Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

An algorithm for the solution of a quadratic equation using continued fractions /

Thesis (M. S.)--University of Illinois at Urbana-Champaign, 1972.

Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Antioxidant activity of rosemary and oregano ethanol extracts in soybean oil under thermal oxidation

Four experiments were conducted to measure the antioxidant activity of ethanol extracts of rosemary and oregano compared with synthetic antioxidants such as TBHQ and BHA/BHT. The antioxidant activity was determined and results differed from those of the Oven test at 63º C. Peroxide values and absorptivities at 232 nm of soybean oil under Oven test were lower in treatments with 25, 50, 75, 100 and 200 mg.Kg-1 TBHQ than in treatments with 1000 mg.Kg-1 oregano extract (O), 500 mg.Kg-1 rosemary extract (R) and their mixture R+O. All the treatments were effective in controlling the thermal oxidation of oils; the natural extracts were as effective as BHA+BHT and less effective than TBHQ. The natural extracts were mixed with 25, 50, 75 and 100 mg.Kg-1 TBHQ and then added to the oil. No improvement in antioxidative properties was observed. The best antioxidant concentration could be determined from polynomial regression and quadratic equation from the experimental data.

MA160exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA160exam00pdf

Exam questions and solutions in PDF

Retrievals of sea surface temperature from infrared imagery: origin and form of systematic errors

We show that retrievals of sea surface temperature from satellite infrared imagery are prone to two forms of systematic error: prior error (familiar from the theory of atmospheric sounding) and error arising from nonlinearity. These errors have different complex geographical variations, related to the differing geographical distributions of the main geophysical variables that determine clear-sky brightness-temperatures over the oceans. We show that such errors arise as an intrinsic consequence of the form of the retrieval (rather than as a consequence of sub-optimally specified retrieval coefficients, as is often assumed) and that the pattern of observed errors can be simulated in detail using radiative-transfer modelling. The prior error has the linear form familiar from atmospheric sounding. A quadratic equation for nonlinearity error is derived, and it is verified that the nonlinearity error exhibits predominantly quadratic behaviour in this case.

Modelos matemáticos para estimar as exigências de lisina digestível para aves de corte ISA Label

O objetivo neste estudo foi avaliar diferentes modelos ajustados às respostas de ganho de peso obtidas em experimento com aves da linhagem ISA Label no período de 1 a 28 dias de idade. Foram utilizados 480 pintos de ambos os sexos, distribuídos em delineamento inteiramente casualizado, em arranjo fatorial 4 X 2 (níveis de lisina X sexo), com três repetições, com 20 aves por unidade experimental. Uma ração basal foi formulada para atender às exigências das aves, exceto em lisina. Essa ração foi suplementada com L-lisina HCl em substituição ao ácido L-glutâmico, resultando em rações experimentais isonitrogênicas e isoenergéticas contendo 0,85; 0,97; 1,09 e 1,21% de lisina digestível. As respostas de ganho de peso foram ajustadas de acordo com os níveis de lisina da ração pelos modelos Linear Reponse Plateau (LRP), segmentado de duas inclinações, polinomial quadrático e exponencial. A primeira intersecção da equação quadrática com o platô do LRP também foi utilizado para estimar o nível ótimo. Os níveis de lisina digestível estimados pelos modelos LRP, segmentado e quadrático, foram 0,999; 1,010 e 1,116%, respectivamente. Na combinação do modelo quadrático com o LRP, a estimativa da exigência de lisina digestível foi de 1,041%. O modelo exponencial proporcionou estimativa de 1,066%, considerando 95% da resposta assintótica. Com base nos custos com alimentação, esse mesmo modelo gerou estimativas de 1,000 e 1,030% quando o custo do quilograma de L-lisina HCl foi R$ 8,50 e R$ 6,50, respectivamente. Considerando as limitações de cada um dos modelos propostos, o procedimento para estimar as exigências de lisina digestível pela primeira intersecção da equação quadrática com o platô do LRP foi o mais adequado para melhorar o ganho de peso das aves quando variáveis econômicas não foram consideradas.

Efficacy of pre- and postinoculation application of Fungicides to expanding young citrus leaves for control of melanose, scab, and alternarial brown spot

In greenhouse trials, copper hydroxide, pyraclostrobin, and famoxadone were applied to actively crowing young citrus seedlings to determine the duration of protection of young leaves provided by these fungicides against melanose, caused by Diaporthe citri, citrus scab, caused by Elsinoe fawcettii, and Alternaria brown spot, caused by Alternaria alternata. Fungicides were applied to different sets of potted plants of grapefruit for control of melanose, of rough lemon for control of scab, and of Dancy tangerine for control of Afternaria brown spot 1 to 6 days prior to inoculation. as well as on the day of inoculation. Leaf area of treated shoots was estimated on the day of fungicide application and the day of inoculation and disease severity evaluated subsequently. In most cases. copper hydroxide and famoxadone provided at least 50% control of all three diseases for only about 2 days after application. Generally, there was little or no disease control when the products were applied 4 or more days before inoculation. In contrast, pyraclostrobin usually provided a high level of control of all three diseases when applied up to 5 days prior to inoculation. The level of disease control decreased as the interval between a fungicide application and inoculation increased and the relationship between disease control and leaf expansion best fit a quadratic equation. Effective disease control was observed with copper hydroxide and famoxadone until leaf area had increased by 100 to 200%, whereas control with pyraclostrobin was observed up to 400 to 500% increase in leaf area. In postinoculation tests with scab and melanose, pyraclostrobin provided high levels of disease control (>75%) when applied up to 2 days after inoculation. whereas copper hydroxide and famoxadone had minimal postinoculation activity. Applications of pyraclostrobin to the spring flush growth of citrus trees are much more likely to provide control of melanose, scab, and Alternaria brown spot than those of famoxadone or copper hydroxide.

Spatial and temporal variability of soil CO2 emission in a sugarcane area under green and slash-and-burn managements

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uso de modelos lineales y no lineales para el estudio de la curva de lactancia en búfalos Murrah y sus cruces en sistemas de cría extensiva en el estado de São Paulo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hyperbolic-like estimates for higher order equations

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the extended phase space by means of a function f (t) which depends on the principal part and on the coefficients of the terms of order m - 1. Then we look for sufficient conditions that guarantee the same energy estimate from above in all the extended phase space. We call this class of estimates hyperbolic-like since the energy behavior is deeply depending on the hyperbolic structure of the equation. In some cases, these estimates produce a dissipative effect on the energy. (C) 2012 Elsevier Inc. All rights reserved.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Glomerular filtration rate estimates decrease during high altitude expedition but increase with Lake Louise acute mountain sickness scores

AIM: Acute mountain sickness (AMS) can result in pulmonary and cerebral oedema with overperfusion of microvascular beds, elevated hydrostatic capillary pressure, capillary leakage and consequent oedema as pathogenetic mechanisms. Data on changes in glomerular filtration rate (GFR) at altitudes above 5000 m are very limited. METHODS: Thirty-four healthy mountaineers, who were randomized to two acclimatization protocols, undertook an expedition on Muztagh Ata Mountain (7549 m) in China. Tests were performed at five altitudes: Zurich pre-expedition (PE, 450 m), base camp (BC, 4497 m), Camp 1 (C1, 5533 m), Camp 2 (C2, 6265 m) and Camp 3 (C3, 6865 m). Cystatin C- and creatinine-based (Mayo Clinic quadratic equation) GFR estimates (eGFR) were assessed together with Lake Louise AMS score and other tests. RESULTS: eGFR significantly decreased from PE to BC (P < 0.01). However, when analysing at changes between BC and C3, only cystatin C-based estimates indicated a significant decrease in GFR (P = 0.02). There was a linear decrease in eGFR from PE to C3, with a decrease of approx. 3.1 mL min(-1) 1.73 m(-2) per 1000 m increase in altitude. No differences between eGFR of the two groups with different acclimatization protocols could be observed. There was a significant association between eGFR and haematocrit (P = 0.01), whereas no significant association between eGFR and aldosterone, renin and brain natriuretic peptide could be observed. Finally, higher AMS scores were significantly associated with higher eGFR (P = 0.01). CONCLUSIONS: Renal function declines when ascending from low to high altitude. Cystatin C-based eGFR decreases during ascent in high altitude expedition but increases with AMS scores. For individuals with eGFR <40 mL min(-1) 1.73 m(-2), caution may be necessary when planning trips to high altitude above 4500 m above sea level.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.