Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

Fully Connected PLL Networks: How Filter Determines the Number of Nodes

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first-order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters. Copyright (C) 2009 Atila Madureira Bueno et al.

EFFECTS OF THERMAL TREATMENT ON THE PHYSICOCHEMICAL CHARACTERISTICS OF GIANT BAMBOO

Despite countless use possibilities for bamboo, this material has two major disadvantages. One drawback is the low natural durability of most bamboo species due to presence of starch in their parenchyma cells. The other equally important drawback is the tendency bamboo has to present dimensional variations if subjected to environmental change conditions. In an attempt to minimize these inconveniences, strips (laths) of Dendrocalamus giganteus Munro were taken from different portions of the culm and subjected to several temperatures, namely 140 degrees C, 180 degrees C, 220 degrees C, 260 degrees C and 300 degrees C under laboratory conditions, at the ESALQ-USP college of agriculture. The thermal treatment process was conducted in noninert and inert atmospheres (with nitrogen), depending on temperature Specimens were then subjected to physicomechanical characterization tests in order to determine optimum thermal treatment conditions in which to preserve to the extent possible the original bamboo properties. Results revealed that there is an optimum temperature range, between 140 degrees and 220 degrees C, whereby thermally treated bamboo does not significantly lose its mechanical properties while at the same time showing greater dimensional stability in the presence of moisture.

Eucalyptus sp seedling response to potassium fertilization and soil water

A considerable portion of Brazil's commercial eucalypt plantations is located in areas Subjected to periods of water deficit and grown in soils with low natural fertility, particularly poor In potassium. Potassium is influential in controlling water relations of plants. The objective of this study was to verify the influence of potassium fertilization and soil water potential (psi(w)) oil the dry matter production and oil water relations Of eucalypt seedlings grown under greenhouse conditions. the experimental units were arranged in 4x4x2 randomized blocks factorial design, as follow: four species of Eucalyptus (Eucalyptus grandis, Eucalyptus urophylla, Eucalyptus camaldulensis and hybrid Eucalyptus grandis x Eucalyptus urophylla), four dosages of K (0, 50, 100 and 200 mg dm(-3)) and two soil water potentials (-0.01 M Pa and -0.1 M Pa). Plastic containers with 15 cm diameter and 18 cm height, with Styrofoam base, containing 3.0 dm(3) of soil and two plants per container were used. Soil water potential was kept at -0.01 MPa for 40 days after seeding. Afterward, the experimental units were divided into two groups: in one group the potential was kept at 0.01 MPa, and in the other one, at -0.10 MPa. Sol I water potential was control led gravimetrically twice a day with water replacement until the desired potential was reestablished. A week before harvesting, the leaf water potential (psi), the photosynthetic rate (A), the stomatal conductance (gs) and the transpiration rate were evaluated. The last week before harvesting, the mass of the containers was recorded daily before watering to determine the consumption of water by the plants. After harvesting, total dry matter and leaf area were evaluated. the data were Submitted to analysis of variance, to Tukey's tests and regression analyses. The application of K influenced A, gs and the transpiration rate. Plants deficient in K showed lower A and higher Us and transpiration rates. There were no statistical differences in A, gs and transpiration rates ill plants with and Without water deficit. The addition of K reduced the consumption of water per unit of leaf area and, in general, plants submitted to water deficit presented a lower consumption of water.

NEAR INFRARED SPECTROSCOPY FOR ESTIMATING SUGARCANE BAGASSE CONTENT IN MEDIUM DENSITY FIBERBOARD

Medium density fiberboard (MDF) is an engineered wood product formed by breaking down selected lignin-cellulosic material residuals into fibers, combining it with wax and a resin binder, and then forming panels by applying high temperature and pressure. Because the raw material in the industrial process is ever-changing, the panel industry requires methods for monitoring the composition of their products. The aim of this study was to estimate the ratio of sugarcane (SC) bagasse to Eucalyptus wood in MDF panels using near infrared (NIR) spectroscopy. Principal component analysis (PCA) and partial least square (PLS) regressions were performed. MDF panels having different bagasse contents were easily distinguished from each other by the PCA of their NIR spectra with clearly different patterns of response. The PLS-R models for SC content of these MDF samples presented a strong coefficient of determination (0.96) between the NIR-predicted and Lab-determined values and a low standard error of prediction (similar to 1.5%) in the cross-validations. A key role of resins (adhesives), cellulose, and lignin for such PLS-R calibrations was shown. PLS-DA model correctly classified ninety-four percent of MDF samples by cross-validations and ninety-eight percent of the panels by independent test set. These NIR-based models can be useful to quickly estimate sugarcane bagasse vs. Eucalyptus wood content ratio in unknown MDF samples and to verify the quality of these engineered wood products in an online process.

EFFECT OF FERTILIZATION ON CELL SIZE IN WOOD OF Eucalyptus grandis Hill Ex Maiden

The use of fertilization in forest stands results in yield gains, yet little attention has been directed to its potential effects on the quality of wood produced. Information is scarce about the effect of fertilization on anatomical structures of older Eucalyptus wood. This work aims to study the effect of fertilization on tissue cell size of wood from an Eucalyptus grandis stand at age 21 years, the management system of which is based on selective thinning and fertilizer application at the start of the thinning season. Factors to consider include: presence or absence of fertilizers, two log positions and five radial (pith to bark) positions. Results led to the conclusion that fertilization significantly influenced only vessel frequency. Vessel element length was influenced by tree height. Fiber length, fiber diameter, fiber wall thickness, vessel element length, vessel diameter and vessel frequency were influenced by the radial position of the sample in relation to the log. A positive correlation was observed between fiber length, fiber diameter, fiber wall thickness, vessel element length, vessel diameter, ray width and radial position, while a negative correlation was observed between ray frequency and radial position.

Produção de óleo essencial e balanço nutricional em Corymbia citriodora adubado com lodo de esgoto em diferentes espaçamentos

The Corymbia citriodora is one of the most cultivated species in Brazil for wood and essential oil production. The oil is obtained by the leaves distillation and the yield is around 2%. For the sustainability of leaves extraction is necessary a good nutritional replacement, because the leaves contain a large quantity of nutrients. The sewage sludge application in Corymbia plantations is a way to apply organic fertilizer and is also a good alternative for the final disposal of this residue. In this context, the objective of this study was to evaluate the sewage sludge use as fertilizer for the essential oil production in two different Spacing. The experiment was constituted by 4 blocks and the treatments were: i) Close spacing (1m x 1m) with sewage sludge + K and B; ii) Close spacing with mineral fertilization: iii) Regular spacing (3m x 1m) with sewage sludge + K and B; and iv) Regular spacing with mineral fertilization. When the C. citriodora plots were 12, 18, 24 and 30 months old, leaves and branches biomass and also essential oil production were quantified. It was observed that the system of close planting totalized a higher biomass, 3.8 times more than the conventional system, providing 3 times more essential oil production (363 l ha(-1) at the close spacing and 116 l ha(-1) at the regular Spacing during 30 months). No difference was found in the leaves or oil production with the use of sewage sludge or mineral fertilizer any of spacing studied The use of sewage sludge as fertilizer for Corymbia citriodora plantations may be an interesting alternative. because it supplies large quantities of nutrients and ensures a positive budget of nutrients in the ecosystem.

Efeito da aplicação de fertilização nitrogenada e lodo de esgoto nas características da madeira juvenil de árvores de Eucalyptus grandis

This work evaluated the wood anatomical and physical characteristics of 24 months-old Eucalyptus grandis trees, planted in 3x2m spacing and fertilized with nitrogen (6, 12, 18 month old) and sewage sludge (planting, 8 month old). For each treatment 10 eucalypts trees were cut according to the distribution of basal area. Wood samples were collected in different percentages of the total height to analyze the anatomical (vessels and fibers) and physical (wood density) characteristics. The results showed that the wood apparent density and wood basic density of the eucalypt trees in the nitrogen and sewage sludge were larger in comparison to the control. Radial profiles of wood apparent density, were similar in the three treatments, presenting the exected characteristics of juvenile wood of 24 months-old eucalypt trees. Fiber and vessel dimensions were not affected by fertilization.

INFLUENCE OF ALTITUDE, AGE AND DIAMETER ON YIELD AND ALPHA-BISABOLOL CONTENT OF CANDEIA TREES (Eremanthus erythropappus)

The heartwood of candeia tree is a source of essential oil rich in alpha-bisabolol, a substance widely used in the cosmetic and pharmaceutical industry. Bearing in mind the economic importance of alpha-bisabolol, this work aimed to evaluate the influence of tree age on the yield and content of alpha-bisabolol present in essential oil from candeia, considering two distinct reliefs and three diameter classes, in Aiuruoca region, south Minas Gerais state. The two distinct reliefs correspond respectively to one section of the stand growing at 1,000m of altitude (Area 1) and another section growing at 1,100m of altitude (Area 2). In each section, 15 trees were felled from among 3 different diameter classes. Discs were removed from the base of each tree to estimate their age by doing growth ring count. Soil samples were taken and Subjected to physical and chemical analysis. The logs were reduced into chips and random samples were taken for distillation to extract essential oil. The method used was steam distillation at a pressure of 2 kgf/cm(2)/2.5 h. The chemical analysis was performed in a gas chromatograph (GC) based on the alpha-bisabolol standard reference. The yield of essential oil from trees in Area I was higher than that from trees in Area 2, with the same pattern of influence for older trees. In Area 2, the alpha-bisabolol content was higher in younger trees. No differences were found between the relevant parameters in relation to diameter classes.

SELECTION OF TRICHOGRAMMA PRETIOSUM LINEAGES FOR CONTROL OF GRAPHOLITA MOLESTA IN PEACH

Grapholita molesta (Lepidoptera: Tortricidae) is one of the main pests of peach trees in Brazil, causing fruit losses of 3-5%. Among possible biological control agents, Trichogramma pretiosum (Hymenoptera: Trichogrammatidae) has been found in peach orchards. Our objectives were to study the rearing of T pretiosum in eggs of G. molesta and Anagasta kuehniella (Lepidoptera: Pyralidae), and select lineages of this parasitoid that have the potential to control G. molesta. Selection of best lineages was made from 5 populations of T pretiosum collected from organically-cultivated peach orchards. The study was done under controlled temperature (25 +/- 2 degrees C), relative humidity (70 +/- 10%) and 14:10 h (light:dark) photoperiod conditions. Grapholita molesta eggs were found to be adequate hosts for the development of T pretiosum, and the parameters for number of parasitized eggs, percent parasitized eggs, and sex ratio were similar to those for A. kuehniella eggs. The highest rate of parasitism of G. molesta eggs occurred in eggs with up to 48 h of embryonic development. Among the lineages of T pretiosum that were collected, HO8, PO8, PEL, and L3M showed the best biological performance and are therefore indicated for semi-field and field studies for biological control of oriental fruit moth.

Modelo de programação linear para otimização econômica do projeto de irrigação Baixo Acaraú - CE

The present work had as objective uses a model of lineal programming algorithm to optimize the use of the water in the District of Irrigation Baixo Acarau-CE proposing the best combination of crop types and areas established of 8,0 ha. The model aim maximize the net benefit of small farmer, incorporating the constraints in water and land availability, and constraints on the market. Considering crop types and the constraints, the study lead to the following conclusions: 1. The water availability in the District was not a limiting resources, while all available land was assigned in six of the seven cultivation plans analyzed. Furthermore, water availability was a restrictive factor as compared with land only when its availability was made to reduce to 60% of its actual value; 2. The combination of soursop and melon plants was the one that presented the largest net benefit, corresponding to R$ 5,250.00/ha/yr. The planting area for each crop made up to 50% of the area of the plot; 3. The plan that suggests the substitution of the cultivation of the soursop, since a decrease in annual net revenue of 5.87%. However, the plan that contemplates the simultaneous substitution of both soursop and melon produced the lowest liquid revenue, with reduction of 33.8%.

DEVELOPMENT OF A NOVEL SET OF MICROSATELLITE MARKERS FOR CASTOR BEAN, RICINUS COMMUNIS (EUPHORBIACEAE)

Premise of study: Microsatellite primers were developed for castor bean (Ricinus communis L.) to investigate genetic diversity and population structure, and to provide support to germplasm management. Methods and Results: Eleven microsatellite loci were isolated using an enrichment cloning protocol and used to characterize castor bean germplasm from the collection at the Instituto Agronomico de Campinas (IAC). In a survey of 76 castor bean accessions, the investigated loci displayed polymorphism ranging from two to five alleles. Conclusions: The information derived from microsatellite markers led to significant gains in conserved allelic richness and provides support to the implementation of several molecular breeding strategies for castor bean.

DEVELOPMENT OF MICROSATELLITE MARKERS FOR AULONEMIA ARISTULATA (POACEAE) AND CROSS-AMPLIFICATION IN OTHER BAMBOO SPECIES

Premise of the study: Microsatellite primers were developed for Aulonemia aristulata, an endangered species of economic interest, to further describe its genetic variability and population structure. We also tested cross-amplification in 18 other bamboo species. Methods and Results: Using an enrichment genomic library, 13 microsatellite loci were isolated and characterized in A. aristulata. Seven of these loci were polymorphic. Twelve markers were cross-amplified in at least ten of the tested bamboo species. Conclusions: These markers will be useful for studies on the genetic diversity and structure of A. aristulata, which are important for future conservation, management and breeding programs of this species.