On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Probing the time course of nonlinear discriminations during human electrodermal conditioning

Animal-based theories of Pavlovian conditioning propose that patterning discriminations are solved using unique cues or immediate configuring. Recent studies with humans, however, provided evidence that in positive and negative patterning two different rules are utilized. The present experiment was designed to provide further support for this proposal by tracking the time course of the allocation of cognitive resources. One group was trained in a positive patterning; schedule (A-, B-, AB+) and a second in a negative patterning schedule (A+, B+, AB-). Electrodermal responses and secondary task probe reaction time were measured. In negative patterning, reaction times were slower during reinforced stimuli than during non-reinforced stimuli at both probe positions while there were no differences in positive patterning. These results support the assumption that negative patterning is solved using a rule that is more complex and requires more resources than does the rule employed to solve positive patterning. (C) 2001 Elsevier Science (USA).

Absorption and dispersion by a multiple driven two-level atom

We investigate the absorption and dispersion properties of a two-level atom driven by a polychromatic field. The driving field is composed of a strong resonant (carrier) frequency component and a large number of symmetrically detuned sideband fields (modulators). A rapid increase in the absorption at the central frequency and the collapse of the response of the system from multiple frequencies to a single frequency are predicted to occur when the Rabi frequency of the modulating fields is equal to the Rabi frequency of the carrier field. These are manifestations of the undressing or a disentanglement of the atomic and driving field states, that leads to a collapse of the atom to its ground state. Our calculation permits consideration of the question of the undressing of the driven atom by a multiple-modulated field and the predicted spectra offer a method of observing undressing. Moreover, we find that the absorption and dispersion spectra split into multiplets whose structures depend on the Rabi frequency of the modulating fields. The spectral features can jump between different resonance frequencies by changing the Rabi frequency of the modulating fields or their initial phases, which can have potential applications as a quantum frequency filter.

The absorption and excretion of fluoride and arsenic in humans

The absorption and excretion of fluoride and arsenic were measured in a group of healthy volunteers given drinking water with naturally high concentration of fluoride (F 2.3 mg/l), or high concentration of arsenic (As 0.15 mg/l), or high concentrations of both fluoride and arsenic (F 2.25 mg/l, As 0.23 mg/l and F 4.05 mg/l, As 0.58 mg/l), respectively. The results indicated that, for arsenic, the absorption rate, the proportion of urinary excretion and the biological-half-life did not show statistically significant differences between drinking water containing high arsenic alone and drinking water containing different levels of high arsenic and fluoride. Excretion and retention of arsenic were positively correlated to the total arsenic intake. Similar results were observed for fluoride. This suggests that there are different metabolic processes for arsenic and fluoride in respect to absorption and excretion; and no joint action can be attributed by these two elements. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Mechanisms for the inhibition of amiloride-sensitive Na+ absorption by extracellular nucleotides in mouse trachea

Purinergic stimulation of airway epithelial cells induces Cl- secretion and modulates Na+ absorption by an unknown mechanism. To gain insight into this mechanism, we used a perfused micro-Ussing chamber to assess transepithelial voltage (V-te) and amiloride-sensitive short-circuit current (Isc-Amil) in mouse trachea. Exposure to apical ATP or UTP (each 100 mumol/l) caused a large initial increase in lumen negative V-te and I-sc corresponding to a transient Cl- secretion, while basolateral application of ATP/UTP induced only a small secretory response. Luminal, but not basolateral, application of nucleotides was followed by a sustained and reversible inhibition of Isc-Amil that was independent of extracellular Ca2+ or activation of protein kinase C and was not induced by carbachol (100 mumol/l) or the Ca2+ ionophore ionomycin (1 mumol/l). Removal of extracellular Cl- or exposure to 200 muM DIDS reduced UTP-mediated inhibition of Isc-Amil Substantially. The phospholipase inhibitor U73122 (10 mumol/l) and pertussis toxin (PTX 200 ng/ml) both attenuated UTP-induced Cl- secretion and inhibition of Isc-Amil. Taken together, these data imply a contribution of Cl- conductance and PTX-sensitive G proteins to nucleotide-dependent inhibition of the amiloride-sensitive Na+ current in the mouse trachea.

Bovine-serum-albumin-containing receptor phase better predicts transdermal absorption parameters for lipophilic compounds

Based on the hypothesis that limited receptor solubility of lipophilic compounds may result in lower observed permeability parameters, the aim of this study was to determine the in vitro human epidermal permeability coefficients and membrane retention of a series of aliphatic alcohols (C1-C10, log p -0.72 to 4.06) using two different receptor solutions (water and 4% bovine serum albumin in phosphate-buffered saline). Aqueous solutions of radiolabeled alcohols were dosed into the stratum corneum side of membranes mounted in side-by-side glass diffusion cells. Appearance of alcohol in the receptor compartment filled with either of the two solutions was monitored over a 7 h period when both stratum corneum (assessed by tape stripping) and the remaining epidermis levels of radioactivity were determined. In a separate study the degree of binding of alcohols to 4% bovine serum albumin was determined. The data showed increased receptor phase solubility in the bovine serum albumin solution and higher permeability coefficients for the more lipophilic alcohols in the series. No changes were seen in the partitioning of the alcohols from the vehicle into either the stratum corneum or tape-stripped epidermis with the two receptor phases; however, a decrease in the amount of the more lipophilic alcohols partitioning into the water receptor phase from the tape-stripped epidermis was observed. We conclude that bovine serum albumin receptor phase allows better estimation of real permeability parameters for lipophilic compounds due to its increased solubility capacity and we question whether permeability parameters for lipophilic solutes from older data sets based on aqueous receptor phases are completely reliable.

Ultrasonic absorption in polymer gel dosimeters

Ultrasonic absorption in polymer gel dosimeters was investigated. An ultrasonic interferometer was used to study the frequency (f) dependence of the absorption coefficient (alpha) in a polyacrylamide gel dosimeter (PAG) in the frequency range 5-20 MHz. The frequency dependence of ultrasonic absorption deviated from that of an ideal viscous fluid. The presence of relaxation mechanisms was evidenced by the frequency dependence of alpha/f(2) and the dispersion in ultrasonic velocity. It was concluded that absorption in polymer gel dosimeters is due to a number of relaxation processes which may include polymer-solvent interactions as well as relaxation due to motion of polymer side groups. The dependence of ultrasonic absorption on absorbed dose and formulation was also investigated in polymer gel dosimeters as a function of pH and chemical composition. Changes in dosimeter pH and chemical composition resulted in a variation in ultrasonic dose response curves. The observed dependence on pH was considered to be due to pH induced modifications in the radiation yield while changes in chemical composition resulted in differences in polymerisation kinetics. (C) 2003 Elsevier B.V. All rights reserved.

Unsaturated diffusivity functions for concrete derived from NMR images

Deterioration of concrete or reinforcing steel through excessive contaminant concentration is often the result of repeated wetting and drying cycles. At each cycle, the absorption of water carries new contaminants into the unsaturated concrete. Nuclear Magnetic Resonance (NMR) is used with large concrete samples to observe the shape of the wetting profile during a simple one-dimensional wetting process. The absorption of water by dry concrete is modelled by a nonlinear diffusion equation with the unsaturated hydraulic diffusivity being a strongly nonlinear function of the moisture content. Exponential and power functions are used for the hydraulic diffusivity and corresponding solutions of the diffusion equation adequately predict the shape of the experimental wetting profile. The shape parameters, describing the wetting profile, vary little between different blends and are relatively insensitive to subsequent re-wetting experiments allowing universal parameters to be suggested for these concretes.

Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element

Based on the refined non-conforming element method for geometric nonlinear analysis, a refined nonlinear non-conforming triangular plate element is constructed using the Total Lagrangian (T.L.) and the Updated Lagrangian (U.L.) approach. The refined nonlinear non-conforming triangular plate element is based on the Allman's triangular plane element with drilling degrees of freedom [1] and the refined non-conforming triangular plate element RT9 [2]. The element is used to analyze the geometric nonlinear behavior of plates and the numerical examples show that the refined non-conforming triangular plate element by the T.L. and U.L. approach can give satisfactory results. The computed results obtained from the T.L. and U.L. approach for the same numerical examples are somewhat different and the reasons for the difference of the computed results are given in detail in this paper. © 2003 Elsevier Science Ltd. All rights reserved.

Absorption of primary macronutrients and soybean growth at different compactation densities and moisture levels in a silt loam soil

ABSTRACT Soybean cultivation is increasing rapidly in the region of Alto Vale do Itajaí, State of Santa Catarina, where there is a predominance of silt soils. The objective of this work was to evaluate the content of primary macronutrients in shoots and shoot and root vegetative growth of soybean (Glicine max L. Merrill) grown in a silt-loam soil under different compactation densities and moisture levels. A randomized block design in a 4x4 factorial arrangement was used, with four compactation densities: 1.00; 1.20; 1.40 and 1.60 Mg m-3, and four soil moisture levels: 0.130; 0.160; 0.190 and 0.220 kg kg-1 and four replications. Each pot consisted of the overlapping of three 150-mm PVC rings, where soil was maintained in the higher and lower part of the pot with a density of 1.00 Mg m-3 and in the intermediate ring, the compactation densities were increased. Values of soil density higher than 120 Mg m-3 negatively affected N, P and K uptake by soybean plants, as well as the plant mass of the shoots and roots. The higher levels of soil moisture reduced the compaction effect and promoted better absorption of P and K.