Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics

Hypersingular integrals of the type I_{\alpha}(T_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{T_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 and I_{\alpha}(U_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{U_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 are investigated for general integers $\alpha$ (positive) and $m$ (non-negative), where $T_n(s)$ and $U_n(s)$ are the Tchebyshev polynomials of the 1st and 2nd kinds, respectively. Exact formulas are derived for the cases $\alpha = 1, 2, 3, 4$ and $m = 0, 1, 2, 3$; most of them corresponding to new solutions derived in this paper. Moreover, a systematic approach for evaluating these integrals when $\alpha > 4$ and $m>3$ is provided. The integrals are also evaluated as $|r|>1$ in order to calculate stress intensity factors (SIFs). Examples involving crack problems are given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. The examples include classical linear elastic fracture mechanics (LEFM), functionally graded materials (FGM), and gradient elasticity theory. An appendix, with closed form solutions for a broad class of integrals, supplements the paper

Start-up circuit for low-power indoor light energy harvesting applications

A start-up circuit, used in a micro-power indoor light energy harvesting system, is described. This start-up circuit achieves two goals: first, to produce a reset signal, power-on-reset (POR), for the energy harvesting system, and secondly, to temporarily shunt the output of the photovoltaic (PV) cells, to the output node of the system, which is connected to a capacitor. This capacitor is charged to a suitable value, so that a voltage step-up converter starts operating, thus increasing the output voltage to a larger value than the one provided by the PV cells. A prototype of the circuit was manufactured in a 130 nm CMOS technology, occupying an area of only 0.019 mm(2). Experimental results demonstrate the correct operation of the circuit, being able to correctly start-up the system, even when having an input as low as 390 mV using, in this case, an estimated energy of only 5.3 pJ to produce the start-up

Agronomic Evaluation of Forage Grasses under Mature Rubber Plantation

The agronomic performance of seven forage grasses, under a mature rubber plantation, was assessed in a cutting trial carried out at Porto Velho, Rondônia. During the rainy season, the higher dry matter yields were obtained with B. brizantha, P. atratum BRA-9610 and B. humidicola. During the dry season, the grasses more productive were B. brizantha and P. atratum BRA-9610. In both seasons, magnesium and potassium contents did not vary among grasses. During the rainy season, the higher nitrogen and phosphorus contents were obtained with P. regnelli BRA-0159 and, P. guenoarum BRA-3824 and B. humidicola, respectively, while P. atratum BRA-9610 and B. humidicola provided higher contents of calcium. During the dry season, P. regnelli BRA-0159 showed the highest nitrogen content, while B. humidicola and B. brizantha gave the highest phosphorus and calcium contents. In order to obtain greater forage yields with better quality, the grasses more promising for pasture establishment in a silvipastoral systems were B. brizantha, B. humidicola and P. atratum BRA-9610

Sistema de produção usando o rejeito da dessalinização de água salobra no semi-árido brasileiro.

Objetivando reduzir os impactos causados pelo rejeito da dessalinização de água salobra, no trópico semi-árido brasileiro, três alternativas de aproveitamento de água com alta salinidade, subproduto da dessalinização foram avaliadas nos campos da Estação Experimental da Embrapa Semi-Árido, em Petrolina-PE. As alternativas foram: (a) produção de tilápia rosa (Oreochromis sp); (b) produção de feno da erva-sal (Atriplex nummularia) irrigado; e (c) engorda de caprino/ovino com feno de erva-sal. A salinidade média da água usada foi de 11,38 ds/m. A tilápia atingiu o peso de 518,72 gramas em 153 dias de cultivo; o rendimento do feno da erva-sal foi de 14.900kg de matéria seca por hectare, e o ganho de peso de ovino/caprino, quando alimentado com 1,5 kg de feno da erva-sal, foi de 138 gramas/dia. Em função dos resultados obtidos com estes estudos, é possível a viabilização do uso do rejeito da dessalinização de água de poços no cristalino do semi-árido brasileiro para a geração de renda

The genetic landscape of the Iberian red deer (Cervus elaphus hispanicus) after 30 years of big-game hunting in southern Spain

© 2015 The Wildlife Society. The Iberian red deer (Cervus elaphus hispanicus) suffered a striking collapse of its populations during the first half of the 20th century due to excessive hunting. In Andalusia, southern Spain, re-colonization took place from a few relict populations through natural dispersal, and through artificial reintroductions for big-game hunting. How the population decline influenced genetic diversity, and its current distribution after the re-colonization and intensive hunting practices are unclear. We addressed these questions by analyzing nuclear microsatellite variability from 58 red deer populations distributed throughout Andalusia. Our results showed a relatively high genetic variability spatially structured into 5 clusters, corresponding to the locations of relict populations. This indicates that the red deer's current genetic background has presumably retained much of the genetic variation present in those relict populations. We also found that a substantial portion (32%) of the populations displays some degree of inbreeding. We suggest that new herds should be established using individuals from the different genetic clusters, and a careful monitoring of the breeder's genetic background to prevent further inbreeding and inadvertent hybridization. Failure to do so could lead to loss of genetic diversity and the dilution of the genetic identity of the Iberian red deer.Peer Reviewe

Macromineral requirements by beef cattle under pasture supplementation.

The objective of this work was to determine macromineral requirements by Zebu steers grazing Brachiaria decumbens supplemented with concentrate. It was used 24 non-castrated steers, at an average age of 7 months and at initial average weight 180 kg. Eight control animals were slaughtered for determining initial body composition. The 16 remaining animals were divided in four four-animal plots, in a complete random design. Each plot received mineral mixture or supplements at the levels 0.75; 1.50 or 2.25 kg/animal/day. The right half-carcass of eight animals, two per group, was dissected in muscle, fat and bones and all body constituents were weighted for determination of empty body weight and body composition. Net requirements of calcium and phosphorus for an animal at 400 kg body weight were 11.13 g and 5.40 g, respectively. To estimate dietary requirements of maintenance and after, sum them to dietary requirements for gain in order to obtain total dietary requirements, it was adopted endogenous losses and bioavailability present in literature for each mineral macroelement. Total dietary requirement for calcium, phosphorus, magnesium, sodium and potassium for a 400-kg BW animal with 1.0-kg daily weight gain were 34.59; 17.36; 7.82; 5.19 and 41.11 g/day, respectively. Macromineral requirements by beef cattle under pasture supplementation are similar to those recommended by BR-Corte for beef cattle in feedlots

Carbon and Nitrogen Stocks in Integrated Crop Livestock

Soil organic matter (SOM) is recognized as an important characteristic of sustainable agricultural systems in the tropics and temperate regions. It is considered an integrated characteristic of physical, chemical and biological soil conditions and has been used as a soil quality index in different land uses and management practices (Lal 2011). Environmental, social, and financial imbalances have occurred, requiring producers to become more efficient. A system of intercropping grain crops with forages can provide enough forage in the dry season to maintain nutritional quality of livestock and even promote weight gain (Castro Filho et al. 1991). An integrated crop-livestock system (ICLS) that includes a crop phase and a pasture phase in rotation has strong potential for sustainable beef and grain crop production (Salton et al. 2011). Perennial pastures can contribute to soil C sequestration. Several studies have shown significant soil organic C accumulation with well-managed grazing of pastures (Maia et al. 2009; Salton et al. 2011). However, there are few studies that compare the efficiency of different grasses to maintain productivity and promote an increase in soil organic C and stocks. We hypothesized that an ICLS with maize cultivated under no-tillage in rotation with grazed pasture (Urochloa P. Beauv. spp. (syn. Brachiaria (Trin.) Griseb. spp.) would result in accumulation of soil organic C and N compared with continuously grazed, degraded pasture or with conventionally tilled monoculture production of maize. Our objective was to evaluate the stocks of soil organic C and N under alternative land uses from the prevailing degraded pasture condition in Sao Paulo state of Brazil