Generalization of the pupil function for the optical systems containing birefringence elements

A pupil function of the optical systems containing birefringence elements is presented. It has been shown that the pupil function in this case may be represented as vector.     

Second-order conditions in stability analysis for state constrained optimal control

The paper presents an outline of the stability results, for state-constrained optimal control problems, recently obtained in Malanowski (Appl. Math. Optim. 55, 255–271, 2007), Malanowski (Optimization, to be published), Malanowski (SIAM J. Optim., to be published). The pricipal novelty of the results is a weakening of the second-order sufficient optimality conditions, under which the solutions and the Lagrange multipliers are locally Lipschitz continuous functions of the parameter. The conditions are weakened by taking into account strongly active state constraints.     

Low-light-induced Violaxanthin De-epoxidation in Shortly Preheated Leaves: Uncoupling from ΔpH-dependent Nonphotochemical Quenching

Plants protect themselves against excessive light by the induction of ΔpH-dependent nonphotochemical quenching (qE) that is associated with de-epoxidation of violaxanthin (V) to zeaxanthin (Z) in thylakoid membranes. In this work, we report that low light (12 μmol photons m⁻² s⁻¹) is sufficient for a marked stimulation of the V to Z conversion in shortly preheated wheat leaves (5 min, 40°C), but without a substantial increase in qE. Re-irradiation of these leaves with high light led to a rapid induction of nonphotochemical quenching, implying a potential photoprotective role of low-light-induced Z in preheated leaves. On the contrary to low light conditions, preheated leaves exposed to high light behaved similar to nonheated leaves with respect to the V to Z conversion and qE induction. The obtained results indicate that low-light-induced lumen acidification in preheated leaves is high enough to activate V de-epoxidation, but not sufficiently high to induce the formation of quenching centers.     

Solid-liquid extraction and cation-exchange solid-phase extraction using a mixed-mode polymeric sorbent of Datura and related alkaloids

Tropane alkaloids solid-liquid extraction methods were developed and comprised ambient pressure ones: extraction with hot solvent, extraction at room temperature, on ultrasonic bath as well as pressurised liquid extraction (PLE) techniques. The highest yields of l-hyoscyamine in methanol PLE method (3 x 5 min, 110 degrees C) and scopolamine extracted with 1% tartaric acid in methanol (15 min, 90 degrees C) were determined. A mixed-mode reversed-phase cation-exchange solid-phase extraction (SPE) procedure was optimised for simultaneous recoveries of L-hyoscyamine, scopolamine, scopolamine-N-oxide from plant extracts as well as quaternary alkaloid representative: scopolamine-N-methyl bromide. First three alkaloids were efficiently eluted (recoveries 80-100%) from an Oasis MCX cartridge with methanol-10% ammonia (3:1, v/v) solution, whereas for the quaternary salt tetrahydrofuran-methanol-25% ammonia (6:1:3, v/v) was used with recoveries 52-6%. HPTLC-densitometric assay on silica gel plates was elaborated at 205 nm without derivatization and included: single development (over a distance 9.5 cm) with acetone-methanol-water-25% ammonia (85:5:5:8, v/v) mobile phase for L-hyoscyamine and scopolamine separation, whereas for scopolamine-N-oxide and scopolamine-N-methyl bromide a second development (to a distance 5.5 cm) with acetonitrile-methanol-85% formic acid (120:5:5, v/v) was applied. Newly elaborated RP-HPLC-diode array detection method was performed on Waters XTerra RP-18 column with gradient of acetonitrile in 15 mM ammonia solution and alkaloids were baseline separated within 20 min. Both chromatographic methods were validated and their quantitative results were compared. Good correlation between HPLC and HPTLC quantitative results was measured (correlation coefficients of mean values were 0.92086 and 0.99995 for L-hyoscyamine and scopolamine, respectively). In the RP-HPLC method, which was from 1.5- up to 7-fold more sensitive than HPTLC, limits of detection (LOD) and limits of quantitation (LOQ, in bracket) were (in ng/microl) as follows: 0.25 (0.82) for L-hyoscyamine, 0.29 (0.97) for scopolamine, 0.13 (0.45) for scopolamine-N-oxide and 0.58 (1.91) for scopolamine-N-methyl bromide. By the use of the optimised chromatographic methods, 14 various samples from the leaves and fruits of Datura sp. were screened for L-hyoscyamine and scopolamine contents and the most promising samples were established.     

Synthesis and alkaline earth metal cation extraction by proton di-ionizable p-tert-butylcalix[4]arene-crown-5 compounds in cone, partial-cone and 1,3-alternate conformations

Synthetic strategies for novel, proton di-ionizable p-tert-butylcalix[4]arene-crown-5 compounds in cone, partial-cone and 1,3-alternate conformations are reported. Selective linkage of the two diametrical phenolic oxygens in p-tert-butylcalix[4]arene with tetraethylene glycol ditosylate gave 1,3-bridged p-tert-butylcalix[4]arene-crown-5. The two remaining phenolic units were alkylated using NaH and KH as the bases to give the cone and partial-cone conformers, respectively. Preparation of the 1,3-alternate conformers utilized a different sequence in which O-alkylation was followed by crown ether ring formation. Structures of these new ligands were elucidated by (1)H and (13)C NMR spectroscopy. These proton-ionizable ligands were tested for their solvent extraction properties toward alkaline earth metal cations. Surprising differences in their extraction behaviors are noted compared to those reported previously for di-ionizable p-tert-butylcalix[4]arenecrown-6 analogues.     

Effect of Fusarium oxysporum f. sp. lycopersici on the degradation of humic acid associated with Cu, Pb, and Ni: an in vitro study

The intent of this work was to gain further insight on the fungus-assisted degradation/solubilization of humic acid and the related changes in metal-binding profiles. In the experimental design, Aldrich reagent humic acid (HA) or HA enriched with Cu, Pb, and Ni (HA(Me)) was added to Fusarium oxysporum f. sp. lycopersici cultures in vitro. The cultures were supplied by different carbon- and nitrogen-containing nutrients (glucose, Glc, or glutamate, Glu and ammonium, NH₄⁺, or nitrate, NO₃⁻, ions, respectively) in order to examine their possible effect on HA and HA(Me) decomposition. During the first 48 h of fungus growth, gradual acidification to pH 2 was observed in medium containing Glc + NH₄⁺, while for other cultures, alkalinization to pH 9 occurred and then, the above conditions were stable up to at least 200 h. Size exclusion chromatography (SEC) with UV/Vis detection showed progressive degradation and solubilization of both HA and HA(Me) with the increasing time of fungus growth. However, the molecular mass distributions of HA-related soluble species were different in the presence of metals (HA(Me)) as referred to HA and were also influenced by the composition of growth medium. The solubilization of Pb, Cu, and Ni and their association with HA molecular mass fractions were studied using inductively coupled plasma mass spectrometry (ICP-MS) detection. Under acidic conditions, relatively high concentrations of low-molecular-mass metallic species were found in culture supernatants, while in alkaline media, metal solubilization was generally poorer. In contrast to low pH culture, SEC-ICP-MS results obtained in alkaline supernatants indicated metal binding to degradation products of humic substances of MM > 5 kDa. In summary, the results of this study suggest that fungus-assisted degradation of HA and HA(Me) might be controlled using appropriate N- and C- sources required for fungus growth, which in turn would affect molecular mass distribution of soluble metallic species thus potentially influencing their actual bioaccessibility. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Mössbauer and magnetic characterization of TbRhSn

The intermetallic compound TbRhSn was investigated in detail by X-ray, magnetic susceptibility measurements and ¹¹⁹Sn Mössbauer spectroscopy. This compound undergoes a transition from a paramagnetic to an antiferromagnetic state at T _N = 20.8(2) K. The ¹¹⁹Sn Mössbauer spectrum recorded at 4.2 K can be well fitted as a composition of three subspectra with the same intensities, magnitudes of H _hf, ΔE _Q, and δ _is, in agreement with the model of triangular-like antiferromagnetic arrangements of equal magnetic Tb moments lying in the basal ab-plane deduced from neutron diffraction studies (Szytu?a et al., J Alloys Compd 244:94–98, 1996).     

Some new results on integration for multifunction

It has been proven in Di Piazza and Musia? (Set Valued Anal 13:167–179, 2005, Vector measures, integration and related topics, Birkhauser Verlag, Basel, vol 201, pp 171–182, 2010) that each Henstock–Kurzweil–Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable (Theorem 3.4). Moreover, in case of strongly measurable (multi)functions, a characterization of the Birkhoff integrability is given using a kind of Birkhoff strong property.