The thesis is structured into 5 chapters as follows: <strong>Chapter 1</strong> is an introduction to the tools and methods we use most frequently. <strong>Chapter 2</strong> Pairs of k-free Numbers, consecutive square-full Numbers. In this chapter, we refine the approximate determinant method by Heath-Brown. We present applications to asymptotic formulas for consecutive k-free integers, and more generally for k-free integers represented by r-tuples of linear forms. We also show how the method can be used to derive an upper bound for the number of consecutive square-full integers. Finally, we apply the method to make a statement about the size of the fundamental solution of Pell equations. <strong>Chapter 3</strong> Power-Free Values of Polynomials. A conjecture by Erdös states that for any irreducible polynomial f of degree d&ge;3 with no fixed (d-1)-th power prime divisor, there are infinfinitely many primes p such that f(p) is (d-1)-free. We prove this conjecture and derive the corresponding asymptotic formulas. <strong>Chapter 4</strong> Integer Points on Bilinear and Trilinear Equations. In the fourth chapter, we derive upper bounds for the number of integer solutions on bilinear or trilinear forms. <strong>Chapter 5</strong> In the fifth chapter, we present a method to count the monomials that occur in the projective determinant method when the method is applied to cubic varieties.

Nowadays, the impact of technological growth‏ ‏on people’s life and our society is remarkable, ‎inevitable and also worrying. The excessive influence of technology in ‎individuals’ lives has caused our community to change towards more privatisation and ‎secluded life. At this point, the role of urban public spaces in social life has become more ‎prominent and significant. Issues of social life in public spaces and the relations with creating a ‎vibrant and dynamic city has not been given too much attention in urban planning and design. ‎This thesis raises the question of considering public spaces and how urban public spaces ‎‎(especially squares) can encourage/persuade citizens ‎to increase social interaction‎. Initially, it describes a clear definition of public spaces and urban squares. Thereafter, the study addresses ‎effectual factors from the human perspective which can help to achieve the successful design of an ‎urban public square. The aim of the work is to comprehend how it might be possible to improve ‎social life and behaviour in public spaces (squares) and consequently to attain a framework in ‎order to design. Ultimately, a design is proposed for Fisktorget (Fish Square), which is one of most important public places in the Karlskrona city in Sweden. The proposed design is based on studies and analyses that have been done throughout this thesis.

Current attempts to make precision measurements of the HI power spectrum at high redshifts have led to the construction of several low-frequency, large-N, interferometric arrays. The computational demands of digital correlators required by these arrays present a significant challenge. These demands stem from the treatment of radio telescopes as collections of two-element interferometers, which results in the need to multiply O(N²) pairs of antenna signals in an N-element array. Given the unparalleled flexibility offered by modern digital processing systems, it is apt to consider whether a different way of treating the signals from antennas in an array might be fruitful in current and future radio telescopes. Such methods potentially avoid the unfavourable N² scaling of computation rate with array size. In this thesis I examine the prospect of using direct-imaging methods to map the sky without first generating correlation matrices. These methods potentially provide great computational savings by creating images using efficient, FFT-based algorithms. This thesis details the design and deployment of such a system for the Basic Element of SKA Training II (BEST-2) array in Medicina, Italy. Here the 32-antenna BEST-2 array is used as a test bed for comparison of FX correlation and direct-imaging systems, and to provide a frontend for a real-time transient event detection pipeline. Even in the case of traditional O(N²) correlation methods, signal processing algorithms can be significantly optimized to deliver large performance gains. In this thesis I present a new mechanism for optimizing the cross-correlation operation on Field Programmable Gate Array (FPGA) hardware. This implementation is shown to achieve a 75% reduction in multiplier usage, and has a variety of benefits over existing optimization strategies. Finally, this thesis turns its focus towards The Square Kilometre Array (SKA). When constructed, the SKA will be the world's largest radio telescope and will comprise a variety of arrays targeting different observing frequencies and science goals. The low-frequency component of the SKA (SKA-low) will feature ~250,000 individual antennas, sub-divided into a number of stations. This thesis explores the impact of the station size on the computational requirements of SKA-low, investigating the optimal array configuration and signal processing realizations.

This study was designed to determine whether chis-quared based tests for independence give reliable estimates (as compared to the exact values provided by Fisher's exact probabilities test) of the probability of a relationship between the variables in 3 X 3, 3 X 4 , and 3 X 5 contingency tables when the sample size is 10, 20, or 30. In addition to the classical (uncorrected) chi-squared test, four methods for continuity correction were compared to Fisher's exact probabilities test. The four methods were Yates' correction, two corrections attributed to Cochran, and Mantel's correction. The study was modeled after a similar comparison conducted on 2 X 2 contingency tables and published by Michael Haber.

The famous Four Color Theorem states that any planar graph can be properly colored using at most four colors. However, if we want to properly color the square of a planar graph (or alternatively, color the graph using distinct colors on vertices at distance up to two from each other), we will always require at least \Delta + 1 colors, where \Delta is the maximum degree in the graph. For all \Delta, Wegner constructed planar graphs (even without 3-cycles) that require about \frac{3}{2} \Delta colors for such a coloring. To prove a stronger upper bound, we consider only planar graphs that contain no 4-cycles and no 5-cycles (but which may contain 3-cycles). Zhu, Lu, Wang, and Chen showed that for a graph G in this class with \Delta \ge 9, we can color G^2 using no more than \Delta + 5 colors. In this thesis we improve this result, showing that for a planar graph G with maximum degree \Delta \ge 32 having no 4-cycles and no 5-cycles, at most \Delta + 3 colors are needed to properly color G^2. Our approach uses the discharging method, and the result extends to list-coloring and other related coloring concepts as well.

GIS (Geographic Information Systems) and remote sensing techniques were used to predict relationships between bald eagle nest presences and land type, distance to land type and impervious surface cover area. Data plots revealed bald eagle nest presence decreases in response to an increase in area of bareland; increases with an increase in area of forested land; decreases with an increase in distance (m) to shoreline, and decreases in response to an increase in area of impervious surfaces. Logistic regression models identified impervious surfaces as an indicator for bald eagle nest presence (P 24% as unsuitable. Unsuitable area covered 17.82% of the total study area, impacted area covered 13.40%, and, sensitive area covered 68.77%. The projected increase in population in the state of Virginia and subsequent increase in impervious surfaces presents a challenge to the future viability of the Virginia Chesapeake Bay bald eagle population. The threshold analysis identified areas of prime conservation concern for bald eagle nest presence within the defined study area. These areas provide the basis for a conservation management plan and for further scientific study.

Synthetic Aperture Radar (SAR) has been identified as a good candidate to provide high-resolution soil moisture information over extended areas. SAR data could be used as observations within a global Data Assimilation (DA) approach to benefit applications such as hydrology and agriculture. Prior to developing an operational DA system, one must tackle the following challenges of soil moisture estimation with SAR: (1) the dependency of the measured radar signal on both soil moisture and soil surface roughness which leads to an ill-conditioned inverse problem, and (2) the difficulty in characterizing spatially/temporally surface roughness of natural soils and its scattering contribution. The objectives of this project are (1) to develop a roughness measurement method to improve the spatial/temporal characterization of soil surface roughness, and (2) to investigate to what extent the inverse problem can be solved by combining multipolarization, multi-incidence, and/or multi-frequency radar measurements. The first objective is achieved with a measurement method based on Structure from Motion (SfM). It is tailored to monitor natural surface roughness changes which have often been assumed negligible although without evidence. The measurement method is flexible, a.ordable, straightforward and generates Digital Elevation Models (DEMs) for a SAR-pixel-size plot with mm accuracy. A new processing method based on band-filtering of the DEM and its 2D Power Spectral Density (PSD) is proposed to compute the classical roughness parameters. Time series of DEMs show that non-negligible changes in surface roughness can happen within two months at scales relevant for microwave scattering. The second objective is achieved using maximum likelihood fitting of the Oh backscattering model to (1) full-polarimetric Radarsat-2 data and (2) simulated multi-polarization / multi-incidence / multi-frequency radar data. Model fitting with the Radarsat-2 images leads to poor soil moisture retrieval which is related to inaccuracy of the Oh model. Model fitting with the simulated data quantifies the amount of multilooking for di.erent combinations of measurements needed to mitigate the critical e.ect of speckle on soil moisture uncertainty. Results also suggest that dual-polarization measurements at L- and C-bands are a promising combination to achieve the observation requirements of soil moisture. In conclusion, the SfM method along with the recommended processing techniques are good candidates to improve the characterization of surface roughness. A combination of multi-polarization and multi-frequency radar measurements appears to be a robust basis for a future Data Assimilation system for global soil moisture monitoring.

Two players take alternating turns filling a rectangular board with unit squares without rotation, but may be otherwise arbitrary. Squares may not overlap and the game ends when there is no space for the next one. The result of the game is the number of turns. The constructor aims to maximize this quantity while the destructor wants to minimize it. We would like to get close to this value, provided that both players use their optimal strategy. We prove some new lower and upper bound for the game. This thesis extends results given by Tamás Hubai in his paper Competitive rectangle filling. Furthermore, we have a look at other board shapes and shapes to fill with.

Primary objective of master's thesis named Media image of changes at Wenceslas Square in the context of urbanism and architectural quality is to analyse the media coverage of important architectural and urban changes of Wenceslas Square between 1997 and 2015. The two main topics chosen for the analysis are the Revitalisation of Wenceslas Square and the development of Euro Palace. The purpose of the analysis is to answer the following question: "Do readers of generally oriented periodicals have an access to objective information about architectural and urban projects?" I will apply a quantitative content analysis to answer this question and prove that media contents are unbiased. After that, we would be able to say in case of Prague the architectural topics are covered enough and readers have a chance to form their own opinions or not.

Approved for public release; distribution is unlimited / Computer simulation studies of a frequency domain adaptive beamforming algorithm are presented. These simulation studies were conducted to determine the multiple broadband target localization capability and the full angular coverage capability of the algorithm. The algorithm was evaluated at several signal-to-noise ratios with varying sampling rates. The number of iterations that the adaptive algorithm took to reach a minimum estimation error was determined. Results of the simulation studies indicate that the algorithm can localize multiple broadband targets and has full angular coverage capability. / http://archive.org/details/computersimulati00behr / Lieutenant, United States Navy