Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Development of a flotation method for preconcentration-separation of trace amounts of some metal ions in plant tissues prior to their FAAS determinations

An efficient flotation method based on the combination of flame atomic absorption spectrometry (FAAS) and separation and preconcentration step for determination of Cr3+, Cu 2+, Co2+, Ni2+, Zn2+, Cd 2+, Fe3+ and Pb2+ ions in various real samples by the possibility of applying bis(2-hydroxyacetophenone)-1,4-butanediimine (BHABDI) as a new collector was studied. The influence of pH, amount of BHABDI as collector, sample matrix, type and amount of eluting agent, type and amount of surfactant as floating agent, ionic strength and air flow rates i.e. variables affecting the efficiency of the extraction system was evaluated. It is ascertained that metal ions such as iron can be separated simultaneously from matrix in the presence of 0.012 mM ligand, 0.025% (w/v) of CTAB to a test sample of 750 mL at pH 6.5. These ions can be eluted quantitatively with 6 mL of 1.0 mol L-1 HNO3 in methanol which lead to the enrichment factor of 125. The detection limits for analyte ions were in the range of 1.3-2.4 ng mL-1. The method has been successfully applied for determination of trace amounts of ions in various real samples.

An electroanalytical application of 2-aminothiazole-modified silica gel after adsorption and separation of Hg(II) from heavy metals in aqueous solution

2-Aminothiazole covalently attached to a silica gel surface was prepared in order to obtain an adsorbent for Hg(II) ions having the following characteristics: good sorption capacity, chemical stability under conditions of use, and, especially, high selectivity. The accumulation voltammetry of mercury(II) was investigated at a carbon paste electrode chemically modified with silica gel functionalized with 2-aminothiazole (SIAMT-CPE). The repetitive cyclic voltammogram of mercury(II) solution in the potential range -0.2 to + 0.6 V versus Ag/AgCl (0.02 mol L-1 KNO3; V = 20 mV s(-1)) show two peaks one at about 0.1 V and other at 0.205 V. The anodic wave peak at 0.205 V is well defined and does not change during the cycles and it was therefore further investigated for analytical purposes using differential pulse anodic stripping voltammetry in differents supporting electrolytes. The mercury response was evaluated with respect to pH, electrode composition, preconcentration time, mercury concentration, cleaning solution, possible interferences and other variables. The precision for six determinations (n = 6) of 0.02 and 0.20 mg L-1 Hg(II) was 4.1 and 3.5% (relative standard deviation), respectively. The detection limit was estimated as 0.10 mu g L-1 mercury(II) by means of 3:1 current-to-noise ratio in connection with the optimization of the various parameters involved and using the highest-possible analyser sensitivity. (c) 2006 Elsevier Ltd. All rights reserved.

The separation of secondary oil-water dispersions in particulate beds

The literature relating to haze formation, methods of separation, coalescence mechanisms, and models by which droplets <100 μm are collected, coalesced and transferred, have been reviewed with particular reference to particulate bed coalescers. The separation of secondary oil-water dispersions was studied experimentally using packed beds of monosized glass ballotini particles. The variables investigated were superficial velocity, bed depth, particle size, and the phase ratio and drop size distribution of inlet secondary dispersion. A modified pump loop was used to generate secondary dispersions of toluene or Clairsol 350 in water with phase ratios between 0.5-6.0 v/v%.Inlet drop size distributions were determined using a Malvern Particle Size Analyser;effluent, coalesced droplets were sized by photography. Single phase flow pressure drop data were correlated by means of a Carman-Kozeny type equation. Correlations were obtained relating single and two phase pressure drops, as (ΔP2/μc)/ΔP1/μd) = kp Ua Lb dcc dpd Cine A flow equation was derived to correlate the two phase pressure drop data as, ΔP2/(ρcU2) = 8.64*107 [dc/D]-0.27 [L/D]0.71 [dp/D]-0.17 [NRe]1.5 [e1]-0.14 [Cin]0.26  In a comparison between functions to characterise the inlet drop size distributions a modification of the Weibull function provided the best fit of experimental data. The general mean drop diameter was correlated by: q_p q_p p_q /β      Γ ((q-3/β) +1) d qp = d fr  .α        Γ ((P-3/β +1 The measured and predicted mean inlet drop diameters agreed within ±15%. Secondary dispersion separation depends largely upon drop capture within a bed. A theoretical analysis of drop capture mechanisms in this work indicated that indirect interception and London-van der Waal's mechanisms predominate. Mathematical models of dispersed phase concentration m the bed were developed by considering drop motion to be analogous to molecular diffusion.The number of possible channels in a bed was predicted from a model in which the pores comprised randomly-interconnected passage-ways between adjacent packing elements and axial flow occured in cylinders on an equilateral triangular pitch. An expression was derived for length of service channels in a queuing system leading to the prediction of filter coefficients. The insight provided into the mechanisms of drop collection and travel, and the correlations of operating parameters, should assist design of industrial particulate bed coalescers.

An electroanalytical application of 2-aminothiazole-modified silica gel after adsorption and separation of Hg(II) from heavy metals in aqueous solution

2-Aminothiazole covalently attached to a silica gel surface was prepared in order to obtain an adsorbent for Hg(II) ions having the following characteristics: good sorption capacity, chemical stability under conditions of use, and, especially, high selectivity. The accumulation voltammetry of mercury(II) was investigated at a carbon paste electrode chemically modified with silica gel functionalized with 2-aminothiazole (SIAMT-CPE). The repetitive cyclic voltammogram of mercury(II) solution in the potential range -0.2 to + 0.6 V versus Ag/AgCl (0.02 mol L-1 KNO3; V = 20 mV s(-1)) show two peaks one at about 0.1 V and other at 0.205 V. The anodic wave peak at 0.205 V is well defined and does not change during the cycles and it was therefore further investigated for analytical purposes using differential pulse anodic stripping voltammetry in differents supporting electrolytes. The mercury response was evaluated with respect to pH, electrode composition, preconcentration time, mercury concentration, cleaning solution, possible interferences and other variables. The precision for six determinations (n = 6) of 0.02 and 0.20 mg L-1 Hg(II) was 4.1 and 3.5% (relative standard deviation), respectively. The detection limit was estimated as 0.10 mu g L-1 mercury(II) by means of 3:1 current-to-noise ratio in connection with the optimization of the various parameters involved and using the highest-possible analyser sensitivity. (c) 2006 Elsevier Ltd. All rights reserved.

Doehlert Design-desirability Function Multi-criteria Optimal Separation Of 17 Phenolic Compounds From Extra-virgin Olive Oil By Capillary Zone Electrophoresis.

In Brazil, the consumption of extra-virgin olive oil (EVOO) is increasing annually, but there are no experimental studies concerning the phenolic compound contents of commercial EVOO. The aim of this work was to optimise the separation of 17 phenolic compounds already detected in EVOO. A Doehlert matrix experimental design was used, evaluating the effects of pH and electrolyte concentration. Resolution, runtime and migration time relative standard deviation values were evaluated. Derringer's desirability function was used to simultaneously optimise all 37 responses. The 17 peaks were separated in 19min using a fused-silica capillary (50μm internal diameter, 72cm of effective length) with an extended light path and 101.3mmolL(-1) of boric acid electrolyte (pH 9.15, 30kV). The method was validated and applied to 15 EVOO samples found in Brazilian supermarkets.

Separation Of Glycosidic Catiomers By Twim-ms Using Co2 As A Drift Gas.

Traveling wave ion mobility mass spectrometry (TWIM-MS) is shown to be able to separate and characterize several isomeric forms of diterpene glycosides stevioside (Stv) and rebaudioside A (RebA) that are cationized by Na(+) and K(+) at different sites. Determination and characterization of these coexisting isomeric species, herein termed catiomers, arising from cationization at different and highly competitive coordinating sites, is particularly challenging for glycosides. To achieve this goal, the advantage of using CO2 as a more massive and polarizable drift gas, over N2 , was demonstrated. Post-TWIM-MS/MS experiments were used to confirm the separation. Optimization of the possible geometries and cross-sectional calculations for mobility peak assignments were also performed. Copyright © 2015 John Wiley & Sons, Ltd.

Preparative separation of flavonoids from the medicinal plant Davilla elliptica St. Hill. by high-speed counter-current chromatography

High-speed counter-current chromatography (HSCCC) is a major tool for the fast separation of natural products from plants. It was used for the preparative isolation of the flavonoid monoglucosides present in the aerial parts of the Davilla elliptica St. Hill. (Dilleniaceae). This species is used in Brazilian folk medicine for the treatment of gastric disorders. The optimum solvent system used was composed of a mixture of ethyl acetate-n-propanol-water (140:8:80, v/v/v) and led to a successful separation of quercetin-3-O-alpha-L-rhamnopyranoside and myricetin-3-O-alpha-L-rhamnopyranoside in approximately 3.0 hours with purity higher than 95%. Identification was performed by ¹H NMR, 13C NMR and HPLC-UV-DAD analyses.

High performance magnetic separation of gold nanoparticles for catalytic oxidation of alcohols

We present the magnetic separation approach to facilitate the recovery of gold nanoparticle (AuNP) catalysts. The use of magnetically recoverable supports for the immobilization of AuNPs instead of traditional oxides, polymers or carbon based solids guarantees facile, clean, fast and efficient separation of the catalyst at the end of the reaction cycle. Magnetic separation can be considered an environmentally benign separation approach, since it minimizes the use of auxiliary substances and energy for achieving catalyst recovery. The catalyst preparation is based on the immobilization of Au(3+) on the surface of core-shell silica-coated magnetite nanoparticles, followed by metal reduction using two different methods. AuNPs were prepared by thermal reduction in air and by hydrogen reduction at mild temperature. Interestingly, the mean particle size of the supported AuNPs was similar (ca. 5.9 nm), but the polydispersity of the samples is quite different. The catalytic activity of both catalysts in the aerobic oxidation of alcohols was investigated and a distinct selectivity for benzyl alcohol oxidation was observed.

Separation of silica from bauxite via froth flotation

This paper reports an innovative development: concentrating gibbsite via reverse froth flotation in order to obtain a metallurgical-grade bauxite concentrate. Tailings from an industrial plant have undergone attrition scrubbing and desliming; the quartz silica contained in the tailings has undergone flotation. Starch was used as a depressant, and ether-amine as the cationic collector. Optimum pH is around 10.0. In pilot plant scale, a metallurgical-grade concentrate was obtained by assaying 42.3% available alumina with an alumina/insoluble silica mass ratio of 11.1. It contained the gibbsite and the iron and titanium bearing minerals. The concentrate was further upgraded by magnetic separation, leading to 54.0% available alumina, with an alumina/insoluble silica mass ratio of 12.6 at an overall available alumina recovery of 69.3% in the final concentrate (non-magnetic product). (C) 2008 Elsevier Ltd. All rights reserved.

Effect of Charge Asymmetry on Adsorption and Phase Separation of Polyampholytes on Silica and Cellulose Surfaces

The relation between the properties of polyampholytes in aqueous solution and their adsorption behaviors on silica and cellulose surfaces was investigated. Four polyampholytes carrying different charge densities but with the same nominal ratio of positive to negative segments and two structurally similar polyelectrolytes (a polyacid and a polybase) were investigated by using quartz crystal microgravimetry using silica-coated and cellulose-coated quartz resonators. Time-resolved mass and rigidity (or viscoelasticity) of the adsorbed layer was determined from the shifts in frequency (Delta f) and energy dissipation (Delta D) of the respective resonator. Therefore, elucidation of the dynamics and extent of adsorption, as well as the conformational changes of the adsorbed macromolecules, were possible. The charge properties of the solid Surface played a crucial role in the adsorption of the studied polyampholytes, which was explained by the capability of the surface to polarize the polyampholyte at the interface. Under the same experimental conditions, the polyampholytes had a higher nominal charge density phase-separated near the interface, producing a soft, dissipative, and loosely bound layer. In the case of cellulose substrates, where adsorption was limited, electrostatic and polarization effects were concluded to be less significant.

Separation of Steroids and the Determination of Estradiol Content in Transdermic Patches by Microemulsion Electrokinetic Chromatography

A novel microemulsion electrokinetic capillary chromatography (MEEKC) method has been developed which separates a range of nine steroids. A microemulsion containing ethyl acetate, butan-1-ol, sodium dodecyl sulfate, 15% (v/v) acetonitrile and 12 mmol L(-1) sodium tetraborate aqueous buffer at pH 9.2 was used with direct UV detection at 200 nm. The method was validated for the determination of 17 beta-estradiol content, a hormone steroid, in transdermal patches. Adequate sensitivity (DL = 0.88 mu g mL(-1); QL = 2.65 mu g mL(-1)) without interference from sample excipients was obtained. 17 beta-Estradiol migrates in approximately 5.4 min. Estrone was used as internal standard and acceptable precision (< 1.2% RSD), linearity (r = 0.9996; range from 40.0 to 60.0 mu g mL(-1)), and recovery (100.4 +/- A 0.9% at three concentration levels) were obtained. The principal advantage of the method is that it is rapid and avoids the need of time consuming and expensive sample pre-treatment steps.

Screening of Variables Influencing the Clavulanic Acid Production by Streptomyces DAUFPE 3060 Strain

Clavulanic acid (CA) is a beta-lactam antibiotic, which has a potent beta-lactamase inhibiting activity. The influence of five variables, namely pH (6.0, 6.4, and 6.8), temperature (28A degrees C, 30A degrees C, and 32A degrees C), agitation intensity (150, 200, and 250 rpm), glycerol concentration (5.0, 7.5, and 10 g/L) and soybean flour concentration (5.0, 12.5, and 20 g/L), on CA production by a new isolate of Streptomyces (DAUFPE 3060) was investigated in 250-mL Erlenmeyer flasks using a fractional factorial design. Temperature and soybean flour concentration were shown to be the two variables that exerted the most important effects on the production of CA at 95% confidence level. The highest CA concentration (494 mg/L) was obtained after 48 h at 150 rpm, 32A degrees C, pH 6.0, 5.0 g/L glycerol, and 20 g/L soybean flour concentrations. Under these conditions, the yields of biomass and product on consumed substrate were 0.26 g(X)/g(S) and 64.3 mg(P)/g(S), respectively. Fermentations performed in 3.0-L bench-scale fermenter allowed increasing the CA production by about 60%.