Exact multiplicity of solutions and S-shaped bifurcation curves for the p-Laplacian perturbed Gelfand problem in one space variable

We study exact multiplicity of positive solutions and the bifurcation curve of the p-Laplacian perturbed Gelfand problem from combustion theory

     

Exact multiplicity and ordering properties of positive solutions of a p-Laplacian Dirichlet problem and their applications

We study the exact multiplicity and ordering properties of positive solutions of the p-Laplacian Dirichlet problem

     

Dispersive micro-solid phase extraction combined with gas chromatography-chemical ionization mass spectrometry for the determination of N-nitrosamines in swimming pool water samples

A simple sample pretreatment technique, dispersive micro-solid phase extraction, was applied for the extraction of N-nitrosodimethylamine (NDMA) and other four N-nitrosamines (NAs) from samples of swimming pool water. The parameters affecting the extraction efficiency were systematically investigated. The best extraction conditions involved immersing 75 mg of carbon molecular sieve, Carboxen™ 1003 (as an adsorbent), in a 50-mL water sample (pH 7.0) containing 5% sodium chloride in a sample tube. After 20 min of extraction by vigorous shaking, the adsorbent was collected on a filter and the NAs desorbed by treatment with 150 μL of dichloromethane. A 10-μL aliquot was then directly determined by large-volume injection gas chromatography with chemical ionization mass spectrometry using the selected ion storage mode. The limits of quantitation were <0.9 ng/L. The precision for these analytes, as indicated by relative standard deviations, were <8% for both intra- and inter-day analyses. Accuracy, expressed as the mean extraction recovery, was between 62% and 109%. A preliminary analysis of swimming pool water samples revealed that NDMA was present in the highest concentration, in the range from n.d. to 100 ng/L.     

A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities

We study the bifurcation diagrams of positive solutions of the two point boundary value problem

     

Simple and rapid method for evaluating stickiness of cotton using thermogravimetric analysis

Thermogravimetric analysis (TGA) with nitrogen and oxygen as carrier gas is used for the analysis of cotton lint samples for evaluating their stickiness. The advantage of the low melting point of trehalulose, a commonly found sugar, in the presence of oxygen as carrier gas is used for the evaluation. The oxidation of sugar present in the cotton lint results in increased weight around the melting point, which is proportional to the sugar content. The decomposition of the sugar further results in weight loss. This method is compared with the sticky cotton thermodetector and viscosity method for the estimation of sugar content. Good agreement between the methods suggests the usefulness and simplicity of TGA for estimation of stickiness in cotton.     

Chemical ionization of substituted naphthalenes using tetrahydrofuran as a reagent in gas chromatography with ion trap mass spectrometry

The ion/molecule reactions of nine monosubstituted naphthalene compounds in chemical ionization mass spectrometry (CI-MS) were studied using tetrahydrofuran (THF) as CI reagent. Proton affinity factors, substituent effects and the preferred site of adduct ion attachment were examined. Good correlation was observed between proton affinity and the formation of [M](+*) and [M+H](+) ions. The influence of substituents on protonation and site-specific adduct [M+13](+) and [M+41](+) ion formation is also observed, with the cyano substituent showing the most stable [M+41](+) ion. Collision-activated dissociation experiments were used to characterize the variety of adducts formed under CI conditions, and provided insight into product ion structures and mechanisms of dissociation and condensation during CI-MS/MS.     

A complete classification of bifurcation diagrams of a p -Laplacian Dirichlet problem

We study the bifurcation diagrams of (classical) positive solutions u with |u |_∞ ∈ (0, ∞) of the p -Laplacian Dirichlet problem (φ_p (u ′(x)))′ + λf_q (u (x))) = 0, –1 ≤ x ≤ 1, u (–1) = 0 = u (1), where p > 1, φ_p (y) = |y |^{p –2} y, (φ_p (u ′))′ is the one-dimensional p -Laplacian, λ > 0 is a bifurcation parameter, and the nonlinearity f_q (u) = |1 – u |^q is defined on [0, ∞) with constant q > 0. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Acomplete classification of bifurcation diagrams of classes of multiparameter p -Laplacian boundary value problems

We study the bifurcation diagrams of positive solutions of the multiparameter p -Laplacian problem (φ _p (u ′(x)))′ + f _λ,μ (u (x)) = 0, –1 < x < 1, u (– 1) = u (1) = 0, where p > 1, φ _p (y) = |y |^{p –2} y, (φ _p (u ′))′ is the one-dimensional p -Laplacian, f _λ,μ (u)= g (u, λ) + h (u, μ), and λ > λ₀ and μ > μ₀ are two bifurcation parameters, λ₀ and μ₀ are two given real numbers. Assuming that functions g and h satisfy hypotheses (H1)–(H4), for fixed μ > μ₀,we give a classification of totally eight qualitatively different bifurcation diagrams. We prove that, on the (λ, ∥u ∥_∞)-plane, each bifurcation diagram consists of exactly one curve which is either a monotone curve or has exactly one turning point where the curve turns to the right. Hence the problem has at most two positive solutions for each λ > λ₀. More precisely, we prove the exact multiplicity of positive solutions. In addition, for all p > 1, we give interesting examples which show complete evolution of bifurcation diagrams as μ varies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)