The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

First order reversal curve analysis of nanocrystalline Pd(80)Co(20) alloy films

Films of isotropic nanocrystalline Pd(80)Co(20) alloys were obtained by electrodeposition onto brass substrate in plating baths maintained at different pH values. Increasing the pH of the plating bath led to an increase in mean grain size without inducing significant changes in the composition of the alloy. The magnetocrystalline anisotropy constant was estimated and the value was of the same order of magnitude as that reported for samples with perpendicular magnetic anisotropy. First order reversal curve (FORC) analysis revealed the presence of an important component of reversible magnetization. Also, FORC diagrams obtained at different sweep rate of the applied magnetic field, revealed that this reversible component is strongly affected by kinetic effect. The slight bias observed in the irreversible part of the FORC distribution suggested the dominance of magnetizing intergrain exchange coupling over demagnetizing dipolar interactions and microstructural disorder. (c) 2009 Elsevier B.V. All rights reserved.

Egg production curve fitting using nonlinear models for selected and nonselected lines of White Leghorn hens

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

Comparison of logistic and neural network models to fit to the egg production curve of White Leghorn hens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Growth curve in Santa Ines sheep

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (112), mean square error (MSE) were calculated using language of technical computing package Matlab(R), 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike's Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R(2), lower MSE and A/C Finally, the parameters A, B and k were adjusted in Matlab(R) 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

Genetic parameters of total milk yield and factors describing the shape of lactation curve in dairy buffaloes

The objective of this study was to apply factor analysis to describe lactation curves in dairy buffaloes in order to estimate the phenotypic and genetic association between common latent factors and cumulative milk yield. A total of 31 257 monthly test-day milk yield records from buffaloes belonging to herds located in the state of São Paulo were used to estimate two common latent factors, which were then analysed in a multi-trait animal model for estimating genetic parameters. Estimates of (co)variance components for the two common latent factors and cumulated 270-d milk yield were obtained by Bayesian inference using a multiple trait animal model. Contemporary group, number of milkings per day (two levels) and age of buffalo cow at calving (linear and quadratic) as covariate were included in the model as fixed effects. The additive genetic, permanent environmental and residual effects were included as random effects. The first common latent factor (F1) was associated with persistency of lactation and the second common latent factor (F2) with the level of production in early lactation. Heritability estimates for Fl and F2 were 0.12 and 0.07, respectively. Genetic correlation estimates between El and F2 with cumulative milk yield were positive and moderate (0.63 and 0.52). Multivariate statistics employing factor analysis allowed the extraction of two variables (latent factors) that described the shape of the lactation curve. It is expected that the response to selection to increase lactation persistency is higher than the response obtained from selecting animals to increase lactation peak. Selection for higher total milk yield would result in a favourable correlated response to increase the level of production in early lactation and the lactation persistency.

CORRELATING THE CURVE DISTANCE BETWEEN THE DISTAL of THE CANINES TO THE COMBINED WIDTH of THE SIX ANTERIOR TEETH WHEN SELECTING DENTURE TEETH FOR DIFFERENT ETHNIC GROUPS

Statement of problem. To select the width of denture teeth, the distance between the marks indicating the location of the canines is usually measured around the curvature of the wax occlusal rim; however, most manufacturers' mold charts provide the measurements of the artificial 6 anterior teeth as if they were on a straight line.Purpose. The purpose of this study was to investigate whether the curve distance between the distal surfaces of the maxillary canines can be related to the combined width (straight measurement) of the 6 anterior teeth in 4 ethnic groups.Material and methods. Maxillary stone casts were obtained for 160 dentate subjects of 4 ethnic groups (40 whites, 40 blacks, 40 multiracial - descendants of white and black parents, and 40 Asians). The width of each maxillary anterior tooth was measured on the casts with sliding calipers. The combined width of the 6 anterior teeth (CW) corresponded to the sum of the width of each anterior tooth. The curve distance between the distal surfaces of the canines (CD) was measured by using dental tape and sliding calipers. The Pearson correlation coefficient and regression analysis were used to evaluate the relationship between CD and CW in each ethnic group (alpha=.05).Results. The mean CD and CW values (in mm) obtained were: whites (CD=52.12; CW=45.65); blacks (CD=56.10; CW=48.13); multiracial (CD=53.58; CW=46.54); and Asians (CD=53.29; CW=46.60). Significant (P<.001) correlations between CD and CW measurements were observed for all ethnic groups studied (whites, r=0.957; blacks, r=0.803; multiracial, r=0.917; and Asians, r=0.881). The following linear regression equations were obtained: whites [CD=1.1(CW)+0.3]; blacks [CD=0.95(CW)+9.3]; multiracial [CD=1.2(CW)-1.1]; and Asians [CD=1.0(CW)+5].Conclusions. The curve distance between the distal surfaces of the maxillary canines can be accurately related to the combined width of the 6 anterior teeth in the selection of denture teeth for the studied ethnic groups. (J Prosthet Dent 2012;107:400-404)

First order reversal curve analysis of nanocrystalline Pd80Co20 alloy films

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

Limit between stages I and II of a seed imbibition curve

O conhecimento das fases de absorção de água das diferentes espécies é importante em pesquisas objetivando melhorar a qualidade das sementes, utilizando tratamentos como condicionamento osmótico, pré-hidratação e uso de bioreguladores. O objetivo do presente trabalho foi estabelecer uma metodologia para determinar o limite entre a primeira e a segunda fase do processo, considerando o modelo W = f(t) - (a - w0)exp(-kt), utilizando testes estatísticos. O limite entre as duas primeiras fases do processo de absorção de água pelas sementes, foi determinado utilizando-se a distribuição assintótica de uma função de estimadores. O ponto a partir do qual esta diferença (W*) deixa de ser significativa foi determinado utilizando-se o teste estatístico T de Student. Para os dados utilizados como exemplo, tem-se o modelo ou =(0,434 + 0,00162 t) - (0,434 - w o)exp(-0,121 t), com r² = 0,98 e W* = (0,434 - w o) exp(-0,121 t). O valor de t encontrado (27,2 horas) é menor do que o valor determinado, considerando-se como critério para mudança de fase a diferença de 1% entre a assíntota e o valor estimado pelo modelo ajustado. Essa diferença de duas horas corresponde a 0,28% de água absorvida.

Using shifts in the electronic emission curve to evaluate polymer surface degradation

The polymer surface degradation and/or modification evolution of Teflon FEP and Mylar C films caused by a low energy electron beam were analyzed using a new method that consists in measuring the second crossover energy shift in the electronic emission curve. Upon prolonged irradiation, the second crossover energy shifts irreversibly to lower values in Teflon FEP but to higher values in Mylar C, indicating distinct mechanisms of surface degradation for the two polymers. The method represents a relatively inexpensive way to monitor early stages of surface degradation since the secondary electron emission comes from a maximum depth below the geometric surface of 100 mn in insulators. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Impact of Z-R relationship on flow estimates in central São Paulo

Mean areal radar rainfall over catchments in the State of São Paulo is an operational product under development by the Meteorological Research Institute - IPMet. A pilot project is being carried out which focuses on the important Corumbatai River basin, under surveillance by the IPMet-operated Bauru radar. Previous work on the project explored the relative impact of factors like time resolution of radar data and reflectivity to rain-rate conversion relationships, when the relevance of the latter was verified. This paper deals with the stratification of those relationships by daily intervals and its impact on flow estimates. Daily values of radar mean rainfall using gauges and different conversion relationships are plotted against the corresponding flow at the basin outlet. Flow estimates derived by applying the rainfall from the different relationships to a previously obtained rainfall-runoff curve for the basin is compared to the historical hydrograph. Preliminary results suggest stratification has hydrological significance.