Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Sobre o teorema de fibração de Milnor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sliding vector fields for non-smooth dynamical systems having intersecting switching manifolds

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effect of sowing time on phytomass production during early growth of two varieties of Stylosanthes guianensis (Aubl.) Sw.

The objective of this research was to determine the effect of two sowing times on phytomass production of two varieties of Slylosanthes guianensis (var. pauciflora and var. vulgaris). Two experimental periods were studied (1: January - May/1998 and 2: November/1998 - March/1999) using a completely randomized factorial design 2 x 2 x 14 (two periods, two varieties and fourteen ages of evaluation), with four replications. The results showed a difference between the periods concerning the growth and development of Stylosanthes, and that period 2 was the most favourable to this forage plant. There was, also, different adaptability between the two varieties concerning the sowing times. The var. pauciflora was more adapted in period 1, and the var. vulgaris, in period 2. The data showed the possibility of selecting Stylosanthes cultivars adapted to different seasonal conditions.

Susceptibility of fruits of the 'Valência' and 'Natal' sweet orange varieties to Guignardia citricarpa and the influence of the coexistence of healthy and symptomatic fruits

Em pomar de laranjeiras 'Valência' e 'Natal' avaliou-se a importância da presença de frutos sintomáticos da mancha preta citros (MPC) na severidade da doença nos frutos cítricos da safra subseqüente. Adicionalmente, avaliou-se o estádio de suscetibilidade dos frutos dessas variedades. Frutos foram protegidos com sacos de papel cristal a partir do estádio de 75% de pétalas caídas em outubro de 2000, até abril de 2001. Frutos foram expostos, em intervalos semanais, da 1ª à 24ª semana. Esse processo se deu tanto em plantas onde os frutos da safra remanescente foram previamente colhidos, como naquelas cujos frutos sintomáticos da safra remanescente permaneceram até a sua queda natural. Avaliou-se a severidade da doença usando uma escala de notas que variou de 0 (ausência de sintomas) a 6 (sintomas severos). Observou-se que para as duas variedades os conídios de Phyllosticta citricarpa, formados nas lesões dos frutos da safra remanescente, não provocaram incremento significativo na severidade da doença dos frutos da safra subseqüente. A proteção dos frutos até 10ª semana após a queda de pétalas não influenciou na quantidade final de lesões, indicando que as descargas de ascósporos que ocorreram a partir desse momento foram, provavelmente, responsáveis pela severidade da doença. Frutos que ficaram expostos entre a 20ª a 24ª semanas após a queda de 75% de pétalas mostraram-se sintomáticos, indicando que nesse estádio frutos encontravam-se suscetíveis ao patógeno.

The feeding preferences of Spodoptera frugiperda (J. E. SMITH) (Lepidoptera: Noctuidae) on cotton plant varieties

Avaliou-se atratividade e não-preferência alimentar de lagartas recém-eclodidas de Spodoptera frugiperda por partes de plantas e plantas de variedades de algodoeiro. Testes foram realizados a 27 ± 1ºC, UR de 70% ± 10% e fotofase de 14h. Folhas, brácteas, botões florais e cascas de maçãs da variedade BRS Itamarati-90 e folhas de Fibermax-966, Fibermax-977, DeltaOpal, DeltaPenta, BRS Acala-90, Coodetec-408, Coodetec-409, Coodetec-410, BRS-Cedro, BRS-Ipê, BRS-Aroeira, IPR-96, IPR-120, BRS-Araçá, IAC-24 e BRS Itamarati-90 foram utilizadas nos testes de atratividade e não-preferência para alimentação, com e sem chance de escolha. Utilizaram-se 20 lagartas de S. frugiperda por placa de Petri (sistema de arena) por teste, com 10 repetições. Contaram-se lagartas para avaliar atratividade por 60 min e não-preferência para alimentação por 24 h. Folha foi mais atrativa e preferida para alimentação por lagartas de S. frugiperda. em livre escolha, Coodetec-410 foi mais atrativa e BRS Acala-90, Fibermax-966 e DeltaPenta, as de menor atratividade à S. frugiperda; BRS-Araçá, mais preferida para alimentação e BRS-Cedro, BRS Itamarati 90, DeltaPenta, Coodetec-408 e BRS-Aroeira, menos preferidas. Considera-se 46 min., tempo mais adequado para avaliar atratividade de algodoeiro a lagartas de S. frugiperda.

Resistance of stored bean varieties to Acanthoscelides obtectus (Coleoptera : Bruchidae)

During bean seed storage, yield can be lost due to infestations of Acanthoscelides obtectus Say, the bean weevil. The use of resistant varieties has shown promising results in fighting these insects, reducing infestation levels and eliminating chemical residues from the beans. The expression of resistance to A. obtectus in bean varieties is frequently attributed to the presence of phytohemagglutinins, protease inhibitors and alpha-amylase, and especially to variants of the protein arcelin, which reduce the larval viability of these insects. To evaluate the effect of bean seed storage time on the resistance expression of bean varieties to A. obtectus, tests with seeds of three ages (freshly-harvested, 4-month-old, and 8-month-old) were conducted in the laboratory, using four commercial varieties: Carioca Pitoco, Ipa 6, Porrillo 70, Onix; four improved varieties containing arcelin protein: Are. 1, Arc.2, Arc. 3, Arc.4; and three wild varieties also containing arcelin protein: Arc. IS, Arc.3S, and Arc. 5S. The Arc.5S, Arc. IS, and Arc.2 varieties expressed high antibiosis levels against the weevil; Arc. I and Arc3S expressed the same mechanism, but at lower levels. The occurrence of oviposition non-preference was also observed in Arc.5S and Arc. IS. The Arc.3 and Arc. 4 varieties expressed low feeding non-preference levels against A. obtectus. The expression of resistance in arcelin-bearing, wild or improved varieties was affected during the storage of seeds, and was high under some parameters but low in others. The results showed that addition of chemical resistance factors such as protein arcelin via genetic breeding may be beneficial in improving the performance of bean crops.

EFFECT of TYPES of NOZZLES on SPRAY DEPOSITION on TWO SOYBEAN VARIETIES IN STAGE V3

The effect of application with different nozzle types and volume rates on spray deposition in the V3 stage of two soybean cultivars was evaluated. The experiments were conducted in the Facultad de Ciencias Agronomicas of the UNESP-Botucatu/SP. The nozzles evaluated were an air induced flat fan nozzle (Al 11015 at 150 L ha(-1), Al 11002 at 200 and 250 L ha(-1)), a twin flat fan nozzle (TJ 60 11002 at 150, 200 and 250 L ha(-1)), and a cone nozzle (TX 6 at 150 L ha(-1), TX 8 at 150 L ha(-1) and TX 10 at 250 L ha(-1)). To evaluate spray deposition on the plants, a tracer (Brilliant Blue FD&C-1) was added. The experimental design was random blocks with four replications. Deposition on plants was determined by absorbancy reading in 630 nm wavelength. The data were adjusted to a calibration curve and transformed into deposited spray volume in mL. The relationship deposition per unit of dry matter was adjusted to a regression curve (Gompertz model). In cultivar CD 208, the highest deposit was for the larger volumes and for the treatment TX 8 200 L ha(-1). The most uniform treatments were all the nozzles with the volume 150 L ha(-1) and the TJ60 nozzle for 200 1, ha(-1). In cultivar CD 216, the greatest spray depositions were achieved with the treatments Al at 200 and 250 L ha(-1) and TJ 60 at 250 L ha(-1), and the most uniform treatments were the TX 6 and TJ60 nozzles for the volume150 L ha(-1).

GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Radical scavenging activity of orange and tangerine varieties cultivated in Brazil

Four citrus fruit varieties cultivated in Brazil (two kinds of sweet orange and two kinds of tangerine) were analyzed for physicochemical characteristics contents of total phenolics, total carotenoids and ascorbic acid, and antioxidant activities. The antioxidant activities of aqueous, methanolic, and acetone extracts of the citrus fruit juices were assessed on the basis of their ability to scavenge 1,1-diphenyl-2-picrylhydrazyl (DPPH(center dot)). The cravo tangerine has the highest content of citric acid, while the pera orange is richest in ascorbic acid. The lima orange has the highest total phenolic contents, and the ponkan the highest total carotenoids. The antioxidant activities, expressed as the concentration of antioxidant able to scavenge 50% of the initial DPPH(center dot) (EC(50)), ranged from 139.1+/-27.3 to 182.2+/-28.8 g extract/l for juice of orange varieties and 186.3+/-29.6 to 275.5+/-3.3g extract/l for juice of tangerine citrus varieties. In methanolic extracts the EC(50) ranged from 192.5+/-43.1 to 267.4+/-41.4 g extract/l for orange varieties and from 225.2+/-69.8 to 336.3+/-27.2 g extract/l for tangerine varieties. For EC(50) values of acetone fractions, there were no statistically significant differences between the different varieties. For every citrus fruit in the present study, the radical scavenging capacity was higher in the aqueous than in the methanolic or acetone fractions.

Population genetic relationships between Casearia sylvestris (Salicaceae) varieties occurring sympatrically and allopatrically in different ecosystems in south-east Brazil

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

Characterization of native and oxidized starches of two varieties of Peruvian carrot (Arracacia xanthorrhiza, B.) from two production areas of Paraná state, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Constructions of algebraic lattices

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10.

Phenolic Composition of the Brazilian Seedless Table Grape Varieties BRS Clara and BRS Morena

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