Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure

Agricultural impacts of hydrobiogeochemical cycling in the Amazon: is there any solution?

Abstract: Expansion of agriculture in the Brazilian Amazon has been driven not just by demands from traditional, rural producers, but also large agriculture and cattle producers, both of whom have put considerable pressure on remaining forests and their watersheds. Monitoring of these watersheds has been a focus of intensive study for the past 20 years and although this work has greatly increased our understanding, considerable gaps still remain in our ability to provide adequate recommendations for land management and associated public policies. In this study we present a summary of findings from these previous results. For small properties, the use of fire to prepare land for cultivation remains controversial, while in large properties, forest conversion to pasture and/or crop production has had a meaningful and adverse effect on water quality. Riparian forest conservation can make a significant difference in reducing impacts of land-use change. Secondary vegetation can also play an important role in mitigating these impacts. New types of sustainable agricultural production systems, together with incentives such as payments for ecosystem service can also contribute. Continued monitoring of these changes, together with robust sustainable development plans, can help to preserve forest while still addressing the social and economic needs of Amazonian riverine inhabitants

Optimizing Connectivity through Network Gradients for the Restricted Boltzmann Machine

Leveraging sparse networks to connect successive layers in deep neural networks has recently been shown to provide benefits to large scale state-of-the-art models. However, network connectivity also plays a significant role on the learning performance of shallow networks, such as the classic Restricted Boltzmann Machines (RBM). Efficiently finding sparse connectivity patterns that improve the learning performance of shallow networks is a fundamental problem. While recent principled approaches explicitly include network connections as model parameters that must be optimized, they often rely on explicit penalization or have network sparsity as a hyperparameter. This work presents a method to find optimal connectivity patterns for RBMs based on the idea of network gradients (NCG): computing the gradient of every possible connection, given a specific connection pattern, and using the gradient to drive a continuous connection strength parameter that in turn is used to determine the connection pattern. Thus, learning RBM parameters and learning network connections is truly jointly performed, albeit with different learning rates, and without changes to the objective function. The method is applied to the MNIST and other datasets showing that better RBM models are found for the benchmark tasks of sample generation and input classification. Results also show that NCG is robust to network initialization, both adding and removing network connections while learning

CO2-driven cation leaching after tropical forest clearing.

The objective of this study was to investigate the role of dissolved CO2 (H2CO3*) as a mechanism of cation removal from surface soils under secondary land uses in the tropics. Soil leachate columns were prepared with 0?10 cm soils from mature and secondary forest, and managed pastures, and extracted with H2CO3* from deionized water equilibrated with 0%, 0.5%, 1%, and 10% CO2 (g). Extraction of soil cations slowed over time following an exponential form for the cumulative data. The rate of cation concentration decline varied as a function of CO2 concentration with the 10% solution resulting in a greater percent decline with extraction volume. Potassium removal from the exchange sites of all soils and for all solutions was nearly complete ranging from 85% to 97% while removals of Mg (31% to 71%) and Ca (12% to 42%) were lower. The asymptotic patterns of cation loss observed in this study suggest that H2CO3* acid-driven losses of cations may become self-limiting over time. Other stronger acids from atmospheric deposition or organic sources may serve to perpetuate cation removal, and re-forestation on these cleared lands would certainly re-distribute cations from soils to vegetation

Fatores de forma para 20 espécies florestais comerciais da Amazônia.

Em plano de manejo florestal, o inventário censitário das árvores, com diâmetro à altura do peito a partir de 30 cm, apresenta como principal objetivo o conhecimento de estimativas de volume comercial de madeira para a atual colheita e árvores potenciais destinadas ao futuro ciclo. O fator de forma é uma opção antiga que deve ser utilizada nas situações em que não se tenha nenhuma informação sobre a forma da árvore ou, ainda, quando for necessário rapidez no trabalho de inventário. Ele fornece estimativas confi áveis, desde que se controle a tipologia florestal, espécie e classe diamétrica. Apesar do conceito simples do fator de forma, são escassos os trabalhos que fornecem informações técnicas dessa natureza para árvores de florestas tropicais que considerem espécie florestal e classe diamétrica na Região Amazônica.bitstream/CPAF-AC-2010/23018/1/cot173.pd

Transformations of Heun's equation and its integral relations

We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011) 07520