Solid phase microextraction assisted by droplets-based liquid-liquid microextraction for analysis of volatile aromatic hydrocarbons in water by gas chromatography

A new technique for the analysis of volatile aromatic hydrocarbons by combining liquid-liquid microextraction with solid phase microextraction has been developed. The analytes were extracted from aqueous samples by an immobilized polydimethylsiloxane fiber assisted by the droplets of an appropriate organic solvent. Benzene, toluene, ethylbenzene, and o-xylene were used as target analytes. The main factors potentially affecting the microextraction such as the nature and the volume of organic solvent, polydimethylsiloxane (PDMS) swelling, extraction time, agitation, temperature, and salts were optimized. The method requires a very low consumption of organic solvent. The relative enrichment factor is in the range of 7.1-32.4 for extraction in the presence of dichloromethane at an optimum volume of 18 μL mL(-1) of aqueous sample. This enhancement over regular polydimethylsiloxane fiber is primarily the result of the fiber swelling and of a stable thin layer of organic solvent attached to the surface of the PDMS fiber. The limit of detection ranges from 0.02 to 0.65 ng mL(-1) for the target compounds using a 7-μm bonded polydimethylsiloxane coating and a flame ionization detector. The validity of this method is demonstrated by the analysis of a real waste water sample.     

Electronic transport of a T-shaped double-quantum-dot system in the Coulomb blockade regime

We studied the electronic transport properties of a T-shaped double-quantum-dot system in the Coulomb blockade regime when the onsite Coulomb interaction parameters U ₁ and U ₂ have finite values in both component dots. Our analysis is done in the so-called beyond Hartree-Fock approximation that includes contributions related to both normal and mixed averages of various number-like operators in the system. We provide an analytic formula for the main’s dot Green function in the case of large onsite Coulomb interaction parameters (U ₁ = U ₂ → ∞), and find that with a good approximation, this limit is realized when the ratio U ₁/t = U ₂/t ≥ 30, t being the interdot electron tunneling between the two component dots of the structures. In the most general situation of the Coulomb blockade regime (U ₁ ≠ U ₂) the system conductivity presents two dips corresponding to the Fano-Kondo effect and the system’s shot noise and electronic current present a series of plateaus that should be visible in experimental setups.     

Calculation of the quantum efficiency for the absorption on confinement levels in quantum dots

The quantum efficiency of the absorption on quantum confinement levels is investigated. This is achieved by modeling the electron confinement in a spherical quantum dot (QD). The confinement levels are calculated using both infinite and finite rectangular quantum wells. The spectral internal quantum efficiency is evaluated within both the models, by computing Einstein’s coefficients for the transitions between confinement levels. The size of QDs (1–3 nm radius) leads to negligible many body effects. The nature of the QD material and of the matrix embedding is taken into account in the finite rectangular quantum well approximation and introduces only a small correction. The temperature dependence of the efficiency is also taken into account. A numerical application is performed for a silicon QD of 2.5 nm radius, embedded in amorphous silica. It is proved that the absorption threshold shifts toward the far infrared limit and that the spectral internal quantum efficiency reaches 4–5% at the threshold.     

A spirobicyclic complex of Schmidpeter's ligand,bis(tetraphenylimidodiphosphinato)beryllium,Be(OPh2PNPPh2O)2, an inorganic analog of beryllium bis(β‐diketonates)

The crystal structure of bis(tetra‐phenylimidodiphosphinato)beryllium (as a benzene solvate), Be(OPh₂PNPPh₂O)₂. C₆H₆, was determined by X‐ray diffraction and compared with that of beryllium acetylacetonate, Be(OCMeCHCMeO)₂. The imidodiphosphinate is an inorganic spirobicyclic system, Be(OPNPO)₂, with tetrahedrally coordinated beryllium. Unlike the planar BeO₂C₃ rings in the acetylacetonate, the two six‐membered BeO₂P₂N inorganic rings are nonplanar and display a skew boat conformation. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:244–248, 2000     

Acetonyl­di­chloro­[(Z)‐2‐chloro‐2‐phenyl­vinyl]­tellurium(IV), helical chains of metal complexes

The primary geometry about the Te^IV atom in the title compound, [TeCl₂(C₈H₆Cl)(C₃H₅O)] or C₁₁H₁₁Cl₃OTe, is a pseudo‐trigonal‐bipyramidal arrangement, with two Cl atoms in apical positions, and the lone pair of electrons and C atoms in the equatorial plane. The Te^IV atom is involved in three secondary interactions, two intramolecular [Te?O = 2.842 (3) Å and Te?Cl3 = 3.209 (1) Å] and one intermolecular [Te?Cl = 3.637 (1) Å], the latter giving rise to a helical chain. These helices are linked by C—H?O interchain interactions.     

The first example of a recursive function which is not primitive recursive

The first example of a recursive function which is not primitive recursive is usually attributed to W. Ackermann. The authors of the present paper show that such an example can also be found in a paper by G. Sudan, published concomitantly with Ackermann's paper.     

Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

This paper introduces tensorial calculus techniques in the framework of POD to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an online complexity of , where k is the dimension of POD basis and therefore is independent of full space dimension. However, it is efficient only for quadratic nonlinear terms because for higher nonlinearities, POD model proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two‐dimensional SWE test problem to compare the performance of tensorial POD, POD, and POD/discrete empirical interpolation method (DEIM). Numerical results show that tensorial POD decreases by 76× the computational cost of the online stage of POD model for configurations using more than 300,000 model variables. The tensorial POD SWE model was only 2 to 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM SWE model to compute its offline stage faster than POD and tensorial POD approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Analyticity of the Planar Limit of a Matrix Model

Using Chebyshev polynomials combined with some mild combinatorics, we provide an alternative approach to the analytical and formal planar limits of a random matrix model with a 1-cut potential V. For potentials ${V(x)=x^{2}/2-\sum_{n\ge1}a_{n}x^{n}/n}$ , as a power series in all a _n , the formal Taylor expansion of the analytic planar limit is exactly the formal planar limit. In the case V is analytic in infinitely many variables {a _n } _n ≥ 1 (on the appropriate spaces), the planar limit is also an analytic function in infinitely many variables and we give quantitative versions of where this is defined. Particularly useful in enumerative combinatorics are the gradings of ${V,V_{t}(x)=x^{2}/2-\sum_{n\ge1}a_{n}t^{n/2}x^{n}/n}$ and ${V_{t}(x)=x^{2}/2-\sum_{n\ge3}a_{n}t^{n/2 -1}x^{n}/n}$ . The associated planar limits F(t) as functions of t count planar diagram sorted by the number of edges respectively faces. We point out a method of computing the asymptotic of the coefficients of F(t) using the combination of the wzb method and the resolution of singularities. This is illustrated in several computations revolving around the important extreme potential ${V_{t}(x)=x^{2}/2+\log(1-\sqrt{t}x)}$ and its variants. This particular example gives a quantitative and sharp answer to a conjecture of ’t Hooft’s, which states that if the potential is analytic, the planar limit is also analytic.     

Water soluble complexes of methyl β-cyclodextrin and sulconazole nitrate

Complexation between methyl β-cyclodextrin (Me βCD) and sulconazole nitrate (SULC) was realized both under freeze drying and ultrasonication conditions. The process was carried out in solution and in solid state. In solution, the complexation was evaluated using solubility studies, nuclear magnetic resonance spectroscopy (¹H-NMR) and UV–Vis absorption studies. In the solid state, differential scanning calorimetry (DSC), and X-ray diffraction studies were used. Solubility studies indicate the existence of inclusion complexes between SULC and Me βCD. ¹H-NMR data showed that the inclusion complexes have different structures, according with the method we used for synthesis: for the freeze dried method the complex is obtained by complexation of dichlorobenzene ring of SULC into inner cavity of CD while for ultrasonication method the complex is obtained by complexation of imidazole graph of SULC into the CD molecule. DSC and X-ray studies bring supplementary information concerning the formation of complex Me βCD–SULC. As a result of the inclusion process into Me βCD, the solubility of SULC increase significant, being 10 times more comparative with the pure drug. We anticipate that these modifications will have a significant impact on the biological effects of the drug, making the SULC–Me βCD complex an appropriate candidate for a new drug delivery system.     

Couplings of Brownian Motions of Deterministic Distance in Model Spaces of Constant Curvature

We consider the model space \(\mathbb {M}^{n}_{K}\) of constant curvature K and dimension \(n\ge 1\) (Euclidean space for \(K=0\), sphere for \(K>0\) and hyperbolic space for \(K<0\)), and we show that given a function \(\rho :[0,\infty )\rightarrow [0, \infty )\) with \(\rho (0)=\mathrm {dist}(x,y)\) there exists a coadapted coupling (X(t), Y(t)) of Brownian motions on \(\mathbb {M}^{n}_{K}\) starting at (x, y) such that \(\rho (t)=\mathrm {dist}(X(t),Y(t))\) for every \(t\ge 0\) if and only if \(\rho \) is continuous and satisfies for almost every \(t\ge 0\) the differential inequality

$$\begin{aligned} -(n-1)\sqrt{K}\tan \left( \tfrac{\sqrt{K}\rho (t)}{2}\right) \le \rho '(t)\le -(n-1)\sqrt{K}\tan \left( \tfrac{\sqrt{K}\rho (t)}{2}\right) +\tfrac{2(n-1)\sqrt{K}}{\sin (\sqrt{K}\rho (t))}. \end{aligned}$$

In other words, we characterize all coadapted couplings of Brownian motions on the model space \(\mathbb {M}^{n}_{K}\) for which the distance between the processes is deterministic. In addition, the construction of the coupling is explicit for every choice of \(\rho \) satisfying the above hypotheses.