Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch

A plane elastic wedge-shaped solid was split through the application of a rigid punch. It was assumed that the coefficient of friction on the the contact area was constant, and the problem had a plane of symmetry with respect to loading and geometry, with the crack in the plane of symmetry. The problem was formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution was obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area

Smoothing estimates for weakly nonlinear internal waves in a rotating ocean

In this paper we study the effect of rotation on nonlinear wave phenomena in weakly dispersive media modeled by the Korteweg-de Vries equation on the real line. It is well known that smoothing in the case of the KdV equation with periodic boundary conditions is a result of the presence of high frequency waves that weaken the nonlinearity through time averaging, \cite{bit}, \cite{et1}. High frequency interactions through normal form transformations can be thought of as adding a fast rotating term in certain toy PDE models that arrest the development of singularities, \cite{bit}. It is crucial for this phenomena that the zero Fourier mode can be removed due to the conservation of the mean. On the real line this mechanism breaks down as the resonance sets close to zero frequency are sizable and normal form transformations are not useful, \cite{imt}, and hence smoothing fails. The model we study is a perturbation of the KdV equation on a rotating frame of reference. A combination of a suitable normal form transformation along with the restricted norm method of Bourgain \cite{Bou2} implies smoothing on the real line.Comment: 17 page

Analytic and asymptotic properties of generalized Linnik probability densities

Cataloged from PDF version of article.This paper studies the properties of the probability density function pα,ν,n(x) of the n-variate generalized Linnik distribution whose characteristic function φα,ν,n(t) is given by where {norm of matrix}t{norm of matrix} is the Euclidean norm of t ∈ ℝn. Integral representations of pα,ν,n(x) are obtained and used to derive the asymptotic expansions of pα,ν,n(x) when {norm of matrix}x{norm of matrix}→0 and {norm of matrix}x{norm of matrix}→∞ respectively. It is shown that under certain conditions which are arithmetic in nature, pα,ν,n(x) can be represented in terms of entire functions. © 2009 Birkhäuser Boston

Qualitative features of periodic solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree

Highly senstivive determination of 2.4,6-Trinitrotolunene and Related Byproducts Using a Diol Functionalized Column for High Performance Liquid Chromatography

Cataloged from PDF version of article.In this work, a new detection method for complete separation of 2,4,6-trinitrotoluene (TNT); 2,4-dinitrotoluene (2,4-DNT); 2,6-dinitrotoluene (2,6-DNT); 2-aminodinitrotoluene (2-ADNT) and 4-aminodinitrotoluene (4-ADNT) molecules in high-performance liquid-chromatography (HPLC) with UV sensor has been developed using diol column. This approach improves on cost, time, and sensitivity over the existing methods, providing a simple and effective alternative. Total analysis time was less than 13 minutes including column re-equilibration between runs, in which water and acetonitrile were used as gradient elution solvents. Under optimized conditions, the minimum resolution between 2,4-DNT and 2,6-DNT peaks was 2.06. The recovery rates for spiked environmental samples were between 95-98%. The detection limits for diol column ranged from 0.78 to 1.17 μg/L for TNT and its byproducts. While the solvent consumption was 26.4 mL/min for two-phase EPA and 30 mL/min for EPA 8330 methods, it was only 8.8 mL/min for diol column. The resolution was improved up to 49% respect to two-phase EPA and EPA 8330 methods. When compared to C-18 and phenyl-3 columns, solvent usage was reduced up to 64% using diol column and resolution was enhanced approximately two-fold. The sensitivity of diol column was afforded by the hydroxyl groups on polyol layer, joining the formation of charge-transfer complexes with nitroaromatic compounds according to acceptor-donor interactions. Having compliance with current requirements, the proposed method demonstrates sensitive and robust separation. © 2014 Gumuscu et al

Exopolysaccharides from vaginal lactobacilli modulate microbial biofilms

Background: Exopolysaccharides (EPS) secreted by beneficial lactobacilli exert a plethora of positive activities, but little is known about their effects on biofilms of opportunistic vaginal pathogens and especially on biofilms of lactobacilli themselves. Here, the EPS produced by six vaginal lactobacilli, belonging to Lactobacillus crispatus (BC1, BC4, BC5) and Lactobacillus gasseri (BC9, BC12, BC14) species were isolated from cultural supernatants and lyophilized. Results: Lactobacillus EPS were chemically characterized in terms of monosaccharide composition by liquid chromatography (LC) analysis coupled to UV and mass spectrometry (MS) detection. Moreover, the ability of EPS (0.1, 0.5, 1 mg/mL) to stimulate the biofilm formation of lactobacilli and to inhibit the formation of pathogens’ biofilms was evaluated by crystal violet (CV) staining and 3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyl-2H-tetrazolium bromide (MTT) assay. Isolated EPS (yields 133–426 mg/L) were heteropolysaccharides mainly composed of d-mannose (40–52%) and d-glucose (11–30%). For the first time we demonstrated that Lactobacillus EPS were able to stimulate in a dose-dependent manner (p < 0.05) the formation of biofilms of ten strains belonging to L. crispatus, L. gasseri and Limosilactobacillus vaginalis species, in terms of cell viability (84–282% increase at 1 mg/mL) and especially biofilm biomass (40–195% increase at 1 mg/mL), quantified with MTT assay and CV staining, respectively. EPS released from L. crispatus and L. gasseri were found to better stimulate the biofilms of the same producer species rather than that of other species, including producing strains themselves and other strains. Conversely, the biofilm formation of bacterial (Escherichia coli, Staphylococcus spp., Enterococcus spp. and Streptococcus agalactiae) and fungal (Candida spp.) pathogens was inhibited. The anti-biofilm activity was dose-dependent and was more marked for L. gasseri-derived EPS (inhibition up to 86%, 70%, and 58% at 1 mg/mL, 0.5 mg/mL, and 0.1 mg/mL, respectively), whilst L. crispatus-derived EPS resulted overall less efficient (inhibition up to 58% at 1 mg/mL and 40% at 0.5 mg/mL) (p < 0.05). Conclusions: Lactobacilli-derived EPS favour the biofilm formation of lactobacilli preventing, at the same time, that of opportunistic pathogens. These results support the possible employment of EPS as postbiotics in medicine as a therapeutic/preventive strategy to counteract vaginal infections