The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Influence of potassium and sodium nutrition on leaf area components in Eucalyptus grandis trees

Background and Aims: Recent studies showed a positive tree response to Na addition in K-depleted tropical soils. Our study aimed to gain insight into the effects of K and Na fertilizations on leaf area components for a widely planted tree species. Methods: Leaf expansion rates, as well as nutrient, polyol and soluble sugar concentrations, were measured from emergence to abscission of tagged leaves in 1-year-old Eucalyptus grandis plantations. Leaf cell size and water status parameters were compared 1 and 2 months after leaf emergence in plots with KCl application (+K), NaCl application (+Na) and control plots (C). Results: K and Na applications enhanced tree leaf area by increasing both leaf longevity and the mean area of individual leaves. Higher cell turgor in treatments +K and +Na than in the C treatment resulting from higher concentrations of osmotica contributed to increasing both palisade cell diameters and the size of fully expanded leaves. Conclusions: Intermediate total tree leaf area in treatment +Na compared to treatments C and +K might result from the capacity of Na to substitute K in osmoregulatory functions, whereas it seemed unable to accomplish other important K functions that contribute to delaying leaf senescence. © 2013 Springer Science+Business Media Dordrecht.

Nitrogen and potassium fertilization on the yield and intensity of the maize white spot

A plant’s nutritional balance can influence its resistance to diseases. In order to evaluate the effect of increasing doses of N and K on the yield and severity of the maize white spot, two experiments were installed in the field, one in the city of Ijaci, Minas Gerais, and the other in the city of Sete Lagoas, Minas Gerais. The experimental delimitation was in randomized blocks with 5 x 5 factorial analysis of variance, and four repetitions. The treatments consisted of five doses of N (20; 40; 80; 150; 190 Kg ha-1 of N in the experiments 1 and 2) and five doses of K (15; 30; 60; 120; 180 Kg ha-1 of K in experiment 1 and 8.75; 17.5; 35; 50; 100 Kg ha-1 of K in experiment 2). The susceptible cultivar 30P70 was planted in both experiments. The plot consisted of four rows 5 meters long, with a useful area consisting of two central rows 3 meters each. Evaluations began 43 days after emergence (DAE) in the first experiment and 56 DAE in the second one. There was no significant interaction between doses of N and K and the disease progress. The effect was only observed for N. The K did not influence the yield and the severity of the disease in these experiments. Bigger areas below the severity progress curve of the white spot and better yield were observed with increasing doses of N. Thus, with increasing doses of N, the white spot increased and also did the yield.

A new flavonoid derivative from leaves of Oxandra Sessiliflora R. E. Fries

A fração em acetato de etila (EtOAc) obtida a partir da partição do extrato de etanol (EtOH) das folhas de O. sessiliflora R. E. Fries (Annonaceae) foi submetida a diversos procedimentos cromatográficos, incluindo cromatografia líquida de alta eficiência (HPLC), o que resultou no isolamento dos flavonóides: quercetina-3-O-α-L-ramnopiranosil-(1→4)-β-D-glucopiranosídeo (1), inédito na literatura, canferol-3-O-α-L-ramnopiranosil-(1→4)-β-D-glucopiranosídeo (2), rutina (3) e canferol-3-O-rutinosídeo (4). As estruturas foram definidas através da análise dos espectros de ressonância magnética nuclear (NMR) de ¹H e de 13C (1D e 2D) e espectrometria de massas.

Hydroxyapatite/beta-tricalcium phosphate and enamel matrix derivative for treatment of proximal class II furcation defects: a randomized clinical trial

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

Simple and direct potentiometric determination of potassium ions in biodiesel microemulsions at a glassy carbon electrode modified with nickel(II) hexacyanoferrate nanoparticles

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

Potassium nutrition in the first and second ratoon sugarcane grown in an Oxisol by a conservationist system

The presence of mulch on the soil surface after the mechanical harvesting of sugarcane (Saccharum officinarum L.) enhances the cycling of nutrients, especially K, which can decrease K fertilizer recommendations for the crop. The aim of this study was to evaluate the effect of K addition to an Oxisol, with an initial concentration 0.07 cmol(c) K kg(-1), in first and second ratoon (no-till) sugarcane cultures by a conservationist system, i.e. rational use of fertilizers, use of alternative inputs and especially the maintenance of residues in soil that was previously burned to facilitate cutting. The following K doses were tested: 0, 32.5, 65, 130, and 195 kg K2O ha(-1), arranged in a randomized block design with five replicates. Potassium content in the soil and in the plant, as well as the yield and the quality of stalks were evaluated. Soil K application increased K concentration in soil and plant, and was reflected in the prodUction of stalks, with higher production (87.5 and 107.5 t ha(-1)) with the use of 120 and 123 kg K2O ha(-1) in first and second ratoon sugarcane, respectively. At the first 2 yr it was not possible to reduce the K fertilization in ratoon. Therefore, with the introduction of the conservationist system there was an increase (20 t ha(-1)) at the second ratoon regarding the first one with the same applied rate.

Effects of potassium and sodium supply on drought-adaptive mechanisms in Eucalyptus grandis plantations

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

Effects of potassium application and soil moisture on the growth of Corymbia citriodora plants

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

Effect of potassium sources and rates on arabica coffee yield, nutrition, and macronutrient export

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

Thermo-sensitive chitosan-cellulose derivative hydrogels: swelling behaviour and morphologic studies

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A simple and fast method for assessment of the nitrogen-phosphorus-potassium rating of fertilizers using high-resolution continuum source atomic and molecular absorption spectrometry

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

Higher-derivative non-Abelian gauge fields via the Faddeev-Jackiw formalism

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)