A Design Methodology for the Compensation of Positioning Deviation in Gantry Manipulators

This work presents recent results concerning a design methodology used to estimate the positioning deviation for a gantry (Cartesian) manipulator, related mainly to structural elastic deformation of components during operational conditions. The case-study manipulator is classified as gantry type and its basic dimensions are 1,53m x 0,97m x 1,38m. The dimensions used for the calculation of effective workspace due to end-effector path displacement are: 1m x 0,5m x 0,5m. The manipulator is composed by four basic modules defined as module X, module Y, module Z and terminal arm, where is connected the end-effector. Each module controlled axis performs a linear-parabolic positioning movement. The planning path algorithm has the maximum velocity and the total distance as input parameters for a given task. The acceleration and deceleration times are the same. Denavit-Hartemberg parameterization method is used in the manipulator kinematics model. The gantry manipulator can be modeled as four rigid bodies with three degrees-of-freedom in translational movements, connected as an open kinematics chain. Dynamic analysis were performed considering inertial parameters specification such as component mass, inertia and center of gravity position of each module. These parameters are essential for a correct manipulator dynamic modelling, due to multiple possibilities of motion and manipulation of objects with different masses. The dynamic analysis consists of a mathematical modelling of the static and dynamic interactions among the modules. The computation of the structural deformations uses the finite element method (FEM).

Standard-curve competitive RT-PCR quantification of myogenic regulatory factors in chicken embryos

The reverse transcription-polymerase chain reaction (RT-PCR) is the most sensitive method used to evaluate gene expression. Although many advances have been made since quantitative RT-PCR was first described, few reports deal with the mathematical bases of this technique. The aim of the present study was to develop and standardize a competitive PCR method using standard-curves to quantify transcripts of the myogenic regulatory factors MyoD, Myf-5, Myogenin and MRF4 in chicken embryos. Competitor cDNA molecules were constructed for each gene under study using deletion primers, which were designed to maintain the anchorage sites for the primers used to amplify target cDNAs. Standard-curves were prepared by co-amplification of different amounts of target cDNA with a constant amount of competitor. The content of specific mRNAs in embryo cDNAs was determined after PCR with a known amount of competitor and comparison to standard-curves. Transcripts of the housekeeping ß-actin gene were measured to normalize the results. As predicted by the model, most of the standard-curves showed a slope close to 1, while intercepts varied depending on the relative efficiency of competitor amplification. The sensitivity of the RT-PCR method permitted the detection of as few as 60 MyoD/Myf-5 molecules per reaction but approximately 600 molecules of MRF4/Myogenin mRNAS were necessary to produce a measurable signal. A coefficient of variation of 6 to 19% was estimated for the different genes analyzed (6 to 9 repetitions). The competitive RT-PCR assay described here is sensitive, precise and allows quantification of up to 9 transcripts from a single cDNA sample.

Process variables in the osmotic dehydration of sliced peaches

This paper evaluated the influence of temperature and concentration of the sucrose syrup on the pre-osmotic dehydration of peaches. Physical (colour and texture) and chemical variables (soluble solid content; total sugar, reducing and non-reducing sugar contents; and titratable acidity) were investigated, as well as the osmotic dehydration parameters (loss of weight and water; solids incorporation). An experimental central composite design was employed varying the temperature (from 30 to 50 ºC) and concentration (from 45 to 65 ºBrix) and maintaining the syrup to fruit ratio (4:1), process time (4 hours), and format (slices). The degree of acceptance was used in the sensory analysis evaluating the following characteristics: appearance, taste, texture, colour, and overall quality using a hedonic scale. The results were modelled using the Statistica program (v. 6.0) and the Response Surface Methodology. The mathematical models of the following dimensionless variations yielded significant (p < 0.05) and predictive results: soluble solids content, total and non-reducing sugar contents, titratable acidity, colour parameter L*, and water loss. The models of the attributes colour and appearance yielded significant (p < 0.10) but not predictive results. Temperature was the prevalent effect in the models. The process conditions in the range from 50 to 54.1 ºC and from 45 to 65 ºBrix led to greater water losses and better sensory performances.

Incerteza e não ergodicidade: crítica aos neoclássicos

The starting point of this essay is to show that, in our view, the problem of the traditional economics is not in the deductive method nor the mathematical methods used, but to attribute to economic agents "power" on the future and prescribe the existence of ergodic stochastic processes in their economic analyzes. Thus, building a theory on the ground whose bases are not able to sustain a proper understanding of the world, mainstream economics has difficulties in using the modeling for establishing deductions and conclusions that help understanding the system. Thus, the logical-mathematical rigor in economic models and deduction can be used with appropriate axioms, which is not the case of mainstream economics. Our hypothesis is that the inability of the mainstream in predicting economic crisis is due to the non-recognition of some principles that best describe the dynamics of financialized contemporary capitalism, as the principles of non-ergodicity and Keynesian uncertainty.

The general equilibrium theory as economic metatheory

Many economists show certain nonconformity relative to the excessive mathematical formalization of economics. This stems from dissatisfaction with the old debate about the lack of correspondence between mainstream theoretical models and reality. Although we do not propose to settle this debate here, this article seeks to associate the mismatch of mathematized models with the reality of the adoption of the hypothetical-deductive method as reproduced by general equilibrium. We begin by defining the main benefits of the mathematization of economics. Secondly, we address traditional criticism leveled against it. We then focus on more recent criticism from Gillies (2005) and Bresser-Pereira (2008). Finally, we attempt to associate the reproduction of the hypothetical-deductive method with a metatheoretical process triggered by Debreu's general equilibrium theory. In this respect, we appropriate the ideas of Weintraub (2002), Punzo (1991), and mainly Woo (1986) to support our hypothesis.

Sôbre um sistema de equações relativas a um modêlo matemático de populações de Himenópteros endogâmicos

This paper deals with the solution of a system of equations relating with a mathematical model of populations of endogamic Hymenoptera. The Author proves that, unless inequality (5.1) 4R5 + 8R R4 - 4R R³ + 8R² (R -1) R² - A a A a A a a A - R² (4R² + 4R - 1) R +2R³ < 0 a a A a is satisfied, one of the genes is eliminated from the population. He shows that the relative frequencies of different kinds of matings in the population can be obtained when the root R between zero and VRa of equation 2R4 + 2R³ -2R² (RA + Ra) - R(RA +Ra) + 2RA Ra =0 is known. In special, if we let b = RA / Ra > 1 , inequation (5.1) shows that we must have __________________ b³ + 2b² + b + V2b4 + 2b³ - 2b² + 2b Ra < __________________________________ = f(b) 2 (b4 + 2b³ + 2b - 1) The greatest value of f (b) is 0,75 and is obtained for b = 1, that is for RA = Ra.

Contribuição ao estudo da aplicação do método da diagnose foliar ao algodoeiro (Grossypium hirsutum L., var. I. A. C. 817) II

This paper deal with one experiment carried out in order to study the correlation between petioles analysis and seed cotton yield. A 3X3X3 factorial with respect to N, P2 0(5) and K2 O was installed in a sandy soil with low potash content and medium amounts of total N and easily extractable P. Two kinds of petioles, newly mature were collected for analysis: those attached to fruit hearing branches, and petioles located on the stem; the first group is conventionally named "productive petioles"; The second one is called "not productive petioles". Petioles' sampling was done when the first blossoms appeared. Yield date showed a marked response to potash, both nitrogen and phosphorus having no effect. Very good correlation was found between petioles potash and yield. Both types of petioles samples were equally good indicators of the potash status of the plants. By mathematical treatment of the date it followes that the highed yield which was possible under experimental conditions, 1.562 kg of seed cotton per hectare would be reacher by using 128 kg of K2O per hectare. With this amount of potash supplied to the plants the following K levels would be expected in the petioles: "productive petioles" "not productive petioles" 1,93 % K 1,85 % K

Alimentação de quatro espécies de Leporinus (Characiformes, Anostomidae) durante a formação de um reservatório no sudeste do Brasil

The study reports the changes ocurred in feeding ecology of fish species during a tropical river reservoir formation. It was analysed the stomachal contents of 399 individuals belonging to four species of genus Leporinus (L. elongatus Valenciennes, 1849, n=157; L.friderici (Bloch, 1794), n=87; L. octofasciatus Steindachner, 1917, n=107; L.amblyrhynchus Garavello & Britski, 1987, n=48) during formation of Nova Ponte reservoir, State of Minas Gerais, Brazil, in 1993 and 1994. Specimens were separated by sampling period, according with the rate of filling of the reservoir, and standard lenght classes. The species had included in diet vegetal and animal items of autochtone and alochtone origin in several proportions. L. amblyrhynchus fed on basically dipterans in all the sampling periods and length classes. L. elongatus had presented a diverse diet, with predominance of dipterans and vegetal items, and changed the consumed items proportions along the sampling periods and between lenght classes. L. friderici diet was composed mainly by terrestrial insects during the rapid filling period, that were later substituted by fishes and vegetal items. Ontogenetic trophic changes were observed in this species. L. octofasciatus presented a well characterized herbivorous diet, without trophic ontogeny, but with a opportunistic character. Just three pair-species, L. amblyrhynchus-L. elongatus, L. friderici-L. octofasciatus and L. elongatus-L. octofasciatus, have presented some high value of trophic overlap in at least one sampling period. In spite of the fishes of the genus Leporinus being classified like omnivorous in a general way, the differences found between diets of these four species suggest that there is structuration of trophic niches in the reservoir.

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Aplicação de modelo matemático às propriedades reológicas de géis mistos de agarose e de goma guar

Certain biopolymers are capable of forming physically cross-linked gels in aqueous medium, stabilized by forces such as Coulombic, charge transfer, hydrogen bonding, dipole-dipole, van der Waals, and hydrophobic interactions. The mathematical description of these physical networks are difficult, but should contribute to a better understanding of the gelling process. The Clark and Ross-Murphy model was applied to experimental data for agarose-guar gum mixed systems, in which only agarose is the gelling polysaccharide. A computational routine based on the statistical maximum likehood principle was employed to estimate the f, K and a characteristic parameters. Statistical t-test and F-test were used to analyse the set of parameters.

Adsorção/dessorção do explosivo tetril em turfa e em argissolo vermelho amarelo

This paper presents the study of adsorption/desorption of the explosive tetryl (2,4,6-trinitrophenylmethyl-nitramine) in different matrices, such as in natura soil, roasted soil, humic acid of soil, in natura peat, roasted peat and humic acid of peat. The aim of the study is to evaluate the interaction capacity of those matrices with the explosive. The analytic technique used was HPLC (high performance liquid chromatography), with UV-detection at 230 nm. The Freundlich isotherms were utilized for the mathematical treatment of the data. The results indicated that in natura soil and in natura peat (with organic substances) are excellent matrices for the retention of tetryl, adsorbing it and keeping it immovable, preventing it from contaminating the groundwater. The largest adsorption of the explosive ocurred in in natura soil, while the smallest desorption was observed in in natura peat. After the calcination of the matrices, the smallest adsorption was observed, indicating that the retention occurs in the organic substance.

Uso de scanner em espectrofotometria de absorção molecular: aplicação em experimento didático enfocando a determinação de ácido ascórbico

Quantitative analysis of colored substances is generally performed using a spectrophotometer for detection of radiation. However, the combination of digital images and mathematical conversion of colors is an alternative for quantitative procedures based on colored chemical reactions. This work proposes a didactic experiment using a scanner for determination of ascorbic acid in medicines based on the formation of the Prussian blue complex. Results were in good agreement with a conventional spectrophotometer method and the procedure is attractive for instrumental analysis undergraduate courses.

Desenvolvimento de método analítico para quantificação do efavirenz por espectrofotometria no UV-Vis

An UV-Vis spectrophotometry analytical method for quantifying Efavirenz was developed and validated as an alternative to replace the HPLC current method. The report method presents sample concentration of 10 μg mL-1, dissolved in a solution ethanol:water (60:40, v/v), economic and technically adequate for the purpose adopted. The results and the statistical treated proved that the method being considered an precise and accurate analytical low cost alternative for laboratory routine. The adaptability of this method in product and other analytical methods development has been challenged by mathematical calculation of drug extinction coefficient in water and methanol and practical experiments, showing interesting results.

Variación del grado de avance de reacción en sistemas cerrados en equilibrio químico que modifican la temperatura a volumen constante

In this paper it is presented a thermodynamic analysis that aims to find the mathematical expression of the variation of extent of reaction with the infinitesimal variation in the temperature at constant volume of a chemical equilibrium mixture. The goal of this paper is to establish an alternative approach to avoid both the Le Chatelier's principle and the problems that emerge when trying to apply its qualitative statements. This attempt is based on the laws of thermodynamics.

Estudo de reações químicas homogêneas via método de Monte Carlo

By using the Monte Carlo simulation platform with probabilistic mathematical functions of the Boltzmann type, , having activation energy and temperature as parameters, it was possible to assess important dynamic aspects of homogeneous chemical reactions of the types A → B and A B. The protocol proved a useful tool in work with the basic concepts of Kinetics and Thermodynamics allowing its application both in class activities and for assisting experimental procedures.