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Lafferty, Matthew J. "The square threshold problem in number fields." Connect to this title online, 2008. http://etd.lib.clemson.edu/documents/1211398636/.
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Wilson, J. "Curves of genus 2 with real multiplication by a square root of 5." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268031.
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Our aim in this work is to produce equations for curves of genus 2 whose Jacobians have real multiplication (RM) by $\mathbb{Q}(\sqrt{5})$, and to examine the conjecture that any abelian surface with RM by $\mathbb{Q}(\sqrt{5})$ is isogenous to a simple factor of the Jacobian of a modular curve $X_0(N)$ for some $N$. To this end, we review previous work in this area, and are able to use a criterion due to Humbert in the last century to produce a family of curves of genus 2 with RM by $\mathbb{Q}(\sqrt{5})$ which parametrizes such curves which have a rational Weierstrass point. We proceed to give a calculation of the $\mbox{\ell}$-adic representations arising from abelian surfaces with RM, and use a special case of this to determine a criterion for the field of definition of RM by $\mathbb{Q}(\sqrt{5})$. We examine when a given polarized abelian surface $A$ defined over a number field $k$ with an action of an order $R$ in a real field $F$, also defined over $k$, can be made principally polarized after $k$-isogeny, and prove, in particular, that this is possible when the conductor of $R$ is odd and coprime to the degree of the given polarization. We then give an explicit description of the moduli space of curves of genus 2 with real multiplication by $\mathbb{Q}(\sqrt{5})$. From this description, we are able to generate a fund of equations for these curves, employing a method due to Mestre.
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Kinet, Maxime. "MHD turbulence at low magnetic Reynolds number: spectral propertiesand transition mechanism in a square duct." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210271.
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Magnetohydrodynamics describes the motions of an electrically conducting fluid under the influence of magnetic fields. Such flows are encountered in a large variety of applications, from steel industry to heat exchangers of nuclear fusion reactors. <p><p>Here we are concerned with situations where the magnetic field is relatively strong and the flow manifests turbulent motions. The interaction of the fluid with the electromagnetic field is still insufficiently understood and efficient predicting methods are lacking. Our goal is to provide more insight on this problem by making heavy use of numerical methods. In this work, two different classes of problem are investigated. <p><p>First we consider that the turbulent character of the fluid is well developed and that solid boundaries are sufficiently far away to be completely neglected. The main effects of a strong magnetic field in that case are to damp the motion and to homogenize the flow along its direction, leading to a quasi two dimensional state. Using numerical simulations we have studied the dynamics of the flow in Fourier space and in particular the non linear energy transfers between turbulent eddies. Further we investigated the scale-by-scale anisotropy and compared various methods to address this quantity. Finally, the evolution of a passive scalar embedded in the flow was analyzed and it turned out that the characteristic anisotropy of the velocity field is reflected in the distribution of the scalar quantity. <p><p>In the second problem, the flow in a duct of square cross section subject to a transverse magnetic field has been considered. Here, unlike in the previous situation, the magnetic field has globally a destabilizing effect on the flow, because of the strong inhomogeneities it produces. For instance, high velocity regions develop along the walls that are parallel to the magnetic field. There, we are mostly interested in the possible development of persistent time-dependent fluctuations. It is observed that the transition between laminar and turbulent regimes occurs through at least two distinct bifurcations. The first one takes place at moderate Reynolds number and is characterized by highly organized fluctuations. The second is encountered at higher Reynolds number and presents very strong and localized disturbances.<p>/Il existe un grand nombre d'applications industrielles dans lesquelles un écoulement de métal liquide est soumis à un champ magnétique. La production d'acier par coulée continue, la fabrication de matériaux semi-conducteurs ou encore les échan-geurs de chaleur des futurs réacteurs à fusion nucléaire en sont de bons exemples. L'interaction du liquide conducteur avec le champ magnétique est à l'origine de nombreux phénomènes inhabituels en hydrodynamique classique et doit dès lors être décrite par la magnétohydrodynamique (ou MHD en abrégé). Le but de ce travail est d'étudier la physique de ces interactions, en se basant sur la résolution numérique des équations qui les gouvernent.<p><p>Plusieurs aspects du problème ont été considérés indépendamment. Tout d'abord, l'étude de la turbulence homogène a permis de mettre en evidence les comportements du fluide loin de toute paroi solide. Ceci est mis un oeuvre dans un domaine spatial périodique, où les variables sont représentées par leur série de Fourier. L'influence du champ magnétique dans ce cas consiste à dissiper les fluctuations turbulentes et à rendre le champ de vitesse anisotrope. Les principaux résultats obtenus dans ce cadre concernent la distribution ainsi que le transfert d'énergie dans l'espace spectral, l'anisotropie des différentes échelles turbulentes de l'écoulement ainsi que le transport d'un scalaire passif au sein du fluide. <p><p>Dans un deuxième temps, le travail a porté sur l'écoulement dans une conduite rectangulaire soumise à un champ magnétique et dont les parois sont conductrices d'électricité. La particularité de cet écoulement réside dans les zones de vitesse élevées qui se développent le long des parois parallèles au champ magnétique. Celles-ci donnent lieu à un intense cisaillement qui a généralement pour effet de rendre l'écoulement instable. La simulation numérique de ce problème a permis l'étude des instabilités au sein du fluide et de la transition du régime laminaire vers la turbulence. <p><br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Hill, Sally. "Problems related to number theory : sum-and-distance systems, reversible square matrices and divisor functions." Thesis, Cardiff University, 2018. http://orca.cf.ac.uk/111467/.
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We say that two sets $A$ and $B$, each of cardinality $m$, form an $m+m$ \emph{sum-and-distance system} $\{A,B\}$ if the sum-and-distance set $A^*B$ comprised of all the absolute values of the sums and distances $a_i\pm b_j$ contains either the consecutive odd integers $\{1,3,5,\ldots 4m^2-1\}$ or with the inclusion of the set elements themselves, the consecutive integers $\{1,2,3,\ldots,2m(m+1)\}$ (an inclusive sum-and-distance system). Sum-and-distance systems can be thought of as a discrete analogue of the union of a Minkowski sum system with a Minkowski difference system. We show that they occur naturally within a traditional reversible square matrix, where conjugation with a specific orthogonal symmetric involution, always reveals a sum-and-distance system within the block structure of the conjugated matrix. Moreover, we show that the block representation is an algebra isomorphism. Building upon results of Ollerenshaw, and Br\'ee, for a fixed dimension $n$, we establish a bijection between the set of sum-and-distance systems and the set of traditional principal reversible square matrices of size $n\times n$. Using the $j$th non-trivial divisor function $c_j (n)$, which counts the total number of proper ordered factorisations of the integer $n= p_1^\ldots p_t^$ into $j$ parts, we prove that the total number of $n+n$ principal reversible square matrices, and so sum-and-distance systems, $N_n$, is given by \[ N_n = \sum_^ \left( c_j(n)^2 +c_(n)c_j(n) \right)=\sum_^ c_j^(n) c_j^(n). \] \[=\sum_^ \left(\sum^j_(-1)^ \prod_^t \right ) \left ( \sum^j_(-1)^ \prod_^t \right), \] where $\Omega(n)=a_1 + a_2 + \ldots + a_t$ is the total number of prime factors (including repeats) of $n$. Further relations between the divisor functions and their Dirichlet series are deduced, as well as a construction algorithm for all sum-and-distance systems of either type. Superalgebra structures relating to the matrix symmetry properties are identified, including those for the reversible and most-perfect square matrices of those considered by Ollerenshaw and Br\'ee. For certain symmetry types, links between the block representation constructed from a sum-and-distance system, and quadratic forms are also established.
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Lam, Wing Chung. "Second moment of the central values of the symmetric square L-functions." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429139505.
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Coatney, Ryan D. "Mean Square Estimate for Primitive Lattice Points in Convex Planar Domains." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2501.
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The Gauss circle problem in classical number theory concerns the estimation of N(x) = { (m1;m2) in ZxZ : m1^2 + m2^2 <= x }, the number of integer lattice points inside a circle of radius sqrt(x). Gauss showed that P(x) = N(x)- pi * x satisfi es P(x) = O(sqrt(x)). Later Hardy and Landau independently proved that P(x) = Omega_(x1=4(log x)1=4). It is conjectured that inf{e in R : P(x) = O(x^e )}= 1/4. I. K atai showed that the integral from 0 to X of |P(x)|^2 dx = X^(3/2) + O(X(logX)^2). Similar results to those of the circle have been obtained for regions D in R^2 which contain the origin and whose boundary dD satis fies suff cient smoothness conditions. Denote by P_D(x) the similar error term to P(x) only for the domain D. W. G. Nowak showed that, under appropriate conditions on dD, P_D(x) = Omega_(x1=4(log x)1=4) and that the integral from 0 to X of |P_D(x)|^2 dx = O(X^(3/2)). A result similar to Nowak's mean square estimate is given in the case where only "primitive" lattice points, {(m1;m2) in Z^2 : gcd(m1;m2) = 1 }, are counted in a region D, on assumption of the Riemann Hypothesis.
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Vitali, Raffaella. "Natural convection in a square cavity with discrete heat sources: an experimental and numerical analysis." Doctoral thesis, Università Politecnica delle Marche, 2016. http://hdl.handle.net/11566/242977.
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Lo studio della convezione naturale in cavità quadrata con sorgenti discrete è svolto sia sperimentalmente che numericamente. Sperimentalmente attraverso l'interferometria olografica e il Particle Image Velocimetry mentre numericamente attraverso l'utilizzo del software CFD ANSYS Fluent. Sono presentati 7 diversi studi di configurazioni della cavità dove vengono esaminati gli effetti sulla trasmissione di calore della dimensione delle sorgenti, dell'aspect ratio, della presenza di uno o due ostacoli orizzontali o verticali di diversa lunghezza e della presenza di una quinta sorgente al centro della cavità.
I risultati ottenuti dalle prove sperimentali e numeriche sono stati analizzati e confrontati nella forma di isoterme, streamlines, velocity maps e numero di Nusselt per numeri di Rayleigh da 2∙103 a 5∙105. E' stato studiata e sviluppata una correlazione tra il numero di Nusselt medio e il numero di Rayleigh per ogni configurazione. I risultati evidenziano le influenze delle modifiche apportate alla cavità sulla convezione naturale. L'applicazione industriale della cavità stabilirà poi la scelta dei parametri di progetto: se il progetto necessita di uno scambio termico maggiore, dovranno essere scelte le proporzioni e la ripartizione delle fonti di calore in modo appropriato, riducendo o eliminando la presenza di ostacoli nella cavità in modo di avere un maggiore scambio termico.<br>Natural convection in a square cavity with discrete heat sources is studied both experimentally and numerically. The results are presented for Rayleigh numbers from 2∙103 to 5∙105. The experimental techniques employed are Holographic Interferometry and Particle Image Velocimetry. ANSYS Fluent is the CFD software chosen for the numerical analysis. The case studies performed examine how heat transfer in the cavity is affected by modifying its characteristics. Case study 1 tests the influence of the heat sources’ size on heat transfer. The influence of cavity aspect ratio and presence of a baffle is studied in case study 2. Case Study 3 explores the effect baffle length has on natural convection in an enclosure. The effect of the length of a pair of horizontal baffles on natural convection is tested in case study 4. Case study 5 examines the effect the height of a pair of vertical baffles has on natural convective heat transfer in a cavity. The final case studies introduce a fifth heat source on the bottom cavity wall of a cavity with four heat sources. In case study 6, the effect of the position of the fifth heat source on natural convection in the cavity is analyzed. In case study 7, the effect of two heating configurations on heat transfer is evaluated.
The results obtained from the experimental and numerical tests in the form of isotherms, streamlines, velocity maps and average Nusselt numbers are analyzed and compared. A correlation between the average Nusselt and Rayleigh numbers for each configuration was studied and developed. The results showed that the characteristics altered in the case studies presented, modify heat transfer inside an enclosure. The intended application of the cavity will establish the choice of its design parameters: if natural convection is to be maximized, the aspect ratio and allocation of the heat sources will be chosen so as to have a greater temperature and fluid flow, reducing or eliminating the presence of baffles in the enclosure.
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Arslan, Bahar. "Functions of structured matrices." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/functions-of-structured-matrices(75511801-f8b8-4ac3-9434-35f88b1d0bb0).html.
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The growing interest in computing structured matrix functions stems from the fact that preserving and exploiting the structure of matrices can help us gain physically meaningful solutions with less computational cost and memory requirement. The work presented here is divided into two parts. The first part deals with the computation of functions of structured matrices. The second part is concerned with the structured error analysis in the computation of matrix functions. We present algorithms applying the inverse scaling and squaring method and using the Schur-like form of the symplectic matrices as an alternative to the algorithms using the Schur decomposition to compute the logarithm of symplectic matrices. There are two main calculations in the inverse scaling and squaring method: taking a square root and evaluating the Padé approximants. Numerical experiments suggest that using the Schur-like form with the structure preserving iterations for the square root helps us to exploit the Hamiltonian structure of the logarithm of symplectic matrices. Some type of matrices are nearly structured. We discuss the conditions for using the nearest structured matrix to the nearly structured one by analysing the forward error bounds. Since the structure preserving algorithms for computing the functions of matrices provide advantages in terms of accuracy and data storage we suggest to compute the function of the nearest structured matrix. The analysis is applied to the nearly unitary, nearly Hermitian and nearly positive semi-definite matrices for the matrix logarithm, square root, exponential, cosine and sine functions. It is significant to investigate the effect of the structured perturbations in the sensitivity analysis of matrix functions. We study the structured condition number of matrix functions defined between smooth square matrix manifolds. We develop algorithms computing and estimating the structured condition number. We also present the lower and upper bounds on the structured condition number, which are cheaper to compute than the "exact" structured condition number. We observe that the lower bounds give a good estimation for the structured condition numbers. Comparing the structured and unstructured condition number reveals that they can differ by several orders of magnitude. Having discussed how to compute the structured condition number of matrix functions defined between smooth square matrix manifolds we apply the theory of structured condition numbers to the structured matrix factorizations. We measure the sensitivity of matrix factors to the structured perturbations for the structured polar decomposition, structured sign factorization and the generalized polar decomposition. Finally, we consider the unstructured perturbation analysis for the canonical generalized polar decomposition by using three different methods. Apart from theoretical aspect of the perturbation analysis, perturbation bounds obtained from these methods are compared numerically and our findings show an improvement on the sharpness of the perturbation bounds in the literature.
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Wamala, Jacob Kasozi. "Stochastic modeling of flows behind a square cylinder with uncertain Reynolds numbers." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/74914.
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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 72-73).<br>In this thesis, we explore the use of stochastic Navier-Stokes equations through the Dynamically Orthogonal (DO) methodology developed at MIT in the Multidisciplinary Simulation, Estimation, and Assimilation Systems Group. Specifically, we examine the effects of the Reynolds number on stochastic fluid flows behind a square cylinder and evaluate computational schemes to do so. We review existing literature, examine our simulation results and validate the numerical solution. The thesis uses a novel open boundary condition formulation for DO stochastic Navier-Stokes equations, which allows the modeling of a wide range of random inlet boundary conditions with a single DO simulation of low stochastic dimensions, reducing computational costs by orders of magnitude. We first test the numerical convergence and validating the numerics. We then study the sensitivity of the results to several parameters, focusing for the dynamics on the sensitivity to the Reynolds number. For the method, we focus on the sensitivity to the: resolution of in the stochastic subspace, resolution in the physical space and number of open boundary conditions DO modes. Finally, we evaluate and study how key dynamical characteristics of the flow such as the recirculation length and the vortex shedding period vary with the Reynolds number.<br>by Jacob Kasozi Wamala.<br>S.B.
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Young, Brent O. J. "An examination of class number for [reproduction of quadratic extensions] where [reproduction of square root of d] has continued fraction expansion of period three /." Electronic version (PDF), 2005. http://dl.uncw.edu/etd/2005/youngb/brentyoung.pdf.
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Bronner, Alain. "Étude didactique des nombres réels : idécimalité et racine carrée." Grenoble 1, 1997. http://www.theses.fr/1997GRE10004.
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Cette these porte sur les roles -effectifs et possibles- des notions de racine carree et de nombre decimale dans la construction du concept de nombre reel au niveau de l'enseignement secondaire. Dans un premier temps, nous analysons les rapports aux nombres qui se sont developpes dans les institutions savantes, ainsi que l'evolution de la transposition didactique du concept de nombre dans l'enseignement secondaire depuis 1850. Nous avons ensuite etudie les rapports personnels d'eleves et d'enseignants actuels a ce concept. Ces differentes etudes nous ont permis de formuler des hypotheses sur les conditions d'apprentissage des nombres reels et le role de la racine carree et des nombres decimaux dans la reduction des vides didactiques reperes. Enfin, nous proposons un ensemble de situations didactiques qui satisfait certaines des conditions d'apprentissage precedentes
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Richardson, Robert. "On the Number of Integers Expressible as the Sum of Two Squares." Connect to resource online, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1265123768.
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Rix, James Gregory. "Hypercube coloring and the structure of binary codes." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2809.
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A coloring of a graph is an assignment of colors to its vertices so that no
two adjacent vertices are given the same color. The chromatic number of a
graph is the least number of colors needed to color all of its vertices. Graph
coloring problems can be applied to many real world applications, such as
scheduling and register allocation. Computationally, the decision problem
of whether a general graph is m-colorable is NP-complete for m ≥ 3.
The graph studied in this thesis is a well-known combinatorial object,
the k-dimensional hypercube, Qk. The hypercube itself is 2-colorable for all
k; however, coloring the square of the cube is a much more interesting problem.
This is the graph in which the vertices are binary vectors of length k,
and two vertices are adjacent if and only if the Hamming distance between
the two vectors is at most 2.
Any color class in a coloring of Q2k is a binary (k;M, 3) code. This thesis
will begin with an introduction to binary codes and their structure. One
of the most fundamental combinatorial problems is finding optimal binary
codes, that is, binary codes with the maximum cardinality satisfying a specified
length and minimum distance. Many upper and lower bounds have
been produced, and we will analyze and apply several of these. This leads
to many interesting results about the chromatic number of the square of the
cube.
The smallest k for which the chromatic number of Q2k is unknown is
k = 8; however, it can be determined that this value is either 13 or 14.
Computational approaches to determine the chromatic number of Q28 were
performed. We were unable to determine whether 13 or 14 is the true value;
however, much valuable insight was learned about the structure of this graph
and the computational difficulty that lies within. Since a 13-coloring of Q28
must have between 9 and 12 color classes being (8; 20; 3) binary codes, this
led to a thorough investigation of the structure of such binary codes.
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Matějíček, Jaroslav. "Generátory náhodných čísel pro kryptografii." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236519.
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The content of this thesis is the design and statistical tests of two di erent hardware random number generators. It also includes an overview of the sources of entropy, algorithms used to correct deviations from the normal distribution and the description of statistical tests.
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Constable, Jonathan A. "Kronecker's Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares." UKnowledge, 2016. http://uknowledge.uky.edu/math_etds/35.
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In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence.
In the second chapter we introduce the class number, proper class number and complete class number as well as two refinements, which facilitate the development of a connection with binary quadratic forms.
Our third chapter is devoted to deriving several class number formulas in terms of divisors of the determinant. This chapter also contains lower bounds on the class number for bilinear forms and classifies when these bounds are attained.
Lastly, we use the class number formulas to rigorously develop Kronecker's connection between binary bilinear forms and binary quadratic forms. We supply purely arithmetic proofs of five results stated but not proven in the original paper. We conclude by giving an application of this material to the number of representations of an integer as a sum of three squares and show the resulting formula is equivalent to the well-known result due to Gauss.
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Ghidelli, Luca. "On Gaps Between Sums of Powers and Other Topics in Number Theory and Combinatorics." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40014.
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One main goal of this thesis is to show that for every K it is possible to find K consecutive natural numbers that cannot be written as sums of three nonnegative cubes. Since it is believed that approximately 10% of all natural numbers can be written in this way, this result indicates that the sums of three cubes distribute unevenly on the real line. These sums have been studied for almost a century, in relation with Waring's problem, but the existence of ``arbitrarily long gaps'' between them was not known. We will provide two proofs for this theorem. The first is relatively elementary and is based on the observation that the sums of three cubes have a positive bias towards being cubic residues modulo primes of the form p=1+3k.
Thus, our first method to find consecutive non-sums of three cubes consists in searching them among the natural numbers that are non-cubic residues modulo ``many'' primes congruent to 1 modulo 3. Our second proof is more technical: it involves the computation of the Sato-Tate distribution of the underlying cubic Fermat variety {x^3+y^3+z^3=0}, via Jacobi sums of cubic characters and equidistribution theorems for Hecke L-functions of the Eisenstein quadratic number field Q(\sqrt{-3}). The advantage of the second approach is that it provides a nearly optimal quantitative estimate for the size of gaps: if N is large, there are >>\sqrt{log N}/(log log N)^4 consecutive non-sums of three cubes that are less than N. According to probabilistic models, an optimal estimate would be of the order of log N / log log N.
In this thesis we also study other gap problems, e.g. between sums of four fourth powers, and we give an application to the arithmetic of cubic and biquadratic theta series. We also provide the following additional contributions to Number Theory and Combinatorics: a derivation of cubic identities from a parameterization of the pseudo-automorphisms of binary quadratic forms; a multiplicity estimate for multiprojective Chow forms, with applications to Transcendental Number Theory; a complete solution of a problem on planar graphs with everywhere positive combinatorial curvature.
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Barajas, Leandro G. "Process Control in High-Noise Environments Using A Limited Number Of Measurements." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/7741.
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The topic of this dissertation is the derivation, development, and evaluation of novel hybrid algorithms for process control that use a limited number of measurements and that are suitable to operate in the presence of large amounts of process noise.
As an initial step, affine and neural network statistical process models are developed in order to simulate the steady-state system behavior. Such models are vitally important in the evaluation, testing, and improvement of all other process controllers referred to in this work. Afterwards, fuzzy logic controller rules are assimilated into a mathematical characterization of a model that includes the modes and mode transition rules that define a hybrid hierarchical process control. The main processing entity in such framework is a closed-loop control algorithm that performs global and then local optimizations in order to asymptotically reach minimum bias error; this is done while requiring a minimum number of iterations in order to promptly reach a desired operational window.
The results of this research are applied to surface mount technology manufacturing-lines yield optimization. This work achieves a practical degree of control over the solder-paste volume deposition in the Stencil Printing Process (SPP). Results show that it is possible to change the operating point of the process by modifying certain machine parameters and even compensate for the difference in height due to change in print direction.
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Thiebaut, Nicolene Magrietha. "Statistical properties of forward selection regression estimators." Diss., University of Pretoria, 2011. http://hdl.handle.net/2263/29520.
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Davison, Benjamin Kenneth. "Universal graph literacy: understanding how blind and low vision students can satisfy the common core standards with accessible auditory graphs." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47621.
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Auditory graphs and active point estimation provide an inexpensive, accessible alternative for low vision and blind K-12 students using number lines and coordinate graphs. In the first phase of this research program, a series of four psychophysics studies demonstrated an interactive auditory number line that enables blind, low vision, and sighted people to find small targets with a laptop, headphones, and a mouse or a keyboard. The Fitts' Law studies showed that, given appropriate auditory feedback, blind people can use a mouse. In addition, auditory feedback can generate target response patterns similar to when people use visual feedback. Phase two introduced SQUARE, a novel method for building accessible alternatives to existing education technologies. The standards-driven and teacher-directed approach generated 17 graphing standards for sixth grade mathematics, all of which emphasized point estimation. It also showed that how only few basic behavioral components are necessary for these graphing problems. The third phase evaluated active point estimation tools in terms of training, classroom situations, and a testing situation. This work shows that students can learn to graph in K-12 environments, regardless of their visual impairment. It also provides several technologies used for graphing, and methods to further develop education accessibility research.
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Deratany, Jay Paul. "Justice Square." Thesis, University of California, Riverside, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=1543191.
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<p> A young American woman who lost her mother in 9/11 needs a heart transplant and discovers that her only hope is to pay a small fortune for her Muslim doctor to escort her to Iran for the operation. Reluctantly putting her mistrust aside, she agrees to the bargain but once in Iran her doctor's mysterious behavior and the terrible social injustice she finds propel her to become enmeshed in the tragic case of two young boys framed and threatened with execution for homosexuality. Her doctor finally reveals what her behavior is endangering, a secret clinic he runs to aid those abused by the system. He wants her to ignore the plight of the boys but she refuses. Her discovery of the heart that had been buried under the scar tissue of 9/11 nearly destroys them both, but in the end their passion for justice saves them and brings two opposing cultures a bit closer.</p>
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Zakharchuk, I. O. "Central square." Thesis, Буковинський державний медичний університет, 2012. http://dspace.bsmu.edu.ua:8080/xmlui/handle/123456789/1404.
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Defty, Tracey L. "Square pegs." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2004. https://ro.ecu.edu.au/theses/855.
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This thesis comprises two parts: a creative component consisting of a first-draft script for a feature film, followed by an exegesis. The intention with the creative component was to work within the parameters of a low budget feature that is set in Perth and that makes use of a multi-strand narrative structure and extensive character development. The exegesis comprises a theoretical analysis of the creative component ‘Square Pegs’, and placing it within the context of an examination of feature film script development, in particularly multi-strand (or multi-plot) narrative structure, character development, individual storyline development and structure.
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Workalemahu, Tsegaselassie. "Singular Value Decomposition in Image Noise Filtering and Reconstruction." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/52.
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The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods assume that the images have been degraded by the application of a blurring function and the addition of noise. Finally, we present numerical experiments for the SVD restoration and compression to evaluate our computation.
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Langenau, Holger. "Squaring the square." Universitätsbibliothek Chemnitz, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-233031.
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Given a square with integer side length n, we ask for the number of different ways to divide it into sub-squares, considering only the list of parts. We enumerate all possible lists and check whether a placement with those squares is possible. In order to do this, we propose a new algorithm for creating perfect square packings.
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Poirier, Schmitz Alfredo. "Approximating square roots." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96654.
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Mazzon, Andrea. "Processo Square Root." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/3834/.
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Mayer, Sebastian. "Hilbert modular forms for the fields Q([square root]5), Q([square root]13) and Q([square root]17)." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985767022.
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Li, Luming. "Grand Theater Square - Shanghai." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2611.
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Thesis (M.Arch.) -- University of Maryland, College Park, 2005.<br>Thesis research directed by: Architecture. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Helfrick, John C. "Cyclic square wave voltammetry." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/30681.
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Eskiyerli, Mirat Hayri. "Square root domain filters." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299973.
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吳智豪 and Chi-ho Ng. "Metamorphosis of Statue Square." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31982116.
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Fryklind, Emelie. "Don´t be square." Thesis, Konstfack, Textil, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:konstfack:diva-5183.
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Ng, Chi-ho. "Metamorphosis of Statue Square." Hong Kong : University of Hong Kong, 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25944903.
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Van, Pelt Tom Gregory. "University Square Development Proposal." DigitalCommons@CalPoly, 2014. https://digitalcommons.calpoly.edu/theses/1275.
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The University Square Development Proposal (USDP) explores the redevelopment of the underutilized University Square site (the Site) in the City of San Luis Obispo (the City.) The Sites proximity to California Polytechnic State University, San Luis Obispo (Cal Poly), a university with significant student housing needs, makes it an ideal location for student housing. The City has also expressed interest in the Site, having identified it in the General Plan Land Use and Circulation Element (LUCE) update as a “Special Planning Area”. The LUCE proposes a new mixed-use typology on the Site that may include a mixture of multi-family housing, retail services, entertainment, and recreation.
The USDP is an early take on redevelopment of the Site, and provides a development option that accommodates both the objectives of Cal Poly, by providing student housing, and the City, by proposing a mixed-use development typology. To this end, the USDP includes a site assessment, project program, design vision, and financial analysis. The USDP concludes with project evaluations and lessons learned.
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Yelle, Céline. "Stack Number, Track Number, and Layered Pathwidth." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40348.
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In this thesis, we consider three parameters associated with graphs : stack number, track number, and layered pathwidth. Our first result is to show that the stack number of any graph is at most 4 times its layered pathwidth. This result complements an existing result of Dujmovic et al. that showed that the queue number of a graph is at most 3 times its layered pathwidth minus one (Dujmovic, Morin, and Wood [SIAM J. Comput., 553–579, 2005]). Our second result is to show that graphs of track number at most 3 have layered pathwidth at most 4. This answers an open question posed by Banister et al. (Bannister, Devanny, Dujmovic, Eppstein, and Wood [GD 2016, 499–510, 2016, Algorithmica, 1–23, 2018]).
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GOUVEA, LAURA VIEIRA DE. "CONTEMPORARY CARIOCA SQUARE: NA ERGONOMIC ANALYSIS OF THE BUILT ENVIRONMENT AT EDMUNDO BITTENCOURT SQUARE." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23924@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>Esta pesquisa apresenta uma avaliação ergonômica dos aspectos físicos de praças urbanas, desenvolvida com base na opinião da população. Buscou compreender a relação entre o mobiliário urbano e seus usuários, e ainda, a importância desta troca na vivência do espaço denominado Praça - espaços livres públicos, de lazer, de estar, de contestar, de viver. O cenário desta análise foi a cidade do Rio de Janeiro, facilitando assim a pesquisa de campo. A partir de uma seleção prévia, algumas praças cariocas foram avaliadas através da utilização de técnicas, com o objetivo de entender o seu sistema e sua funcionalidade. Por fim, uma única praça foi selecionada como objeto de estudo: a Praça Edmundo Bittencourt. A partir dos resultados obtidos através dos métodos aplicados durante a pesquisa foi possível avaliar a real importância e influência do mobiliário urbano no ambiente construído observado. Foi identificada uma dificuldade da parte dos usuários em compreender o espaço público como um conjunto de objetos. O design, o conforto e a qualidade dos mobiliários ficaram em segundo plano, diante da acessibilidade, da limpeza e do conforto ambiental.<br>This research presents an ergonomic evaluation the physical aspects of urban squares, developed based on the opinion of the population. Furthermore try to comprehend the relation between the urban furniture and the square visitors, and its importance in the existence of the space called Square - public open spaces, leisure, living, to challenge, to live. This analysis took place in Rio de Janeiro, turning easier the process of field research. From an initial selection, some carioca squares where evaluated through the application of techniques, with the objective of understanding its system and functionality. Eventually only one square was chosen as the object of study: the Edmundo Bittencourt Square. From the results obtained through the methods applied during this research, it was possible to evaluate the real importance and influence of the urban furniture in the considered environment in which it was built. It was identified a difficulty among part of users to understand the public space as a set of objects. The design, comfort and quality of the urban furniture remained in the background, in front of accessibility, cleanliness and the environments comfort.
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Schmidtke, Maximilian [Verfasser], and Annette [Akademischer Betreuer] Huber. "On the motivic Tamagawa number of number fields." Freiburg : Universität, 2018. http://d-nb.info/1166559335/34.
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Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.
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袁淸文 and Ching-man Yuen. "Redevelopment of Yue Man Square." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B3198373X.
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Yang, Zhicheng. "Dynamic buckling of square tubes." Thesis, University of Liverpool, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243260.
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Soloway, Scott M. (Scott Michael). "Wooster Square : revisiting urban renewal." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/77854.
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Yuen, Ching-man. "Redevelopment of Yue Man Square." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25955421.
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Taran, A. "Number Phi." Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/35106.
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Fibonacci is one of the most famous names in mathematics. This would come as a surprise to Leonardo Pisano, the mathematician we now know by that name. And he might have been equally surprised that he has been immortalised in the famous sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – rather than for what is considered his far greater mathematical achievement – helping to popularise our modern number system in the Latin-speaking world.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35106
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Khayat, Joy. "Effet du calcul mental et de la comparaison de nombres sur la performance de mouvements complexes." Thesis, Lyon, 2019. https://n2t.net/ark:/47881/m6n87950.
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Les nombres et les opérations sur les nombres contribuent à structurer notre rapport au monde. Il est ainsi logique que plusieurs études aient tenté de clarifier les mécanismes sous-tendant la cognition numérique ou les mécanismes cérébraux responsables de la dyscalculie. Ces études ont suggéré que les représentations mathématiques pourraient s’ancrer dans des expériences corporelles et/ou que la cognition numérique et la préparation du mouvement pourraient être sous-tendues par des mécanismes cérébraux similaires. Plusieurs études ont suggéré que des mouvements segmentaires ou du corps dans sa globalité peuvent influer sur la performance de tâches numériques ou arithmétiques. L’effet de telles taches sur la performance motrice demeurait en revanche à examiner, en particulier dans le cas des mouvements à haute intensité. Cet éventuel effet a été examiné via deux études impliquant au total 206 étudiants de sexe masculin, en Licence à la faculté de santé publique de l’Université Libanaise (Beyrouth, Liban). Une première étude (deux séries de deux expérimentations) a examiné les effets de la lecture d’un nombre et de la soustraction mentale complexe sur la hauteur de saut en squat jump vertical (SJV) et sur le temps de réponse d’un mouvement de pointage manuel (MPM). Dans chaque série, ces effets ont été examinés dans le cas de nombres en chiffres arabes et de nombres écrits en toutes lettres. Une seconde étude a examiné l’effet de tâches d’arithmétique mentale sur le temps de réponse d’un MPM. Trois expérimentations (1-3) ont étudié l’effet de la soustraction (complexe) et, respectivement, de : (1) l’addition (simple ou complexe), (2) la multiplication (simple ou complexe) et (3) la comparaison d’ensembles de points et la comparaison de nombres. Tout nombre était écrit en chiffres arabes. Dans ces deux études, les données ont été analysées en recourant à un modèle linéaire multiniveaux à effets mixtes. Les résultats de la première étude ont avéré une amélioration modérée de la performance en SJV (statistiquement significative, p < 0,05) suite à la lecture d’un nombre écrit en toutes lettres et un net effet de la performance en SJV et en MPM après une soustraction mentale (complexe) avec nombres en chiffres arabes (p < 0,001). Les résultats de la seconde étude ont avéré une amélioration statistiquement significative de la performance en MPM suite aux seuls calculs complexes (p < 0,001) et à la seule comparaison de nombres (p < 0,003). Ces résultats suggèrent que la relation entre une tâche arithmétique et la performance d’un mouvement à haute intensité est influencée par le format numérique, le recours à des nombres en chiffres arabes (à la différence de celui à des nombres écrits en toutes lettres ou à des ensembles de points) s’avérant conditionner un effet positif sur la performance motrice. Ces résultats ont cependant montré que cette condition n’est pas suffisante, la performance motrice étant améliorée après les tâches arithmétiques (avec chiffres arabes) favorisant le recours à des stratégies procédurales plutôt que le recours à des stratégies par recouvrement (en mémoire) de faits arithmétiques. Au regard de la littérature, l’effet des calculs mentaux complexes (soustraction, addition et multiplication) et de la comparaison de nombres, en notation arabique, sur la performance motrice peut s’expliquer par différents mécanismes. Cet effet peut être lié à la mobilisation de mécanismes d’encodage et/ou de mémorisation spécifiques des chiffres arabes. L’addition et la multiplication complexes et, éventuellement, la comparaison de nombres, peuvent en outre avoir favorisé une attention à la trajectoire optimale du mouvement subséquent. L’influence des calculs complexes et de la comparaison de nombres, avec notation arabique, sur la performance motrice pourrait enfin tenir à l’implication de régions cérébrales motrices, mobilisées durant une activité effective de calcul ou de comparaison<br>Numbers and operations on numbers help shape our relationship to the environment. It is thus unexceptional that several studies aimed at understanding the mechanisms of numerical cognition in the human brain and in particular those concerning the neural basis of dyscalculia. These studies have suggested that mathematical representations may be rooted in bodily experiences and/or that numerical cognition and movement preparation may share similar cerebral mechanisms. Several results have suggested that the performance of numerical and arithmetical tasks may be influenced by segmental and/or whole-body movements. The reverse influence of such tasks on motor performance remained however to be fully clarified especially in the case of maximal-intensity complex movements. This possibility has been approached by two studies involving a total of 206 male students (undergraduate students) at the Faculty of Public Health of the Lebanese University (Beirut, Lebanon). A first study including two series of two experiments examined the effects of number reading and mental subtraction (complex) on the height of a squat vertical jump (SVJ) and on the response time of a manual-pointing movement (MPM). In each series these effects have been examined in separate experiments using numbers written as words and in Arabic digits. A second study examined the effect of different arithmetical tasks on the response time of a MPM. Three experiments (1-3) examined the effect of mental subtraction (complex) and, respectively, of: (1) mental addition (simple or complex), (2) mental multiplication (simple or complex) and (3) the comparison of dot sets and number comparison. Each number was written in Arabic. In both studies the obtained data have been analyzed using a multilevel linear mixed-effect model. The results of the first study have shown a moderate increase of SVJ height (although statistically significant: p < .05) after number reading as words and a clear-cut increase of both MPT and SVJ performance after mental subtraction with Arabic digits (p < .001). The results of the second study have shown a statistically significant improvement of MPM performance only after the complex calculations (p < .001) and after number comparison (p < .003). These results suggest that the relationship between an arithmetical task and the performance of a high-intensity movement is influenced by the numerical format. It was found that the use of Arabic digits (but not the use of numbers written as words or represented by dot sets) is a condition to a positive effect of an arithmetical task upon motor performance. The results also showed that this condition is not sufficient. Motor performance was found to be improved only after arithmetical tasks (with Arabic digits) favoring the use of procedural strategies and not by arithmetical tasks favoring the use of retrieval strategies (of arithmetical facts). With regard to the literature, the effects of the complex calculations (subtraction, addition and multiplication) and of number comparison, with Arabic notation, on motor performance may be explained by different mechanisms. The effect of complex calculations and number comparison, with Arabic digits, on motor performance might be linked to mechanisms of encoding and/or memorization specific to this numerical format. Attention to the optimal path of movement might also has been favored by the spatial representation of numbers used to realize complex additions or subtraction and, possibly, to compare numbers. The influence of complex calculation and of number comparison, with Arabic digits, on motor performance might also be driven by a possible involvement, during actual calculation and comparison, of motor regions in the brain
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Lin, Yang. "Encounters with A Baroque Square and Skyscrapers: The urban transformation of Zhongshan Square Dalian China." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321642088.
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Xu, Hongyi. "Large eddy simulation of turbulent flows in square and annular ducts and confined square coaxial jet." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0006/NQ27860.pdf.
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Srar, Jalal Abdulsayed. "Adaptive antenna array beamforming using a concatenation of recursive least square and least mean square algorithms." Thesis, Curtin University, 2011. http://hdl.handle.net/20.500.11937/618.
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In recent years, adaptive or smart antennas have become a key component for various wireless applications, such as radar, sonar and cellular mobile communications including worldwide interoperability for microwave access (WiMAX). They lead to an increase in the detection range of radar and sonar systems, and the capacity of mobile radio communication systems. These antennas are used as spatial filters for receiving the desired signals coming from a specific direction or directions, while minimizing the reception of unwanted signals emanating from other directions.Because of its simplicity and robustness, the LMS algorithm has become one of the most popular adaptive signal processing techniques adopted in many applications, including antenna array beamforming. Over the last three decades, several improvements have been proposed to speed up the convergence of the LMS algorithm. These include the normalized-LMS (NLMS), variable-length LMS algorithm, transform domain algorithms, and more recently the constrained-stability LMS (CSLMS) algorithm and modified robust variable step size LMS (MRVSS) algorithm. Yet another approach for attempting to speed up the convergence of the LMS algorithm without having to sacrifice too much of its error floor performance, is through the use of a variable step size LMS (VSSLMS) algorithm. All the published VSSLMS algorithms make use of an initial large adaptation step size to speed up the convergence. Upon approaching the steady state, smaller step sizes are then introduced to decrease the level of adjustment, hence maintaining a lower error floor. This convergence improvement of the LMS algorithm increases its complexity from 2N in the case of LMS algorithm to 9N in the case of the MRVSS algorithm, where N is the number of array elements.An alternative to the LMS algorithm is the RLS algorithm. Although higher complexity is required for the RLS algorithm compared to the LMS algorithm, it can achieve faster convergence, thus, better performance compared to the LMS algorithm. There are also improvements that have been made to the RLS algorithm families to enhance tracking ability as well as stability. Examples are, the adaptive forgetting factor RLS algorithm (AFF-RLS), variable forgetting factor RLS (VFFRLS) and the extended recursive least squares (EX-KRLS) algorithm. The multiplication complexity of VFFRLS, AFF-RLS and EX-KRLS algorithms are 2.5N2 + 3N + 20 , 9N2 + 7N , and 15N3 + 7N2 + 2N + 4 respectively, while the RLS algorithm requires 2.5N2 + 3N .All the above well known algorithms require an accurate reference signal for their proper operation. In some cases, several additional operating parameters should be specified. For example, MRVSS needs twelve predefined parameters. As a result, its performance highly depends on the input signal.In this study, two adaptive beamforming algorithms have been proposed. They are called recursive least square - least mean square (RLMS) algorithm, and least mean square - least mean square (LLMS) algorithm. These algorithms have been proposed for meeting future beamforming requirements, such as very high convergence rate, robust to noise and flexible modes of operation. The RLMS algorithm makes use of two individual algorithm stages, based on the RLS and LMS algorithms, connected in tandem via an array image vector. On the other hand, the LLMS algorithm is a simpler version of the RLMS algorithm. It makes use of two LMS algorithm stages instead of the RLS – LMS combination as used in the RLMS algorithm.Unlike other adaptive beamforming algorithms, for both of these algorithms, the error signal of the second algorithm stage is fed back and combined with the error signal of the first algorithm stage to form an overall error signal for use update the tap weights of the first algorithm stage.Upon convergence, usually after few iterations, the proposed algorithms can be switched to the self-referencing mode. In this mode, the entire algorithm outputs are swapped, replacing their reference signals. In moving target applications, the array image vector, F, should also be updated to the new position. This scenario is also studied for both proposed algorithms. A simple and effective method for calculate the required array image vector is also proposed. Moreover, since the RLMS and the LLMS algorithms employ the array image vector in their operation, they can be used to generate fixed beams by pre-setting the values of the array image vector to the specified direction.The convergence of RLMS and LLMS algorithms is analyzed for two different operation modes; namely with external reference or self-referencing. Array image vector calculations, ranges of step sizes values for stable operation, fixed beam generation, and fixed-point arithmetic have also been studied in this thesis. All of these analyses have been confirmed by computer simulations for different signal conditions. Computer simulation results show that both proposed algorithms are superior in convergence performances to the algorithms, such as the CSLMS, MRVSS, LMS, VFFRLS and RLS algorithms, and are quite insensitive to variations in input SNR and the actual step size values used. Furthermore, RLMS and LLMS algorithms remain stable even when their reference signals are corrupted by additive white Gaussian noise (AWGN). In addition, they are robust when operating in the presence of Rayleigh fading. Finally, the fidelity of the signal at the output of the proposed algorithms beamformers is demonstrated by means of the resultant values of error vector magnitude (EVM), and scatter plots. It is also shown that, the implementation of an eight element uniform linear array using the proposed algorithms with a wordlength of nine bits is sufficient to achieve performance close to that provided by full precision.
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Lettington, Matthew C. "Topics related to the theory of numbers : integer points close to convex hypersurfaces, associated magic squares and a zeta identity." Thesis, Cardiff University, 2008. http://orca.cf.ac.uk/54865/.
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Let C be the boundary surface of a strictly convex d-dimensional body. Andrews obtained an upper bound in terms of M for the number of points on MC, the M-fold enlargement of C. We consider the integer points within a distance 5 of the hypersurface MC. Introducing S requires some uniform approximability condition on the surface C, involving determinants of derivatives. To obtain an asymptotic formula (main term the volume of the search region) requires the Fourier transform with conditions up to the Gd-th derivative. We obtain an upper bound subject to a Curvature Condition that re quires only first and second derivatives, that MC has a tangent hyperplane everywhere, and each two-dimensional normal section has radius of curvature in the range cqM +1/2 < p <C M 1/2, where cq and c are non-zero constants. Our main result is Theorem 2. THEOREM 2. Let C be a strictly convex hypersurface in d-dimensional space (d > 3), satisfying the Curvature Condition at size M. Then the total number, N, of integer points lying within a distance 6 of MC is bounded by the sum of two terms, one from Andrews's bound, the other from the hypervolume of the search region, with explicit constant factors involving 6, cq and c . In the body of the thesis, to simplify the notation, we use C for the enlarged surface called MC in this summary. In Part II we enumerate a class of special magic squares. We observe a new identity between values of the zeta functions at even integers.
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Ito, Masayuki, 直史 高木, Naofumi Takagi, and Shuzo Yajima. "Square rooting by iterative multiply-additions." Elsevier, 1996. http://hdl.handle.net/2237/2752.
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Britton, Michael C. "Practical square cross-section helical antennas." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0001/MQ43337.pdf.
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