Dissertations / Theses: 'Two Numbers'

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McNamara, James N. "Two new Ramsey numbers /." Online version of thesis, 1992. http://hdl.handle.net/1850/11146.

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Lin, Wensong. "Circular chromatic numbers and distance two labelling numbers of graphs." HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/591.

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Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis. In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently large even integer is the sum of two odd primes and k powers of two. Here k = 13, or = 7 under the generalized Riemann hypothesis. In 2010, B. Green and T. Tao obtained that every pair of linear equations in four prime variables with coefficients matrix A = (a_ij)s×t with s ≤ t, satisfying nondegenerate condition, that is, A has full rank and the only elements of the row-space of A over Q with two or fewer nonzero entries is the zero vector, is solvable. The restriction on the coefficient matrix means that they excluded the case of the binary Goldbach problem. Motivated by the above results, it is obtained that for every pair of sufficiently large positive even integers B1, B2, the simultaneous equation {█({B1 = p1 + p2 + 2v1 + 2v2 + · · · + 2vk ,@B2 = p3 + p4 + 2v1 + 2v2 + · · · + 2vk ,)┤ (1) is solvable, where p1, · · · , p4 are odd primes, each vi is a positive integer, and the positive integer k ≥ 63 or ≥ 31 under the generalized Riemann hypothesis. Note that, in 1989, M.C. Liu and K.M. Tsang have obtained that subject to some natural conditions on the coefficients, every pair of linear equations in five prime variables is solvable. Therefore one class of pairs of linear equations in four prime variables with special coefficient matrix and powers of two is considered. Indeed, it is deduced that every pair of integers B1 and B2 satisfying B1 ≡ 0 (mod 2), 3BB1 > e^(eB^48 ), B2 ≡ ∑_1^4▒= 1^(a_i ) (mod 2) and |B2| < BB1, where B = max1≤j≤4(2, |aj|), can be represented as {█(B1 = 〖p1〗_1 + p2 + 2^(v_1 ) + 2^(v_2 )+ · · · + 2^(v_k )@B2 = a1p1 + a2p2 + a3p3 + a4p4 + 2^(v_1 )+ 2^(v_2 )+ · · · + 2^(v_k ) )┤ (2) with k being a positive integer. Here p1, · · · p4 are odd primes, each 〖v 〗_iis a positive integer and the integral coefficients ai (i = 1, 2, 3, 4) satisfy {█((〖a 〗_1- 〖a 〗_2, 〖a 〗_3, 〖a 〗_4) = 1,@〖a 〗_1 〖a 〗_2< 0, 〖a 〗_3 〖a 〗_4<0,)┤ Moreover it is calculated that the positive integer k ≥ g(〖a 〗_1- 〖a 〗_2, 〖a 〗_3, 〖a 〗_4) where g(〖a 〗_21- 〖a 〗_22, 〖a 〗_23, 〖a 〗_24) = [(log⁡〖G(〖a 〗_21, …, 〖a 〗_24 〗)-log⁡〖F (〖a 〗_21, …, 〖a 〗_24)〗)/log0.975805-84.0285], (3) G(〖a 〗_21, 〖a 〗_22, 〖a 〗_23, 〖a 〗_24) = (min(1/(|a_24 |), 1/(|a_23 |)) - (〖|a〗_(21 )- a_22 |)/(|〖a_23 a〗_24 |) 〖(3B)〗^(-1) ×〖(3B)〗^(-1) (1-0.000001)- 〖(3B)〗^(-1-4), with B = max1≤j≤4(2, |a2j|), and F(a_21, …, a_24) = √(f(a_21)f〖(a〗_22 )) with f(a_2i) = {█(4414.15h (a_21-1)+5.088331 if a_21≠1@59.8411 if a_21=1,)┤ for i = 1, 2, and h(n) =∏_(p|n,p>2)▒(p-1)/(p-2). This result, if without the powers of two, can make up some of the cases excluded in Green and Tao’s paper. published_or_final_version Mathematics Doctoral Doctor of Philosophy

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Armulik, Villem-Adolf. "Ramsey Numbers and Two-colorings ofComplete Graphs." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-44610.

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Ramsey theory has to do with order within disorder. This thesis studies two Ramsey numbers, R(3; 3) and R(3; 4), to see if they can provide insight into finding larger Ramsey numbers. The numbers are studied with the help of computer programs. In the second part of the thesis we try to create a coloring of K45 which lacks monochromatic K5 and where each vertex has an equal degree for both color of edges. The results from studying R(3; 3) and R(3; 4) fail to give any further insight into larger Ramsey numbers. Every coloring of K45 we produce contains a monochromatic K5.

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Coward, Daniel R. "Sums of two rational cubes." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320587.

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Fernandez, Manuel Franco. "Local root numbers of two-dimensional symplectic representations." Thesis, University of Southampton, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432725.

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Djang, Claire. "Two-Coloring Cycles In Complete Graphs." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1370618319.

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Han, Sang-Geun. "Two applications of p-adic L-functions /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu148733154171079.

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Straw, N. A. "Resource limitation and competition in two tephritid flies attacking the flowerheads of lesser burdock (Arctium minus)." Thesis, University of Cambridge, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384516.

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Stone, Megan Elizabeth, and Megan Elizabeth Stone. "Eigenvalue Densities for the Hermitian Two-Matrix Model and Connections to Hurwitz Numbers." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/626370.

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This dissertation investigates the limiting distribution of eigenvalues of pairs of matrices (M_1,M_2) belonging to the Hermitian two-matrix model. This model is an example of a larger class of models, "multi-matrix models", which aim to generalize the Hermitian one-matrix model. The interaction between matrices in multi-matrix models makes the analysis of the eigenvalue distributions more difficult than those for the one-matrix model. This dissertation makes use of a recent result which connects the interaction term for the two-matrix model to a combinatorial geometry problem. In particular, the interaction term is written as the Harish-Chandra-Itzykson-Zuber integral, which is expanded in a neighborhood of \tau=0, where \tau is the coupling constant appearing in the interaction term. The expansion involves monotone double Hurwitz numbers, which count a collection of ramified coverings of the two-sphere. Using this expansion, and its connection to monotone double Hurwitz numbers, this dissertation purports to describe a variational problem which describes the joint eigenvalue densities for the two-matrix model up to order \tau^2.

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Moss, Joan. "Deepening children's understanding of rational numbers, a developmental model and two experimental studies." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0021/NQ49900.pdf.

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Dimas, Athanassios A. "Interaction between a two-dimensional wake and the free surface at low Froude numbers." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14730.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1988, and (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1988. Bibliography: leaf 84. by Athanassios A. Dimas. M.S.

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Lin, C. A. "Computational study of compressibility effects in two-dimensional steady turbulent junction flow at high subsonic mach numbers." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380181.

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Rasch, Dieter, Thomas Rusch, Marie Simeckova, Klaus D. Kubinger, Karl Moder, and Petr Simecek. "Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers." Springer, 2009. http://dx.doi.org/10.1070/s00362-009-0254-4.

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In variety testing as well as in psychological assessment, the situation occurs that in a two-way ANOVA-type model with only one replication per cell, analysis is done under the assumption of no interaction between the two factors. Tests for this situation are known only for fixed factors and normally distributed outcomes. In the following we will present five additivity tests and apply them to fixed and mixed models and to quantitative as well as to Bernoulli distributed data. We consider their performance via simulation studies with respect to the type-I-risk and power. Furthermore, two new approaches will be presented, one being a modification of Tukey's test and the other being a new experimental design to test for interactions.

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Rivedal, Nikolai Hydle. "Two-dimensional Simulations of Particle Deposition on a Cylinder in a Turbulent Cross Flow at Intermediate Reynolds Numbers." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13994.

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The behaviour of particles in turbulent flow, with emphasis on particle deposition on both the frontside and backside of a cylinder, was investigated by means of Direct Numerical Simulations. One-way coupling between the fluid and the particles was applied. Simulations of turbulence forced at small, intermediate and large scales were run on a three-dimensional domain. The turbulence was used as inlet on a two-dimensional flow domain, where a Lagrangian tracker was used to compute the particle motions. The Reynolds numbers used were Rec = 421 and Rec = 1685. For intermediate Stokes numbers, or particle sizes, the number of particles deposited increased when the Reynolds number was raised. The presence of turbulence lead to a further increase in the deposition for these Stokes numbers, compared to the deposition in laminar flow. The increase was at its highest for large scale forced turbulence. The increased deposition of intermediate Stokes numbers on the frontside of the cylinder in turbulent flow was found to be related to the variance of the effective Stokes number, resulting from the fluctuating nature of the turbulent velocity. The deposition of particles with small Stokes numbers was also altered by the presence of turbulence, but this could not be explained by the variance of Stokes number. The mechanism leading to deposition of these smallest particles is related to the turbulent eddies close to the boundary layer of the cylinder, and will need further study. At the backside of the cylinder, the increased deposition at raised Reynolds number and at the presence of turbulence was related to the magnitude of vorticity. Furthermore, preferential concentration of particles in turbulence was observed in the Rec = 1685 cases, demonstrating the effect of the vorticity magnitude being sustained throughout the domain.

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Trespalacios, Jesus. "The Effects of Two Generative Activities on Learner Comprehension of Part-Whole Meaning of Rational Numbers Using Virtual Manipulatives." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/26508.

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The study investigated the effects of two generative learning activities on students’ academic achievement of the part-whole representation of rational numbers while using virtual manipulatives. Third-grade students were divided randomly in two groups to evaluate the effects of two generative learning activities: answering-questions and generating-examples while using two virtual manipulatives related to part-whole representation of rational numbers. The study employed an experimental design with pre- and post-tests. A 2x2 mixed analysis of variance (ANOVA) was used to determine any significant interaction between the two groups (answering questions and generating-examples) and between two tests (pre-test and immediate post-test). In addition, a 2x3 mixed analysis of variance (ANOVA) and a Bonferroni post-hoc analysis were used to determine the effects of the generative strategies on fostering comprehension, and to determine any significant differences between the two groups (answering-questions and generating-examples) and among the three tests (pre-test, immediate post-test, and delayed posttest). Results showed that an answering-questions strategy had a significantly greater effect than a generating-examples strategy on an immediate comprehension posttest. In addition, no significant interaction was found between the generative strategies on a delayed comprehension tests. However a difference score analysis between the immediate posttest scores and the delayed posttest scores revealed a significant difference between the answering-questions and the generating-examples groups suggesting that students who used generating-examples strategy tended to remember relatively more information than students who used the answering-questions strategy. The findings are discussed in the context of the related literature and directions for future research are suggested. Ph. D.

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Alfredsson, Jessica. "Molecular Studies of Mast Cell Migration and Apoptosis : Two Ways of Regulating Mast Cell Numbers at Sites of Inflammation." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4807.

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Schirmer, Trenton Frederick. "Two varieties of tunnel number subadditivity." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/3379.

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Knot theory and 3-manifold topology are closely intertwined, and few invariants stand so firmly in the intersection of these two subjects as the tunnel number of a knot, denoted t(K). We describe two very general constructions that result in knot and link pairs which are subbaditive with respect to tunnel number under connect sum. Our constructions encompass all previously known examples and introduce many new ones. As an application we describe a class of knots K in the 3-sphere such that, for every manifold M obtained from an integral Dehn filling of E(K), g(E(K))>g(M).

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Schill, Collberg Adam. "The last two digits of mk." Thesis, Linköpings universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-78532.

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In this thesis the last two digits of m^k, for different cases of the positive integers m and k, in the base of 10 has been determined. Moreover, using fundamental theory from elementary number theory and abstract algebra, results most helpful in finding the last two digits in any base b has been regarded and developed, such as how to reduce large m and k to more manageable numbers.

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Chan, Wai-lan Winnie. "An investigation into two-digit number processing among Chinese children and adults." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B42841495.

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Gaebler, Robert. "Alexander Polynomials of Tunnel Number One Knots." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/162.

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Every two-bridge knot or link is characterized by a rational number p/q, and has a fundamental group which has a simple presentation with only two generators and one relator. The relator has a form that gives rise to a formula for the Alexander polynomial of the knot or link in terms of p and q [15]. Every two-bridge knot or link also has a corresponding “up down” graph in terms of p and q. This graph is analyzed combinatorially to prove several properties of the Alexander polynomial. The number of two-bridge knots and links of a given crossing number are also counted.

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Cochran, Christopher S. "Even-number spin correlations on two-dimensional Ising lattice structures." Virtual Press, 2002. http://liblink.bsu.edu/uhtbin/catkey/1237760.

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Many physical systems can be represented by a regular arrangement of molecules in a lattice structure. Knowing how neighboring molecules in the lattice interact with one another can give great insight into a material's macroscopic behavior. A very popular and effective means of investigating these microscopic interactions is the Ising Model. This model, suggested first by Wilhelm Lenz in 1920 and later expanded by Ernst Ising in 1925, is based on the assumptions that each molecule in a lattice structure can be represented by its spin value (+l or -1) and that only nearest neighbors contribute to the total interaction energy. The Ising Model, which was initially used in the study of ferromagnetic systems, can now be used to study a variety of physical systems. Some of these include antiferromagnetic crystals, binary alloys, DNA, and lattice gasses. Department of Physics and Astronomy

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Norem, Margaret A. "Box Number Two Arrives at the Svalbard Global Seed Vault." University of Arizona (Tucson, AZ), 2012. http://hdl.handle.net/10150/556792.

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Chan, Wai-lan Winnie, and 陳偉蘭. "An investigation into two-digit number processing among Chinese children and adults." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841495.

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Hoehner, Steven D. "The Hasse-Minkowski Theorem in Two and Three Variables." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338317481.

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Childers, Kevin Ronald. "Octahedral Extensions and Proofs of Two Conjectures of Wong." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5314.

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Consider a non-Galois cubic extension K/Q ramified at a single prime p > 3. We show that if K is a subfield of an S_4-extension L/Q ramified only at p, we can determine the Artin conductor of the projective representation associated to L/Q, which is based on whether or not K/Q is totally real. We also show that the number of S_4-extensions of this type with K as a subfield is of the form 2^n - 1 for some n >= 0. If K/Q is totally real, n > 1. This proves two conjectures of Siman Wong.

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Gottapu, Manohar. "Two-phase flow: buoyancy driven flow of a partially miscible droplet at low Reynolds number a thesis presented to the faculty of the Graduate School, Tennessee Technological University /." Click to access online, 2009. http://proquest.umi.com/pqdweb?index=0&did=2000384971&SrchMode=1&sid=3&Fmt=6&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1279288319&clientId=28564.

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Cole, Sarah Elizabeth S. B. Massachusetts Institute of Technology. "Design of two-tailed swimmer to swim at low-Reynolds number." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54530.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009. Cataloged from PDF version of thesis. Includes bibliographical references (p. 30). In the realm of systems with Reynolds numbers less than 1, swimming is a difficult task. Viscous forces from the fluid dominate inertial forces. In order to propel itself, a mechanism must be designed to overcome the viscous forces from the fluid and satisfy the non-reciprocal, cyclic motion requirements of the Scallop Theorem. Furthermore, a swimmer must employ one of the three mechanisms stated by Purcell to be capable of swimming at low Reynolds number, a three link swimmer, a corkscrew, or a flexible tail. Three devices utilizing the flexible-tail paradigm of swimming were tested using silicon oil to simulate a Reynolds number of approximately 0.6. Design parameters were uncovered which determine the successfulness of the swimmer and can be used for creating future successful flexible-tail swimmers. by Sarah Elizabeth Cole. S.B.

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Simpson, Glen E. "PSL(2,7)-Extensions with Certain Ramification at Two Primes." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd469.pdf.

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Derbyshire, John. "The two-stage weighted lottery solution to the Number Problem : a defence." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/the-twostage-weighted-lottery-solution-to-the-number-problem-a-defence(0f658f31-75af-4285-953e-8f5e4ff239a7).html.

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The subject of this thesis is the Number Problem, a question of distributive justice in which an indivisible benefit or burden must be allocated to one group of individuals at the expense of at least one other group, where the groups contain different people. When these groups differ in size, the Number Problem asks whether the interests of the largest group should always prevail in virtue of the greater number of people that stand to benefit. My answer is that they should not, that we should hold a two-stage weighted lottery to decide what to do. My method begins by assessing the relative loss facing each person in the problem, connecting the strength of a person’s claim for aid to the magnitude of the potential loss that they face. Claims are then given a chance of selection in proportion to their relative strengths by way of a lottery in the first stage of my solution. The result of the lottery is then optimized in accordance with the Pareto principle in the second stage, giving the overall result that individuals in larger groups stand a proportionally greater ex ante chance of receiving the good under distribution. The arguments in this thesis divide into two broad thematic sections: arguments in favour of my solution and objections to rival approaches. Included within the former are two arguments that demonstrate how the two-stage weighted lottery result can be derived from the rival positions of equal maximum chances and claim balancing. Similarly, I offer a range of responses to the main objections to the two-stage weighted lottery here. These objections include the ‘incredulous stare’, the criticism that my solution implausibly gives one person some chance of being saved at the expense of everyone else alive. After considering and rejecting three alternative solutions – equal maximum chances, claim balancing and hybrid – the final part of the thesis addresses the expanded Number Problem where the choice concerns both different sized groups and different potential individual losses. Here I demonstrate that the two-stage weighted lottery approach can solve the most complex expanded Number Problem – even when the choice involves overlapping sets of individuals and different probabilities of successfully aiding each person.

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Reasor, Jr Daniel A. "NUMERICAL SIMULATION OF TWO FLOW CONTROL APPROACHES FOR LOW REYNOLDS NUMBER APPLICATIONS." UKnowledge, 2007. http://uknowledge.uky.edu/gradschool_theses/461.

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Current research in experimental and computational fluid dynamics is focused in the area of flow control. Flow control devices are usually classified as either passive or active. Plasma actuators are active flow control devices that require input from an external power source. Current efforts have modeled the effects of plasma actuators as a body force near the electrode. The research presented herein focuses on modeling the fluid-plasma interaction seen in dielectric barrier discharge plasma actuators as a body force vector in the region above the embedded electrode using computational fluid dynamics (CFD). This body force is modeled as the product of the gradient of the potential due to the electric field and the net charge density. In a passive flow control study, two-dimensional simulations using CFD are done with a smooth and bumpy Eppler 398 airfoil with laminar, transition, and turbulent models in an effort to improve the understanding of the flow over bumpy airfoils and to quantify the advantages or disadvantages of the bumps.

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PORTELA, RAQUEL RIBEIRO BARROSO. "LEGENDRIAN KNOTS AND THE MAXIMAL THURSTON-BENNEQUIN NUMBER OF TWO-BRIDGE KNOTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=11429@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO O propósito deste trabalho é apresentar a teoria dos nós legendreanos, que diz respeito a nós tangentes a uma estrutura de contato, assim como demonstrar o Teorema do Número Máximo de Thurston- Bennequin para nós de 2-pontes em termos do polinômio de Kaumman. Iniciamos este trabalho com uma introdução aos nós topológicos. Apresentamos a teoria de nós legendreanos, dando ênfase aos nós legendreanos em R3 tangentes à estrutura de contato canônica neste espa»co. Apresentamos dois invariantes clássicos de nós legendreanos: os números de Thurston- Bennequin e Maslov. Finalmente, obtemos o número máximo de Thurston-Bennequin, motivo de estudos nos dias atuais, para todos os nós legendreanos topologicamente isotópicos aos nós de 2-pontes na estrutura de contato canônica em R3. The purpose of this work is to present the Theory of the Legendrian knots, which refers to knots tangent to a contact structure, and also to prove the Theorem of the Maximal Thurston-Bennequin number for 2- bridge knots in terms of the Kaumman polynomial.We begin this study with an introduction to topological knots. We present the theory of the Legendrian knots, we emphasize Legendrian knots in R3, knots tangent to the standard contact structure in this space. We present two classical invariants of Legendrian knots, the Thurston-Bennequin and Maslov numbers. Finally we show the maximal Thurston-Bennequin number for Legendrian two- bridge knots in standard contact structure on R3, an active area of current research.

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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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Ahmed, Ibrahim H. I. "Mathematical modeling of an epidemic under vaccination in two interacting populations." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_8857_1360922452.

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In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, the susceptible individuals, usually denoted by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected individual, at recovery, moves to the class R. Firstly we develop a model describing two interacting populations with vaccination. Assuming the vaccination rate in both groups or components are constant, we calculate a threshold parameter and we call it a vaccination reproductive number. This invariant determines whether the disease will die out or becomes endemic on the (in particular, local) population. Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally asymptotically stable if the vaccination reproductive number is less than one. Also our stability analysis show that the global stability of the disease free equilibrium depends on the basic reproduction number, not the vaccination reproductive number. If the vaccination reproductive number is greater than one, then the disease free equilibrium is unstable and there exists three endemic equilibrium points in our model. Two of these three endemic equilibria are so-called boundary equilibrium points, which means that the infection is only in one group of the population. The third one which we focus on is the general endemic point for the whole system. We derive a threshold condition that determines whether the endemic equilibria is locally asymptotically stable or not. Secondly, by assuming that the rate of vaccination in the migrant population is constant, we apply optimal control theory to find an optimal vaccination strategy in the local population. Our numerical simulation shows the effectiveness of the control strategy. This model is suitable for modeling the real life situation to control many communicable diseases. Models similar to the model used in the main contribution of our dissertation do exist in the literature. In fact, our model can be regarded as being in-between those of [Jia et al., Theoretical Population Biology 73 (2008) 437-448] and [Piccolo and Billings, Mathematical and Computer Modeling 42 (2005) 291-299]. Nevertheless our stability analysis is original, and furthermore we perform an optimal control study whereas the two cited papers do not. The essence of chapter 5 and 6 of this dissertation is being prepared for publication.

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Arasanipalai, Sriram Sharan. "Two-equation model computations of high-speed (ma=2.25, 7.2), turbulent boundary layers." Thesis, [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-3186.

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Marir, F. "The application of number theoretic transforms to two dimensional convolutions and adaptive filtering." Thesis, University of Newcastle Upon Tyne, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374136.

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37

Peng, Haolei. "Effects of two-way left-turn lane on roadway safety." [Tampa, Fla.] : University of South Florida, 2004. http://purl.fcla.edu/fcla/etd/SFE0000289.

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38

Fu, Yun. "Linear stability of an interface between two incompressible fluids." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1142955745.

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39

Salt, Brittney M. "MONOID RINGS AND STRONGLY TWO-GENERATED IDEALS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/31.

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This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.

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40

Pritchard, David Thomas. "Some problems in two-phase flow : intertidal mudflats and low Reynolds number gravity currents." Thesis, University of Bristol, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391189.

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41

Rival, Elisabeth. "L'Univers de Peter Greenaway : ou L'art du négatif : Films-fictions de "Draughtsman's Contract" à "Baby of Mâcon"." Lille 3, 1999. http://www.theses.fr/1999LIL30001.

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42

Pluntze, Stephen Christian. "Reynolds number trends in computational solutions of two-dimensional airfoils with Taguchi techniques and grid resolution /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/10006.

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43

Dupuy, Benjamin. "Etudes sur les équations de Ramanujan-Nagell et de Nagell-Ljunggren ou semblables." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2009. http://tel.archives-ouvertes.fr/tel-00429631.

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Dans cette thèse, on étudie deux types d'équations diophantiennes. Une première partie de notre étude porte sur la résolution des équations dites de Ramanujan-Nagell $Cx^2+b^{2m}D=y^n$. Une deuxième partie porte sur les équations dites de Ngell-Ljunggren\\ $\frac{x^p+y^p}{x+y}=p^ez^q$ incluant le cas diagonal $p=q$. Les nouveaux résultats obtenus seront appliqués aux équations de la forme $x^p+y^p=Bz^q$. L'équation de Catalan-Fermat (cas $B=1$) fera l'objet d'un traitement à part.

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44

Bennington, Jeremy Lawrence. "Effects of Various Shaped Roughness Elements in Two-Dimensional High Reynolds Number Turbulent Boundary Layers." Thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/34907.

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Modeling the effects of surface roughness is an area of concern in many practical engineering applications. Many current roughness models to this point have involved the use of empirical 'constants' and equivalent sand grain roughness. These underdeveloped concepts have little direct relationship to realistic roughness and cannot predict accurately and consistently the flow characteristics for different roughness shapes. In order to aid in the development of turbulence models, the present research is centered around the experimental investigation of seven various shaped single roughness elements and their effects on turbulence quantities in a two-dimensional turbulent boundary layer. The elements under scrutiny are as follows: cone, cone with spatial variations equal to the smallest sublayer structure length scale, cone with spatial variations equal to 2.5 times the smallest sublayer structure length scale, Gaussian-shaped element, hemisphere, cube aligned perpendicular to the flow (cube at 90°), and a cube rotated 45° relative to the flow. The roughness element heights, k+, non-dimensionalized by the friction velocity (U_tau) of the approaching turbulent boundary layer, are 145, 145, 145, 145, 80, 98, and 98 respectively. Analysis of a three-dimensional fetch of the same Gaussian-shaped elements described previously was also undertaken. In order to analyze the complex flow fields, detailed measurements were obtained using a fine-measurement-volume (50 micron diameter) three-velocity component laser-Doppler velocimetry (LDV) system. The data reveals the formation of a horseshoe vortex in front of the element, which induces the downwash of higher momentum fluid toward the wall. This 'sweep' motion not only creates high Reynolds stresses (v^2, w^2, -uv) downstream of the element, but also leads to higher skin-friction drag. Triple products were also found to be very significant near the height of the element. These parameters are important in regards to the contribution of the production and diffusion of the turbulent kinetic energy in the flow. The 'peakiness' of the roughness element was found to have a direct correlation to the production of circulation, whereas the spatial smoothing does not have an immense effect on this parameter. The peaked elements were found to have a similar trend in the decay of circulation in the streamwise direction. These elements tend to show a decay proportional to (x/d)^-1.12, whereas the cube elements and the hemisphere do not have a common trend. A model equation is proposed for a drag correlation common to all roughness elements. This equation takes into account the viscous drag and pressure drag terms in the calculation of the actual drag due to the roughness elements presence in the boundary layer. The size, shape, frontal and wetted surface areas of the roughness elements are related to one another via this model equation. Flow drawings related to each element are presented which gives rise to a deeper understanding of the physics of the flow associated with each roughness element. Master of Science

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PYLES, JOHN MICHAEL. "AN EXAMINATION OF TWO-DIMENSIONAL ROLL OSCILLATIONS ON THE LIQUID DYNAMICS OF A PARTIALLY FILLED RECTANGULAR TANK." University of Cincinnati / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1162913711.

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46

Bhaumik, Claire Das. "Modelling of two-dimensional suspension flows at low Reynolds number using a novel boundary element formulation." Thesis, Brunel University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.422412.

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47

Karuhanga, Martin. "Estimates for the number of eigenvalues of two dimensional Schrödinger operators lying below the essential spectrum." Thesis, King's College London (University of London), 2016. https://kclpure.kcl.ac.uk/portal/en/theses/estimates-for-the-number-of-eigenvalues-of-two-dimensional-schroedinger-operators-lying-below-the-essential-spectrum(696e1e8c-a43e-43d2-80da-c05e09be5a97).html.

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The celebrated Cwikel-Lieb-Rozenblum inequality gives an upper estimate for the number of negative eigenvalues of Schrödinger operators in dimension three and higher. The situation is much more difficult in the two dimensional case. There has been significant progress in obtaining upper estimates for the number of negative eigenvalues of two dimensional Schrödinger operators on the whole plane. In this thesis, we present upper estimates of the Cwikel-Lieb-Rozenblum type for the number of eigenvalues (counted with multiplicities) of two dimensional Schrödinger operators lying below the essential spectrum in terms of the norms of the potential. The problem is considered on the whole plane with different supports of the potential (in particular, sets of dimension 2 (0; 2)) and on a strip with various boundary conditions. In both cases, the estimates involve weighted L1 norms and Orlicz norms of the potential.

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48

Wenger, Christian W. "Analysis of Two-point Turbulence Measurements for Aeroacoustics." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/30837.

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Simultaneous two-point three-component four-sensor hot-wire velocity measurements taken in three flows of aeroacoustic interest are here analyzed. The analyses provide information on the turbulence structure of the flows as it would be encountered by hypothetical noise producing blades passing through the flows. Two-point measurements taken in the first flow, a lifting wake from a rectangular NACA 0012 half wing, are used to calculate space-time correlation functions and 'pointwise' wave number frequency spectra. Two upwash spectra, calculated for locations in the region of the wake that is roughly homogenous in the spanwise direction, are direct estimates of the full wave number frequency spectra at their locations. As such, they are used to perform aeroacoustic calculations, and the results are compared to results achieved using the von KÃ¡rmÃ¡n isotropic spectrum. Amiet's approximation, where the wave number frequency spectra can be represented by the correlation length scales is found to hold reasonably well for the measured spectra. The two-point measurements in the second flow, a vortex/blade-tip interaction, are analyzed to provide information useful to researchers of blade-wake interaction noise produced by helicopter rotors. Space-time correlation functions and wave number frequency spectra are calculated for five cuts through the region of interaction. The correlation functions provide information concerning the turbulence length scales found in the interaction region. The spectra are compared to the von KÃ¡rmÃ¡n isotropic spectrum and found to be greatly different. However, the spectra do bear some resemblance to spectra calculated in the spanwise homogenous region of the lifting wake. The two-point measurements taken in the third flow, the wake from a fan cascade, are analyzed to provide information of use to modelers of broadband noise produced through rotor wake/stator interactions. In particular, space-time correlation functions are calculated for a grid of two-point measurements, which allows the estimation of the turbulence structure as seen by a passing stator blade. Space-time correlation functions and wave number frequency spectra are calculated for various stator configurations. The implications of engine operating speed and stator configuration for broadband noise production are discussed. [Vita removed March 2, 2012. GMc] Master of Science

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49

Labadin, Jane. "Theory and computation of high Reynolds number fluid flow over and around two and three dimensional obstacles." Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397653.

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50

Jones, Margaret Lewis. "A comparison of two strategies used to reduce the number of dropout-prone students in urban middle schools." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39821.

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The primary purpose of this study was to compare academic achievement and behavioral characteristics of students enrolled in the Career Exploratory Middle School (CEMS), an alternative middle school, with the academic achievement and behavioral characteristics of students in a project called Building and Supplementing Instruction in the Core Skills (BASICS), a dropout prevention program within traditional middle schools. The independent· variable was CEMS. The dependent variables were SRA composite scores, absences, days tardy, grade point average and office referrals. Project BASICS was used as a comparison group. Another purpose of this study was to determine whether or not CEMS and Project BASICS had any effect on selected academic and behavioral criteria. A total of 120 subjects were analyzed from two groups. Each group consisted of 60 randomly selected students. An ex post facto research design was used. Descriptive analyses included mean, media, mode, range, variance and standard deviations. Analysis of covariance was used to determine significant relationships. T-tests were used to compare the performance within both comparison groups. A p<.05 level of significance was used. Based on the Pearson Correlation Coefficient there appears to be a highly positive relationship between student performance in 1986-87 and in 1987-88 for all behavioral variables. The t-test for Grade Point Average (GPA) indicated that the sample means were almost identical within each individual group. All other variables indicated significant within-group improvement. The results suggested that there were no significant differences between the Career Exploratory Middle Schools (CEMS) and project BASICS with regard to Science Research Association (SRA) composite scores, absences, days tardy, GPA and office referrals. This study is designed to compare the effectiveness of two strategies used to reduce the number of dropout-prone middle school students. Ed. D.

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Dissertations / Theses on the topic 'Two Numbers'

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