Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

First- and second-order stimulus length selectivity in New World monkey striate cortex

Motion is a powerful cue for figure-ground segregation, allowing the recognition of shapes even if the luminance and texture characteristics of the stimulus and background are matched. In order to investigate the neural processes underlying early stages of the cue-invariant processing of form, we compared the responses of neurons in the striate cortex (V1) of anaesthetized marmosets to two types of moving stimuli: bars defined by differences in luminance, and bars defined solely by the coherent motion of random patterns that matched the texture and temporal modulation of the background. A population of form-cue-invariant (FCI) neurons was identified, which demonstrated similar tuning to the length of contours defined by first- and second-order cues. FCI neurons were relatively common in the supragranular layers (where they corresponded to 28% of the recorded units), but were absent from layer 4. Most had complex receptive fields, which were significantly larger than those of other V1 neurons. The majority of FCI neurons demonstrated end-inhibition in response to long first- and second-order bars, and were strongly direction selective, Thus, even at the level of V1 there are cells whose variations in response level appear to be determined by the shape and motion of the entire second-order object, rather than by its parts (i.e. the individual textural components). These results are compatible with the existence of an output channel from V1 to the ventral stream of extrastriate areas, which already encodes the basic building blocks of the image in an invariant manner.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

New approximation for free surface flow of groundwater: capillarity correction

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.

Sheet flow sediment transport under waves with acceleration skewness and boundary layer streaming

The effect of acceleration skewness on sheet flow sediment transport rates (q) over bar (s) is analysed using new data which have acceleration skewness and superimposed currents but no boundary layer streaming. Sediment mobilizing forces due to drag and to acceleration (similar to pressure gradients) are weighted by cosine and sine, respectively, of the angle phi(.)(tau)phi(tau) = 0 thus corresponds to drag dominated sediment transport, (q) over bar (s)similar to vertical bar u(infinity)vertical bar u(infinity), while phi(tau) = 90 degrees corresponds to total domination by the pressure gradients, (q) over bar similar to du(infinity)/dt. Using the optimal angle, phi = 51 degrees based on that data, good agreement is subsequently found with data that have strong influence from boundary layer streaming. Good agreement is also maintained with the large body of U-tube data simulating sine waves with superimposed currents and second-order Stokes waves, all of which have zero acceleration skewness. The recommended model can be applied to irregular waves with arbitrary shape as long as the assumption negligible time lag between forcing and sediment transport rate is valid. With respect to irregular waves, the model is much easier to apply than the competing wave-by-wave models. Issues for further model developments are identified through a comprehensive data review.

Characterisation and environmental application of an Australian natural zeolite for basic dye removal from aqueous solution

An Australian natural zeolite was collected, characterised and employed for basic dye adsorption in aqueous solution. The natural zeolite is mainly composed of clinoptiloite, quartz and mordenite and has cation-exchange capacity of 120 meq/100 g. The natural zeolite presents higher adsorption capacity for methylene blue than rhodamine B with the maximal adsorption capacity of 2.8 x 10(-5) and 7.9 x 10(-5) Mot/g at 50 degrees C for rhodamine B and methylene blue, respectively. Kinetic studies indicated that the adsorption followed the pseudo second-order kinetics and could be described as two-stage diffusion process. The adsorption isotherm could be fitted by the Langmuir and Freundlich models. Thermodynamic calculations showed that the adsorption is endothermic process with Delta H degrees at 2.0 and 8.7 kJ/mol for rhodamine B and methylene blue. It has also found that the regenerated zeolites by high-temperature calcination and Fenton oxidation showed similar adsorption capacity but lower than the fresh sample. Only 60% capacity could be recovered by the two regeneration techniques. (c) 2006 Elsevier B.V. All rights reserved.

Geopolymeric adsorbents from fly ash for dye removal from aqueous solution

Adsorbents from coal fly ash treated by a solid-state fusion method using NaOH were prepared. It was found that amorphous aluminosilicate, geopolymers would be formed. These fly ash-derived inorganic polymers were assessed as potential adsorbents for removal of some basic dyes, methylene blue and crystal violet, from aqueous solution. It was found that the adsorption capacity of the synthesised adsorbents depends on the preparation conditions such as NaOH:fly-ash ratio and fusion temperature with the optimal conditions being at 121 weight ratio of Na:fly-ash at 250-350 degrees C. The synthesised materials exhibit much higher adsorption capacity than fly ash itself and natural zeolite. The adsorption isotherm can be fitted by Langmuir and Freundlich models while the two-site Langmuir model producing the best results. It was also found that the fly ash derived geopolymeric adsorbents show higher adsorption capacity for crystal violet than methylene blue and the adsorption temperature influences the adsorption capacity. Kinetic studies show that the adsorption process follows the pseudo second-order kinetics. (c) 2006 Elsevier Inc. All rights reserved.