This thesis discusses several topics related to interpolation and how it is used in numerical analysis. It begins with an overview of the aspects of interpolation theory that are relevant to the discussion at hand before presenting three new contributions to the field. The first new result is a detailed error analysis of the barycentric formula for trigonometric interpolation in equally-spaced points. We show that, unlike the barycentric formula for polynomial interpolation in Chebyshev points (and contrary to the main view in the literature), this formula is not always stable. We demonstrate how to correct this instability via a rewriting of the formula and establish the forward stability of the resulting algorithm. Second, we consider the problem of trigonometric interpolation in grids that are perturbations of equally-spaced grids in which each point is allowed to move by at most a fixed fraction of the grid spacing. We prove that the Lebesgue constant for these grids grows at a rate that is at most algebraic in the number of points, thus answering questions put forth by Trefethen and Weideman about the robustness of numerical methods based on trigonometric interpolation in points that are uniformly distributed but not equally-spaced. We use this bound to derive theorems about the convergence rate of trigonometric interpolation in these grids and also discuss the related question of quadrature. Specifically, we prove that if a function has V ≥ 1 derivatives, the Vth of which is Hölder continuous (with a Hölder exponent that depends on the size of the maximum allowable perturbation), then the interpolants converge uniformly to the function at an algebraic rate; larger values of V lead to more rapid convergence. A similar statement holds for the corresponding quadrature rule. We also consider what analogue, if any, there is for trigonometric interpolation of the famous 1/4 theorem of Kadec from sampling theory that restricts the size of the perturbations one can make to the integers and still be guaranteed to have a set of stable sampling for the Paley-Wiener space. We present numerical evidence suggesting that in the discrete case, the 1/4 threshold takes the form of a threshold for the boundedness of a "2-norm Lebesgue constant" and does not appear to have much significance in practice. We believe that these are the first results regarding this problem to appear in the literature. While we do not believe the results we establish are the best possible quantitatively, they do (rigorously) capture the main features of trigonometric interpolation in perturbations of equally-spaced grids. We make several conjectures as to what the optimal results may be, backed by extensive numerical results. Finally, we consider a new application of interpolation to numerical linear algebra. We show that recently developed methods for computing the eigenvalues of a matrix by dis- cretizing contour integrals of its resolvent are equivalent to computing a rational interpolant to the resolvent and finding its poles. Using this observation as the foundation, we develop a method for computing the eigenvalues of real symmetric matrices that enjoys the same advantages as contour integral methods with respect to parallelism but employs only real arithmetic, thereby cutting the computational cost and storage requirements in half.

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

Orientador: Sergio Antonio Tozoni, Benjamin Bordin / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-22T01:03:43Z (GMT). No. of bitstreams: 1 Fernandes_IaraAndreaAlvares_M.pdf: 1785860 bytes, checksum: 01c06756cd928f586652a8bac96cbfbf (MD5) Previous issue date: 1997 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

Orientadores: José Luiz Pereira, Valéria Christina Amstalden Junqueira / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-18T21:41:27Z (GMT). No. of bitstreams: 1 Santos_RosanaFranciscoSiqueirados_D.pdf: 687405 bytes, checksum: a60c63628979fe94b8cd83acd31712df (MD5) Previous issue date: 2011 / Resumo: Cronobacter spp (Enterobacter sakazakii) é uma bactéria patogênica oportunista, que tem sido associada a surtos e casos esporádicos de meningite, enterocolite necrosante e sepse em recém nascidos. Em 2008 as cepas dessa espécie foram divididas em várias novas espécies e transferidas para o novo gênero Cronobacter spp. Um dos métodos mais recentes para sua detecção é o da ISO 22964 (2006), que inclui duas etapas de enriquecimento, o isolamento de colônias típicas (alfa-glicosidase positivas) no meio seletivo diferencial ESIA (Enterobacter sakazakii Isolation Agar) e a confirmação das culturas através de testes bioquímicos. Há, entretanto, necessidade de métodos e meios de cultura alternativos para o isolamento de Cronobacter spp (Enterobacter sakazakii), objetivo desse trabalho. Para isso, 83 amostras foram analisadas usando a técnica de PCR através do sistema BAX® (Dupont Qualicon), em comparação com o método cultural ISO/TS 22964:2006. Dois meios de cultura seletivos diferenciais foram usados para isolamento de culturas típicas: o Ágar de Isolamento de E.sakazakii (ESIA) e o Ágar Druggan-Forsythe-Iversen (DFI). Cronobacter spp (Enterobacter sakazakii) foi isolado em 13,25% das amostras analisadas, sendo mais freqüente em amostras de soja em grãos (destinada à preparação de bebidas à base de soja), em leite em pó e em amido de milho. Nas fórmulas infantis em pó o micro-organismo foi encontrado em 6% das amostras. A unidade analítica de 25g não se mostrou adequada para o isolamento das cepas, porque a contagem encontrada nas amostras positivas (unidade analítica de 500g) foi muito baixa (variando de <0,22 a >1,61NMP/100g). Em 27% das amostras positivas, Cronobacter spp só foi isolado de colônias atípicas (alfa-glicosidase negativas) no ESIA e/ou no DFI. Em 9% das amostras as cepas isoladas também não apresentaram pigmentação amarela no TSA. Os resultados mostraram desempenho equivalente do ESIA e do DFI, no protocolo de ensaio da ISO/TS 22964 (2006). O método do Sistema BAX® apresentou desempenho inferior ao método ISO/TS 22964 (2006), com uma alta porcentagem de resultados falsos positivos no PCR (73,33%) e uma porcentagem significativa de resultados falsos negativos na confirmação cultural (53,85%). Os resultados indicaram que, a pesquisa de Cronobacter spp (Enterobacter sakazakii) em produtos destinados à alimentação de recém nascidos, deve ser feito com unidade analítica de pelo menos 500g, preferencialmente maior, porque a contagem encontrada nas amostras positivas foi muito baixa / Abstract: Cronobacter spp (Enterobacter sakazakii) is an opportunist pathogenic bacterium, which has been associated to outbreaks and sporadically cases of meningitis, necrotizing enterocolitis and sepses in newborns. In 2008, strains of this species was divided in some new species and transferred to the new genus Cronobacter spp. One of the most recent method used to determine the microorganisms is ISO 22964 (2006), that includes two stages of enrichment, isolation of typical colonies (positive a- glycosidase) in the differential media selective ESIA (Enterobacter sakazakii Isolation Agar) and biochemical tests for confirmation. However, it already exists alternative and rapid methods for the isolation of Cronobacter spp (Enterobacter sakazakii), which were the aim of this study. For this, 83 samples were analyzed using the Polymerase Chain Reaction method (PCR) by BAX® System (DuPont Qualicon), in comparison with ISO/TS 22964:2006 method. Two differential selective media were used to isolation of typical colonies: Agar of Isolation for E. sakazakii (ESIA) and Agar Druggan-Forsythe-Iversen (DFI). Cronobacter spp (Enterobacter sakazakii) was isolated in 13.25% of the analyzed samples being more frequent in bean (designated to prepare soy base drink), powered milk and corn flour samples. In powered infantile formula, 6% of the samples were contaminated. The analytical unit of 25g was not adequate for the isolation this microorganism, where the count detected in the positive samples (analytical unit of 500g) was very low (among of <0.22 and >1,61MPN/100g). In 27% of positive samples, Cronobacter spp (Enterobacter sakazakii) was only isolated from atypical colonies (alpha-glycosidase negative) in ESIA and/or DFI. Nine per cent (9%) of the strains isolated from samples did not show yellow pigment in the TSA. Results showed equivalent performance of both ESIA and DFI medias, following the of ISO/TS 22964 (2006) assay protocol. The PCR method (BAX® System) showed lower performance when compared with ISO/TS 22964 (2006) method. A high percentage of false positive results (73.33%) and a significant percentage of false negative results in the cultural confirmation (53.85%) were observed with PCR method. The results indicated that the research of Cronobacter spp (Enterobacter sakazakii) in products destined to the feeding of just born, must be made with analytical unit of at least 500g (or major quantity) due to the counting found in the positive samples was very low / Doutorado / Ciência de Alimentos / Doutor em Ciência de Alimentos

Magister Public Health - MPH / Background: Appropriate and adequate infant feeding practices are an important factor in achieving optimal health in infants. Inappropriate and inadequate infant feeding practices contribute significantly to ill-health in infants. Both WHO and UNICEF recommend exclusive breastfeeding for the first six months both in the context of HIV and otherwise unless exclusiv formula feeding can meet each of five conditions: acceptable, feasible, affordable, sustainable and safe (AFASS). The modes of infant feeding include exclusive breastfeeding, formula feeding and mixed feeding. Medical recommendations and social pressures related to infant feeding in high HIV-prevalence low-income communities may have shifted infant feeding practices. The aim of this study was to explore factors influencing infant feeding practices and decision making among women in one such community, Kabwata Township, in Lusaka, Zambia. Method: An exploratory qualitative study was conducted at Kabwata Health Centre in Kabwata Township in Lusaka, Zambia. Convenient sampling was used to recruit 32 women for focus group discussions and three key informants (two nurses and one social worker) for individual interviews. Verbal consent was received from all participants. Semi-structured interview guides were used to elicit discussion by all participants. Discussions were tape recorded and transcribed verbatim. Thematic data analysis was used to analyze the qualitative data. Results: Most FGD participants reported that they themselves initiated breastfeeding soon after giving birth, but not all of them breastfed exclusively for the first six months, as is currently recommended. The major factors influencing infant feeding included; influence from family and friends, stigma and discrimination, influence from health care providers, practical realities such as maternal employment and poverty, and cultural/traditional practices. Conclusion: While breastfeeding is valued and accepted, most women do not or cannot exclusively breastfeed for six (6) months for various reasons. Paradoxically, the social value of breastfeeding and the knowledge that breast milk can transmit HIV reinforce mixed feeding as the predominant feeding practice. Key informants reported that women attending health care services at Kabwata health centre were encouraged and taught to breastfeed their infants exclusively for six months. There is a need to re-look at the way the women are being encouraged, taught and supported so that the apparent knowledge and acceptance of breastfeeding can translate into improved infant feeding practices. Awareness campaigns need to include all stakeholders including family members, the community, employers and the women themselves in order to make exclusive breastfeeding easier for the women.

The aim of the research is to derive a set of hermeneutical principles of the author of the book of Hebrews from the introductory formulae and, to a lesser degree, to contrast these with contemporary hermeneutical approaches. The research is important for three reasons. Firstly, the introductory formulae have largely been neglected as a source for consideration when analysing the hermeneutic of a writer, such that this study is, to some degree, ground-breaking in nature. Secondly, the introductory formulae provide the clearest presentation of the author’s hermeneutic in that here may be found the most explicit statements revealing the author’s hermeneutic rather than deriving these. Thirdly, in the book of Hebrews we have the best example of how a New Testament writer interpreted the Old Testament (most quotations and introductory formulae per size of book). The research was conducted along the following lines: A comprehensive and workable list of introductory formulae in Hebrews was derived. This list was compared and contrasted firstly within the book itself and secondly in comparison to that of the other New Testament writers. A set of principles was derived from the introductory formulae of Hebrews and compared to the hermeneutics of contemporary modern approaches. The results of the research are encapsulated in six principles which together summarise the author of Hebrews’ hermeneutic. The Old Testament is understood as, -- spoken not written, -- spoken by a Trinitarian God comprising Father, Son and Holy Spirit, -- dynamic, that is, spoken with equal authority and equal effect to a current generation, -- authoritative and complete, -- the words of God do not require the intervention of man but rather the removal of man permitting God to address His people personally, -- pertaining to the person and work of Christ. The conclusion of the research can be summarised in one sentence: “God (Father, Son and Holy Spirit) is speaking to you now and what He says concerns His Son.” When these principles are compared with contemporary modern hermeneutic, the following is observed; -- the ‘written-and-dated’ nature of God’s revelation instead of an understanding that God is speaking to us today. -- a focus on a single person of the Godhead and a resultant infatuation with some doctrines at the expense of others. -- an illegitimate concern to make God relevant. -- the reader no longer reads in order to understand but reads in order to define meaning and the meaning primarily pertains to himself -- the listener has become the speaker and the speaker is a primarily concerned about himself and how he is coming across not about God. -- the exposition of the Bible has degenerated from theology to anthropology. / Dissertation (MA (Biblical Studies))--University of Pretoria, 2007. / Biblical and Religious Studies / unrestricted

This master's thesis deals with inbound marketing of Nestlé in the area of infant formula. Its aim is to determine whether inbound marketing is a suitable tool for infant formula promotion which is strongly regulated. The thesis is based on a comprehensive analysis of the area of infant formula and analysis of inbound marketing strategy of one of the most dominant companies on the market, Nestlé. In the beginning, attention is focused on important milestones of the development of infant formula and on a case which caused an important change in the promotion of infant formula, Nestlé boycott. The following section deals with the supervision and marketing regulation both in international and the European law. The final chapter of the first part emphasizes on philosophy of inbound marketing. The second part is introduced by outlining the current situation both on global and the Czech market of infant formula. Then, attention is focused on Nestlé. Its introduction is followed by analysis of company's inbound marketing strategy which is then evaluated. For this purpose, analysis of the effectiveness of marketing tools is made with regard to strategic goals of the company.

Goal of the graduation thesis is elaboration of business plan which is aimed at production and distribution of formula cars. The thesis is divided into two parts. First part is devoted to theoretical base about entrepreneurship, entrepreneurs and enterprises followed by decomposed structure of business plan. In second, practical part, specific business plan of author is compiled with all of its requirements including analysis of micro and macro environment and production, marketing and financial plan. In the end, business proposal realization decision is made.

OBJECTIVE: Prior studies suggested rapid weight gain in infancy as a risk factor for the development of obesity. Our aim was to determine if early-childhood treatment for malnutrition is associated with the development of obesity in later-childhood. METHODS: This was a retrospective chart review of 194 children who had been treated and discharged from the Growth and Nutrition Program (GNP) from 1/1/2000 to 7/30/2014, with at least one height and weight recorded after discharge. Subjects predisposed to obesity due to medical conditions or medications were excluded. Obesity was defined using WHO and CDC growth charts, body mass index ≥95th percentile for age and sex, and compared to published prevalence rates. Potential predictors of obesity prevalence were also examined. RESULTS: None of the 194 subjects were obese at time of discharge from GNP. Over the 20-year follow-up period, 7% became obese (well below the national obesity prevalence of 18.5%1. 3 of 11 (27.3%) patients prescribed preterm infant formula became obese in contrast to 10 of 173 (5.8%) who were not prescribed (p=0.007). 6 of 27 (22.2%) subjects identified as African American became obese in contrast to 7 of 157 (4.5%) who did not identify (p=0.001). CONCLUSION: While overall prevalence of obesity was lower than that of the general population, children requiring preterm infant formula and/or identified as African American were more likely to develop obesity in childhood. Findings support the need for more anticipatory guidance regarding preterm infant formula and aggressive weight management and planning prior to GNP discharge. / 2022-06-07T00:00:00Z

abstract: Computability of spray flows is an important issue, from both fundamental and practical perspectives. Spray flows have important applications in fuel injection, agriculture, medical devices, and industrial processes such as spray cooling. For this reason, many efforts have been devoted to experimental, computational and some theoretical aspects of spray flows. In particular, primary atomization, the process of bulk liquid transitioning to small droplets, is a central and probably the most difficult aspect of spray flows. This thesis discusses developed methods, results, and needed improvements in the modeling of primary atomization using a predictive Sauter Mean Diameter (SMD) formula. Primary atomization for round injectors and simplex atomizers is modeled using a three-step procedure. For each spray geometry, a volume-of-fluid simulation is run to resolve the trajectory of the intact liquid core. Atomization criterion is applied to the volume-of-fluid velocity field to determine atomization sites. Local droplet size is predicted at the atomization sites using the quadratic formula for Sauter Mean Diameter. Droplets with the computed drop size are injected from the atomization sites and are tracked as point-particles. A User Defined Memory (UDM) code is employed to compute steady-state Sauter Mean Diameter statistics at locations corresponding to experimental interrogation locations. The resulting Sauter Mean Diameter, droplet trajectory, and droplet velocity are compared against experimental data to validate the computational protocol. This protocol can be implemented on coarse-grid, time-averaged simulations of spray flows, and produces convincing results when compared with experimental data for pressure-atomized sprays with and without swirl. This approach is general and can be adapted in any spray geometry for complete and efficient computations of spray flows. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2020