si y solo si m q = 0. En este trabajo resolvemos el sistema de ecuaciones: logm = 0, m q = 0. De este modo obtenemos a priori la función característica de las proyecciones de Lagrange y también realizamos una primera clasi cación: rectilíneas, formada por tres familias: Cilíndricas conformes, Cónicas y acimutales conformes y Pseudopolares, esta última es nueva en cartografía; y circulares, formada también por tres familias: De Lagrange-Lambert, Unipolares y Apolares, estas dos últimas nuevas en cartografía. En las rectilíneas todos los meridianos o todos los paralelos se transforman en rectas. En las circulares solo algunos meridianos o paralelos son rectilíneos...

Design and implementation of generalized topologies of time-interleaved variable bandpass Σ−Δ modulators

In this thesis, novel analog-to-digital and digital-to-analog generalized time-interleaved variable bandpass sigma-delta modulators are designed, analysed, evaluated and implemented that are suitable for high performance data conversion for a broad-spectrum of applications. These generalized time-interleaved variable bandpass sigma-delta modulators can perform noise-shaping for any centre frequency from DC to Nyquist. The proposed topologies are well-suited for Butterworth, Chebyshev, inverse-Chebyshev and elliptical filters, where designers have the flexibility of specifying the centre frequency, bandwidth as well as the passband and stopband attenuation parameters. The application of the time-interleaving approach, in combination with these bandpass loop-filters, not only overcomes the limitations that are associated with conventional and mid-band resonator-based bandpass sigma-delta modulators, but also offers an elegant means to increase the conversion bandwidth, thereby relaxing the need to use faster or higher-order sigma-delta modulators. A step-by-step design technique has been developed for the design of time-interleaved variable bandpass sigma-delta modulators. Using this technique, an assortment of lower- and higher-order single- and multi-path generalized A/D variable bandpass sigma-delta modulators were designed, evaluated and compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity for ideal and non-ideal topologies. Extensive behavioural-level simulations verified that one of the proposed topologies not only used fewer coefficients but also exhibited greater robustness to non-idealties. Furthermore, second-, fourth- and sixth-order single- and multi-path digital variable bandpass digital sigma-delta modulators are designed using this technique. The mathematical modelling and evaluation of tones caused by the finite wordlengths of these digital multi-path sigmadelta modulators, when excited by sinusoidal input signals, are also derived from first principles and verified using simulation and experimental results. The fourth-order digital variable-band sigma-delta modulator topologies are implemented in VHDL and synthesized on Xilinx® SpartanTM-3 Development Kit using fixed-point arithmetic. Circuit outputs were taken via RS232 connection provided on the FPGA board and evaluated using MATLAB routines developed by the author. These routines included the decimation process as well. The experiments undertaken by the author further validated the design methodology presented in the work. In addition, a novel tunable and reconfigurable second-order variable bandpass sigma-delta modulator has been designed and evaluated at the behavioural-level. This topology offers a flexible set of choices for designers and can operate either in single- or dual-mode enabling multi-band implementations on a single digital variable bandpass sigma-delta modulator. This work is also supported by a novel user-friendly design and evaluation tool that has been developed in MATLAB/Simulink that can speed-up the design, evaluation and comparison of analog and digital single-stage and time-interleaved variable bandpass sigma-delta modulators. This tool enables the user to specify the conversion type, topology, loop-filter type, path number and oversampling ratio.

OFDM-based schemes for next generation wireless systems

The purpose of this study is to investigate two candidate waveforms for next generation wireless systems, filtered Orthogonal Frequency Division Multiplexing (f-OFDM) and Unified Filtered Multi-Carrier (UFMC). The evaluation is done based on the power spectral density analysis of the signal and performance measurements in synchronous and asynchronous transmission. In f-OFDM we implement a soft truncated filter with length 1/3 of OFDM symbol. In UFMC we use the Dolph-Chebyshev filter, limited to the length of zero padding (ZP). The simulation results demonstrates that both waveforms have a better spectral behaviour compared with conventional OFDM. However, the induced inter-symbol interference (ISI) caused by the filter in f-OFDM, and the inter-carrier interference (ICI) induced in UFMC due to cyclic prefix (CP) reduction , should be kept under control. In addition, in a synchronous transmission case with ideal parameters, f-OFDM and UFMC appear to have similar performance with OFDM. When carrier frequency offset (CFO) is imposed in the transmission, UFMC outperforms OFDM and f-OFDM.

Sviluppo e validazione di un algoritmo per la conversione delle incertezze delle effemeridi dell'asteroide Didymos

Per determinare lo stato di un satellite ad ogni istante è necessario un propagatore orbitale, cioè un algoritmo che, partendo da condizioni iniziali note, calcola la traiettoria di un corpo in un intervallo di tempo arbitrario. L’orbita ottenuta è tuttavia soggetta ad errori numerici (errori di propagazione) ed incertezze. Queste ultime derivano da condizioni iniziali non precise, in quanto ricavate da osservazioni, soggette ad errori di misurazione, o ipotesi sui parametri dell’orbita e del corpo. Per questo motivo è importante utilizzare il propagatore anche per verificare l’evoluzione di tali incertezze nel tempo tramite un processo noto come analisi della covarianza. Questo processo permette di valutare l’entità dell’incertezza calcolandone la variazione rispetto allo stato iniziale a cui è generata e la rispondenza ai requisiti di missione. Lo scopo della tesi è l’incremento di precisione del propagatore orbitale esistente e lo sviluppo di strumenti per il supporto della missione LICIACube (Light Italian Cubesat for Imaging of Asteroids). In particolare, saranno implementati effetti secondari nel modello di propagazione ed uno strumento per la propagazione e conversione della rappresentazione di incertezze delle effemeridi. Questo permetterà la valutazione della precisione dell’orbita di Didymos e di LICIACube, dal suo rilascio fino al flyby. Per l’esportazione della traiettoria calcolata viene presentata una funzione che, tramite interpolazione, rappresenti l’orbita generata utilizzando un limitato spazio di memoria.