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This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n and n+1. The first chapter will introduce the functions and the histories of the related problems. The second chapter will take on a variant of the Ruth-Aaron pairs problem, which asks how often sums of primes of two consecutive integers are equal. The third chapter will examine, in depth, a proof by D.R. Heath-Brown of the infinitude of consecutive integer pairs with the same number of divisors---i.e. such that d(n)=d(n+1). After that we examine a similar proof of the infinitude of pairs with the same number of prime factors---ω(n)=ω(n+1).

This study explored the development of student’s conceptual understanding of limit and derivative when specific computational tools were utilized. Fourteen students from a secondary Advanced Placement Calculus AB course explored the limit and derivative concepts from calculus using computational tools in the Maple computer algebra system. Students worked in pairs utilizing the pair-programming collaborative model. Four groups of student pairs constructed computational tools and used them to explore the limit and derivative concepts. The remaining four student pairs were provided similar tools and asked to perform identical explorations. A multiple embedded case design was utilized to explore ways students in two classes, a programming class P and a non-programming class N, constructed understandings focusing upon their interactions with each other and with the computational tools. The Action-Process-Object-Schema (APOS) conceptual model and Constructionist framework guided design and construction of the tools, outlined developmental goals and milestones, and provided interpretive context for analysis. Results provided insights into the effective design and use of computational tools in fostering conceptual understanding. The study found the additional burden of programming redirected students’ attention away from the intended conceptual understandings. The study additionally found, however, that pre-constructed tools effectively promote conceptual understanding of the limit concept when coupled with a mature conceptual model of development. Four themes influencing development of these understandings emerged: An instructional focus on skills over concepts, the instructional sequence, the willingness and ability of students to adopt and utilize computational tools, and the ways cognitive conflict was mediated.

This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n and n+1. The first chapter will introduce the functions and the histories of the related problems. The second chapter will take on a variant of the Ruth-Aaron pairs problem, which asks how often sums of primes of two consecutive integers are equal. The third chapter will examine, in depth, a proof by D.R. Heath-Brown of the infinitude of consecutive integer pairs with the same number of divisors---i.e. such that d(n)=d(n+1). After that we examine a similar proof of the infinitude of pairs with the same number of prime factors---ω(n)=ω(n+1).

In recent year, the single-end transmission line is instead by differential transmission line . Differential signaling has been generally used in the high speed digital interconnection on the PCBs. The advantages of the differential signal with a low noise and high common-mode noise suppression, but the differential mode transmission signal is a very high quality requirements of circuit, the two line should have same length and symmetry, but in the practical package the circuit is not this case, In the limit space ,the differential signal should through the bend, it would lead to the phase skew and produce the differential to common mode conversion noise on the signal integrity and electromagnetic interference(EMI) problem. In this paper a new type of bend is proposed that reduces differential -to-common mode conversion noise for high speed digital circuit. This novel structure can reduce the mode conversion over 20dB at DC to 10GHz, and the differential insertion loss remains low. Also time domain the TDT common mode noise from 0.09V to 0.008V as compared with the bended differential transmission line using the edge couple bend. Moreover, the measurement on proposed structure show a close match with the full-wave simulation result. However, this structure does not have a reference plane, the return path is not complete, the current is easy to radiate out, so I design a guard trace to reduce the radiation in this structure.

<p>Computer simulations play a profound and fundamental role inmodern theoretical physics, chemistry and materials science. Tounderstand the complex physics of metally liquids, metals,quasicrystals and metally glasses a working model imposing thelocal and global order is needed. Experiments and theory havepredicted the local order in liquid metals to beicosahedral.</p><p>The current work has been done using molecular dynamicscomputer simulations of a monatomic system using a simplepair-potential for the interactions. Two new pair-potentialshas been developed, the Zetterling-1(Z1) and Zetterling-2(Z2)potentials. They are specifically modeled to impose icosahedralorder. The basis for the development of the potentials was theold Dzugutov potential which is known to freeze into adodecagonal quasicrystal. The new Zetterling potentials have alonger interaction range and a narrower first minimum. The morenarrow first minimum will enhance the local icosahedralordering and the longer interaction range was introduced toincorporate a second maximum in the potential mimicing theFriedel oscillations found in metallic systems. These Friedeloscillations are due to the singularity which arises at theFermi surface due to the screening of the positive charge bythe electron gas.</p><p>Five papers are included in the study. The first two papersare studies of icosahedral clustering in the liquid andsupercooled liquid. The simulations in Paper I was done usingthe old Dzugutov potential while the new potentials were usedin Paper II using both molecular dynamics and the Basin Hoppingalgorithm presented in Chapter 5. Paper III considers theconcept of dynamical ergodicity in the context of thesuper-cooled liquid behaviour. The simulations were made usingthe old Dzugutov potential. Paper IVr eports a moleculardynamics simulation using the Dzugutov potential undersuper-cooling. A formation of icosahedrally structured domainswith distinctly slow diffusion which grows with cooling in alow-dimensional manner and percolate around Tc, the criticaltemperature of the mode-coupling theory. A sharp slowing downof the structural relaxation relative to diffusion is observed.It is concluded that this effect cannot be accounted for by thespatial variation in atomic mobility. The low-dimensionalclustering is discussed as a possible mechanism of fragility.Paper Vin vestigates the crystallization of a simple monatomicliquid model which utilizes the Zetterling-1 potential. Thesystem forms a thermodynamically stable solid phase exhibitingcubic symmetry. Its diffraction pattern is identified as thatof γ-brass, a tetrahedrally packed crystalline structurewith 52 atoms in the unit cell.</p><p><b>Keywords:</b>simple liquids, molecular dynamics, pairpotential, icosahedral cluster.</p>

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 108-112).

Twisted pan (structured wire) cabling is a principal component in the communications infrastructure, with millions of meters being installed weekly. The rate of increase in upper frequency for this cable appears to be doubling approximately every two years. Clearly, a rigorous approach to the design of these cables is fundamental to achieving data transmission at these frequencies with increasingly stringent performance requirements. This thesis derives a family of equations for the secondary parameters based on an explicit relationship between cable dimensions and materials. These equations have been validated against experimental results and fOWld accurate. Further. equations are developed which calculate the overall S-parameters for cascaded multi.pair cables, the return loss and cross-talk between transmission charmels. In tenns of cable specification. the secondary parameters are the most significant with many of the perfonnance criteria based on these. With designs based largely on the manipulation of physical dimensions, there has been no family of secondary parameter equations given explicitly as functions of cable dimensions and material properties. Similarly, tools have not existed to allow the investigation of design variability or the effects of handling and installation. These are principal requirements in the cable design process. A modelling package, based on Transmission-Line Matrix (TLM) modelling, is developed to a1low the investigation of manufacturing variability and installation handling effects on overall perfonnance of a cable. This modelling technique is validated against both experimental results and analytical results the comparison is excellent. Finally a novel method for the calculation of cross talk between cable pairs is presented. This method is based on a hybrid field·circuit model. Comparisons with measurements show good agreement.

The power/ground plane structure within an electronic system not only delivers power, but also provides return path for the currents associated with the propagating signals. The cavity resonances within the power/ground plane structure affect the signal integrity of the system at high frequencies. The chip complexity and clock speed continue to increase and new structures, such as meshed planes and electromagnetic bandgap structures, are used in plane pair structure design. The signal integrity analysis of the power/ground plane structure becomes exceedingly important and challenging.The primary goal of this research is an in-depth investigation of the impact of the cavity resonances associated with the plane pair structure on the signal integrity. This includes development of modeling, simulation, and measurement methodologies for accurate and efficient characterization or prediction of the time/frequency domain electrical characteristics of power/ground plane pair structures. This research is divided into three parts. First, new SPICE compatible models are proposed for the new structures, such as the meshed plane and EBG embedded plane pair designs, so that the power/ground plane designs with these new structures can be simulated efficiently. Second, the accuracy of the simulation results is vital. The behavior of the benchmark structures is simulated and simulation results are verified either experimentally or by comparing with those from tools that are proven to be accurate. Third, high frequency measurement data is vulnerable to all parasitic parameters. The factors that affect the accuracy of measured data are investigated and methods to improve the accuracy of the measured data are proposed and verified.

Epithelial ovarian cancer (EOC) is difficult to detect in early stage disease, resulting in a high mortality rate. The molecular events underlying EOC development remain largely unknown. Chromosome 3 exhibits frequent deletions and rearrangements in EOC by cytogenetic analysis. In addition, loss of heterozygosity (LOH) mapping of matched ovarian tumour and constitutional DNA samples exhibits specific regions of chromosome 3 loss involving distinct regions: 3p25-p26, 3p24 and a region proximal to 3p14. Thus, chromosome 3p loss points to the location of tumour suppressor genes (TSG) implicated in tumourigenesis, based on Knudson's 'two-hit' model and the paradigm of the classical TSG. The dissertation hypothesis states at least one TSG implicated in EOC is located on chromosome 3p. A novel complementation approach based on the transfer of normal chromosome 3 fragments into OV-90, a tumourigenic EOC cell line harbouring LOH of the 3p arm, was used to generate functional evidence for chromosome 3p TSGs. Three hybrids exhibited complete suppression of tumourigenic potential based on the inability to form colonies in soft agarose, spheroids in cell culture, and tumours in nude mice xenograft models. While all hybrids had acquired various chromosome 3 regions, they all shared in common a 3p12-pcen interval, suggesting at least one common gene may have affected the suppression of tumourigenicity in the OV-90-derived hybrids. Twelve known/hypothetical genes mapping to 3p12-pcen region were characterized based on gene expression and mutation analysis following a classical model for TSG inactivation. To establish the relevance to EOC, gene expression of candidates was investigated in primary cultures of normal ovarian surface epithelial cells and both malignant serous and benign serous tumour samples. The gene expression and genetic analysis identified seven TSG candidates, none of which appeared to be mutated or transcriptionally silenced based on classical mechanisms of TSG inactivation in OV-90, thus suppression of tumourigenicity may have resulted from the functional complementation of one more haploinsufficient 3p12-pcen genes. Several genes (GBE1, VGLL3, ZNF654 ) appeared underexpressed in malignant tumours and these findings suggest the intriguing possibility that more than one 3p12-pcen gene was involved in the suppression of tumourigenicity in OV-90, and by extension, EOC.