Catalan's intervals and realizers of triangulations

The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice which is an extension of the Kreweras lattice. The Stanley order can be defined on the set of Dyck paths of size n as the relation of being above. Hence, intervals in the Stanley lattice are pairs of non-crossing Dyck paths. In a former article, the second author defined a bijection Φ between pairs of non-crossing Dyck paths and the realizers of triangulations (or Schnyder woods). We give a simpler description of the bijection Φ. Then, we study the restriction of Φ to Tamari’s and Kreweras’ intervals. We prove that Φ induces a bijection between Tamari intervals and minimal realizers. This gives a bijection between Tamari intervals and triangulations. We also prove that Φ induces a bijection between Kreweras intervals and the (unique) realizers of stack triangulations. Thus, Φ induces a bijection between Kreweras intervals and stacktriangulations which are known to be in bijection with ternary trees.

Evaluating genetic algorithms with different population structures on a lot sizing and scheduling problem

This paper studies the use of different population structures in a Genetic Algorithm (GA) applied to lot sizing and scheduling problems. The population approaches are divided into two types: single-population and multi-population. The first type has a non-structured single population. The multi-population type presents non-structured and structured populations organized in binary and ternary trees. Each population approach is tested on lot sizing and scheduling problems found in soft drink companies. These problems have two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot sizing and scheduling of raw materials in tanks and products in lines. Computational results are reported allowing determining the better population structure for the set of problem instances evaluated. Copyright 2008 ACM.

WOOD DENSITY VARIATION AND TREE RING DEMARCATION IN Gmelina arborea TREES USING X-RAY DENSITOMETRY

Due to its relationship with other properties, wood density is the main wood quality parameter. Modern, accurate methods - such as X-ray densitometry - are applied to determine the spatial distribution of density in wood sections and to evaluate wood quality. The objectives of this study were to determinate the influence of growing conditions on wood density variation and tree ring demarcation of gmelina trees from fast growing plantations in Costa Rica. The wood density was determined by X-ray densitometry method. Wood samples were cut from gmelina trees and were exposed to low X-rays. The radiographic films were developed and scanned using a 256 gray scale with 1000 dpi resolution and the wood density was determined by CRAD and CERD software. The results showed tree-ring boundaries were distinctly delimited in trees growing in site with rainfall lower than 25 10 mm/year. It was demonstrated that tree age, climatic conditions and management of plantation affects wood density and its variability. The specific effect of variables on wood density was quantified by for multiple regression method. It was determined that tree year explained 25.8% of the total variation of density and 19.9% were caused by climatic condition where the tree growing. Wood density was less affected by the intensity of forest management with 5.9% of total variation.

Variation in the wood anatomical structure of Gmelina arborea (Verbenaceae) trees at different ecological conditions in Costa Rica

The tree Gmelina arborea has been widely introduced in Costa Rica for commercial purposes. This new conditions for melina cause variations on anatomy in secondary xylem of the trees growing in plantations. The objective of the present research was to determine the variation in the anatomy of xylem caused by the ecological conduction variation. Dimensions of fiber, axial parenchyma percentage of cross sections, parameters of vessels and the ray were measured. The results showed that some anatomical characteristics remained stable despite variations of ecological conditions, especially radial parenchyma and anatomical features which were less affected by the altitude. On the other hand, the vessels, axial parenchyma and fiber were less stable because they were affected significantly by the longitude, latitude, altitude and precipitation. Latitude significantly affected vessel percentage, length and diameter of the fiber and lumen. Longitude affected vessel percentage and fiber diameter. Altitude had a significant correlation with the amount of cells at my height. Annual average precipitation affected vessel percentage and diameter, not only of the fiber, but also of the lumen. These results suggest that the new growth conditions of G. arborea trees in Costa Rica have produced an anatomic adaptation.

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.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

The Lobel-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r( T, T') of trees T, T' from the above classes.

BORON UPTAKE AND DISTRIBUTION IN FIELD GROWN CITRUS TREES

In low fertility tropical soils, boron (B) deficiency impairs fruit production. However, little information is available on the efficiency of nutrient application and use by trees. Therefore, this work verified the effects of soil and foliar applications of boron in a commercial citrus orchard. An experiment was conducted with fertigated 4-year-old `Valencia` sweet orange trees on `Swingle` citrumelo rootstock. Boron (isotopically-enriched 10B) was supplied to trees once or twice in the growing season, either dripped in the soil or sprayed on the leaves. Trees were sampled at different periods and separated into different parts for total B contents and 10B/11B isotope ratios analyses. Soil B applied via fertigation was more efficient than foliar application for the organs grown after the B fertilization. Recovery of labeled B by fruits was 21% for fertigation and 7% for foliar application. Residual effects of nutrient application in the grove were observed in the year after labeled fertilizer application, which greater proportions derived from the soil supply.

Nickel sorption capacity of ground xylem of Quercus ilex trees and effects of selected ligands present in the xylem sap

In this work the influence of four different ligands present in the xylem sap of Quercus ilex (histidine, citric, oxalic and aspartic acids) on Ni(II) adsorption by xylem was investigated. Grinded xylem was trapped in acrylic columns and solutions of Ni(II), in the absence and presence of the four ligands prepared in KNO(3) 0-1 mol L(-1) at pH 5.5, were percolated through the column. Aliquots of solutions were recovered in the column end for Ni determination by graphite furnace atomic absorption spectrometry (GFAAS). The experimental. data to describe Ni sorption by xylem in both the presence and absence of ligands was better explained by the Freundlich isotherm model. The decreasing affinity order of ligands for Ni was: oxalic acid > citric acid > histidine > aspartic acid. On the other hand, the Ni(II) adsorption by xylem increased following the inverse sequence of ligands. Potentiometric titrations of acidic groups were carried out to elucidate the sorption site groups available in Q. ilex xylem. The potentiometric titration has shown three sorption sites: pK(a) 2.6 (57.7% of the sorption sites), related to monobasic aliphatic carboxylic acids or nitrogen aromatic bases, pK(a) 8.1 (9.6%) and pK(a) 9.9 (32.7%), related to phenolic groups. (C) 2008 Elsevier GmbH. All rights reserved.

Magnetization studies of binary and ternary Co-rich phases of the Co-Si-B system

CoB, CO(2)B, CoSi, Co(2)Si and CO(5)Si(2)B phases can be formed during heat-treatment of amorphous co-Si-B soft magnetic materials. Thus, it is important to determine their magnetic behavior as a function of applied field and temperature. In this study, polycrystalline single-phase samples of the above phases were produced via arc melting and heat-treatment under argon. The single-phase nature of the samples was confirmed via X-ray diffraction experiments. AC and DC magnetization measurements showed that Co(2)Si and CO(5)Si(2)B phases are paramagnetic. Minor amounts of either Co(2)Si or CoSi(2) in the CoSi-phase sample suggested a paramagnetic behavior of the CoSi-phase, however, it should be diamagnetic as shown in the literature. The diamagnetic behavior of the CoB phase was also confirmed. The paramagnetic behavior of CO(5)Si(2)B is for the first time reported. The magnetization results of the phase CO(2)B have a ferromagnetic signature already verified on previous NMR studies. A detailed set of magnetization measurements of this phase showed a change of the easy magnetization axis starting at 70K, with a temperature interval of about 13K at a very small field of 1 mT. As the strength of the field is increased the temperature interval is enlarged. The strength of field at which the magnetization saturates increases almost linearly as the temperature is increased above 70K. The room temperature total magnetostriction of the CO(2)B phase was determined to be 8 ppm at a field of 1T. (C) 2010 Elsevier B.V. All rights reserved.

Thermodynamic and topological instability approaches for forecasting glass-forming ability in the ternary Al-Ni-Y system

A thermodynamic approach to predict bulk glass-forming compositions in binary metallic systems was recently proposed. In this approach. the parameter gamma* = Delta H-amor/(Delta H-inter - Delta H-amor) indicates the glass-forming ability (GFA) from the standpoint of the driving force to form different competing phases, and Delta H-amor and Delta H-inter are the enthalpies for-lass and intermetallic formation, respectively. Good glass-forming compositions should have a large negative enthalpy for glass formation and a very small difference for intermetallic formation, thus making the glassy phase easily reachable even under low cooling rates. The gamma* parameter showed a good correlation with GFA experimental data in the Ni-Nb binary system. In this work, a simple extension of the gamma* parameter is applied in the ternary Al-Ni-Y system. The calculated gamma* isocontours in the ternary diagram are compared with experimental results of glass formation in that system. Despite sonic misfitting, the best glass formers are found quite close to the highest gamma* values, leading to the conclusion that this thermodynamic approach can lie extended to ternary systems, serving as a useful tool for the development of new glass-forming compositions. Finally the thermodynamic approach is compared with the topological instability criteria used to predict the thermal behavior of glassy Al alloys. (C) 2007 Elsevier B. V. All rights reserved.

Compatible Ternary Blends of Chitosan/poly(vinyl alcohol)/poly(lactic acid) Produced by Oil-in-Water Emulsion Processing

Ternary compatible blends of chitosan, poly(vinyl alcohol), and poly(lactic acid) were prepared by an oil-in-water (O/W) emulsion process. Solutions of chitosan in aqueous acetic acid, poly(vinyl alcohol) (PVA) in water, and poly(lactic acid) (PLA) in chloroform were blended with a high shear mixer. PVA was used as an emulsifier to stabilize the emulsion and to reduce the interfacial tension between the solid polymers in the blends-produced. It proved to work very well because the emulsions were stable for periods of days or weeks and compatible blends were obtained When PVA was added. This effect was attributed to a synergistic effect of PVA and chitosan because the binary blends PVA/PLA and chitosan/PLA were completely incompatible; The blends were characterized by scanning electron microscopy (SEM), differential scanning calorimetry (DSC), thermal mechanical analysis (TMA), stress strain tests, and Fourier transform infrared spectroscopy (FTIR). The results indicated that despite the fact that the system contained distinct phases some degree of molecular miscibility occurred when the three components were present in the blend.

The study of ternary carbides formation during SPS consolidation process in the WC-Co-steel system

Tungsten carbide has a wide range of applications, mainly cemented carbides made of WC and Co, as wear resistant materials. However, the high cost of WC-Co powders encourages the use of a substrate to manufacture a functionally graded material (FGM) tool made of WC-Co and a tool steel. These materials join the high wear resistance of the cemented carbide and the toughness of the steel. This work deals with the study interaction of the WC-Co and H13 steel to design a functionally graded material by means of spark plasma sintering (SPS). The SPS, a novel sintering technique reaching the consolidation of the powders at relatively low temperatures and short dwell times, is a promising technique in processing materials. In this study, WC, H13 steel, WC-Co, WC-H13 steel and WC-Co-H13 steel bulk samples were investigated using scanning electron microscopy and X-ray diffraction techniques to evaluate the phase transformations involved during SPS consolidation process. The W(2)C and W(3)Fe(3)C precipitation were identified after the SPS consolidation of the WC and WC-H13 steel samples, respectively. The precipitation Of W(4)Co(2)C was also identified in the WC-Co and WC-Co-H13 steel samples. The WC-H 13 steel and WC-Co-H13 steel were also evaluated after heat treatments at 1100 degrees C for 9 h, which enhanced the chemical interaction and the precipitation of W(3)Fe(3)C and W(4)Co(2)C, respectively. (C) 2009 Elsevier Ltd. All rights reserved.

Seasonal and diurnal changes in photosynthetic limitation of young sweet orange trees

This study tests the hypothesis that potted sweet orange plants show a significant variation in photosynthesis over seasonal and diurnal cycles. even in well-hydrated conditions. This hypothesis was tested by measuring diurnal variations in leaf gas exchange, chlorophyll fluorescence, leaf water potential, and the responses of CO(2) assimilation to increasing air CO(2) concentrations in 1-year-old `Valencia` sweet orange scions grafted onto `Cleopatra` mandarin rootstocks during the winter and summer seasons in a subtropical climate. In addition, diurnal leaf gas exchange was evaluated under controlled conditions, with constant environmental conditions during both winter and summer. In relation to our hypothesis, a greater rate of photosynthesis is found during the summer compared to the winter. Reduced photosynthesis during winter was induced by cool night conditions, as the diurnal fluctuation of environmental conditions was not limiting. Low air and soil temperatures caused decreases in the stomatal conductance and in the rates of the biochemical reactions underlying photosynthesis (ribulose-1,5-bisphosphate (RuBP) carboxylation and RuBP regeneration) during the winter compared to the values obtained for those markers in the Summer. Citrus photosynthesis during the summer was riot impaired by biochemical or photochemical reactions. as CO(2) assimilation was only limited by stomatal conductance due to high leaf-to-air vapor pressure difference (VPD) during the afternoon. During the winter, the reduction in photosynthesis during the afternoon Was Caused by decreases in RuBP regeneration and stomatal conductance, which are both precipitated by low night temperature. (c) 2009 Elsevier B.V. All rights reserved.

Association between decay fungi and subterranean termites in the wood biodeterioration process of Tipuana tipu (Benth.) O. Kuntze trees of Sao Paulo city, SP

In the present paper the process of wood biodeterioration of tipuana trees planted in 7 regions of the city of Sao Paulo, SP was evaluated. On the sidewalks, 1109 trees were analyzed taking into consideration the occurrence and association of the xylophagous organisms (decay fungi and subterranean termites), the wood deterioration and the BHD (breast height diameter). The percentage of wood internal deterioration (%) was obtained by non destructive analysis, using a penetrometer. The results had shown that 75% of the tipuana trees presented BHD superior to 50 cm, characterizing them as adult. Decay fungi in the roots and/or trunk had been observed in 338 trees (30.5%). Subterranean termites of Heterotermes sp. and Coptotermes gestroi species had occurred in 307 trees (27.7%), the latter in high infestation level. The association between the fungi and termites was observed, as well as its relation with the BHD, where a greater value of BHD meant higher wood biodeterioration intensity. For tipuana trees, the BHD was considered an indicative attribute of the internal deterioration intensity, caused by these xylophagous organisms.