The structure of non-completely regular spaces

F.B. Jones has proved that for many different topological properties P if there exists a non-normal space with property P then there exists a non-completely regular space Y with property P. In this paper we study the topological structure of the space Y and we characterize the topological spaces with a similar structure to that possessed by Y.     

q-concavity and related properties on symmetric sequence spaces

We introduce a new property between the q-concavity and the lower q-estimate of a Banach lattice and we get a general method to construct maximal symmetric sequence spaces that satisfies this new property but fails to be q-concave. In particular this gives examples of spaces with the Orlicz property but without cotype 2.     

Electrochemical valveless flow microsystems for ultra fast and accurate analysis of total isoflavones with integrated calibration

A novel strategy integrating methodological calibration and analysis on board on a planar first-generation microfluidics system for the determination of total isoflavones in soy samples is proposed. The analytical strategy is conceptually proposed and successfully demonstrated on the basis of (i) the microchip design (with the possibility to use both reservoirs), (ii) the analytical characteristics of the developed method (statically zero intercept and excellent robustness between calibration slopes, RSDs < 5%), (iii) the irreversible electrochemical behaviour of isoflavone oxidation (no significant electrode fouling effect was observed between calibration and analysis runs) and (iv) the inherent versatility of the electrochemical end-channel configurations (possibility of use different pumping and detection media). Repeatability obtained in both standard (calibration) and real soy samples (analysis) with values of RSD less than 1% for the migration times indicated the stability of electroosmotic flow (EOF) during both integrated operations. The accuracy (an error of less than 6%) is demonstrated for the first time in these microsystems using a documented secondary standard from the Drug Master File (SW/1211/03) as reference material. Ultra fast calibration and analysis of total isoflavones in soy samples was integrated successfully employing 60 s each; enhancing notably the analytical performance of these microdevices with an important decrease in overall analysis times (less than 120 s) and with an increase in accuracy by a factor of 3.     

A simple and efficient evolution operator for time-dependent Hamiltonians: the Taylor expansion

No compact expression of the evolution operator is known when the Hamiltonian operator is time dependent, like when Hamiltonian operators describe, in a semiclassical limit, the interaction of a molecule with an electric field. It is well known that Magnus [N. Magnus, Commun. Pure Appl. Math. 7, 649 (1954)] has derived a formal expression where the evolution operator is expressed as an exponential of an operator defined as a series. In spite of its formal simplicity, it turns out to be difficult to use at high orders. For numerical purposes, approximate methods such as "Runge-Kutta" or "split operator" are often used usually, however, to a small order (<5), so that only small time steps, about one-tenth or one-hundredth of the field cycle, are acceptable. Moreover, concerning the latter method, split operator, it is only very efficient when a diagonal representation of the kinetic energy operator is known. The Taylor expansion of the evolution operator or the wave function about the initial time provides an alternative approach, which is very simple to implement and, unlike split operator, without restrictions on the Hamiltonian. In addition, relatively large time steps (up to the field cycle) can be used. A two-level model and a propagation of a Gaussian wave packet in a harmonic potential illustrate the efficiency of the Taylor expansion. Finally, the calculation of the time-averaged absorbed energy in fluoroproprene provides a realistic application of our method.     

Effect of zeolite structure on the selective catalytic reduction of NO with ammonia over Mn-Fe supported on ZSM-5, BEA,MOR and FER

A series of catalysts based on Mn-Fe loaded zeolites was prepared by impregnation and their activity in the selective catalytic reduction of NO with ammonia (NH₃-SCR) was investigated. The highest catalytic conversion was recorded for MnFe-ZSM-5 (MnFe-Z), followed by MnFe-BEA (MnFe-B) and MnFe-MOR (MnFe-M), while MnFe-FER (MnFe-F) showed a very poor activity over the entire temperature range. In order to evidence a correlation between the structure and acidity of the zeolites and NO conversion, the prepared samples were characterized by various techniques (ICP-AES, N₂ physisorption at 77 K, XRD, ²⁷NMR, Raman, FTIR spectroscopy of adsorbed ammonia, H₂-TPR, DRS UV–Vis, EPR and XPS). The superior catalytic activity of MnFe-Z at low temperature is attributed to the abundance of Mn⁴⁺ concentration as revealed by XPS, the highest NH₃-L/NH₄⁺ ratio indicative of the contribution of metals in generating Lewis acidic centers as evidenced by IR-NH3, and the better reducibility of manganese and iron on ZSM-5 which increases the kinetics for red-ox cycles as confirmed in TPR analysis. Fe₃Mn₃O₈ mixed oxide phase is also detected by XRD and XPS and can be associated with the high reducibility of MnFe-Z which generates a high oxidation ability favoring NO to NO₂ oxidation. Raman spectroscopy was also used to confirm the existence of a strong synergy between metals and ZSM-5 support revealed by the shift in the signal position and the decrease in band intensities. The results showed that the zeolite framework and acidity generate catalysts with different textural and structural properties which influence the metal dispersion and speciation and hence influence the catalytic performances.

     

Power-normed spaces

To each power-norm \(((E^n, \Vert \cdot \Vert _n):n\in {\mathbb N})\) based on a given Banach space E, we associate two maximal symmetric sequence spaces \(L_\Phi ^E\) and \(L_\Psi ^E\) whose norms \(\Vert (z_k)\Vert _{L_\Phi ^E}\) and \(\Vert (z_k)\Vert _{L_\Psi ^E}\) are defined by \(\sup \{ \Vert (z_1x,\ldots ,z_nx)\Vert _n: \Vert x\Vert =1, n\in {\mathbb N}\}\) and \(\sup \{ \Vert \sum _{k=1}^n z_kx_k\Vert : \Vert (x_1,\ldots ,x_n)\Vert _n=1, n\in {\mathbb N}\}\) respectively. For each \(1\le p\le \infty \), we introduce and study the p-power-norms as those power-norms for which \(L_\Phi ^E=\ell ^p\) and \(L_\Psi ^E=\ell ^{p'}\), where \(1/p+1/p'=1\). As a special cases of p-power-norms we introduce certain smaller class, to be called the class of \(\ell ^p\)-power-norms, which is shown to contain the p-multi-norms defined in (Dales et al., Multi-norms and Banach lattices, 2016), and to coincide with the multi-norms and dual-multi-norms defined in (Dales and Polyakov, Diss Math 488, 2012) in the cases \(p=\infty \) and \(p=1\) respectively. We give several procedures to construct examples of such p-power and \(\ell ^p\)-power-norms and show that the natural formulations of the (p, q)-summing, (p, q)-concave, Rademacher power norms, t-standard power norms among others are examples in these classes. In particular, for instance the Rademacher power norm is a 2-power norm and the (p, q)-summing power-norm is a \(\ell ^r\)-power-norm for \(p>q\) with \(\frac{1}{r}=\frac{1}{q}-\frac{1}{p}\).     

Intrinsic losses of coupled-cavity waveguides in planar-photonic crystals

Coupled-cavity waveguides (CCWs) allow light propagation with strong field confinement in the cavities and small group velocity, which greatly enhances the efficiency of nonlinear effects. In addition, guided modes have zero dispersion at the central region of the transmission miniband. We show that CCWs created in planar photonic crystals, in which index guiding is required in some spatial dimensions, are intrinsically lossy in the region of zero dispersion, which strongly limits their use in nonlinear applications and devices.     

Determination of 2-isopropyl thioxanthone and 2-ethylhexyl-4-dimethylaminobenzoate in milk: comparison of gas and liquid chromatography with mass spectrometry

Liquid chromatography–tandem mass spectrometry (LC-MS/MS) and gas chromatography–mass spectrometry (GC-MS) have been compared for the analysis of 2-isopropyl thioxanthone (ITX) and 2-ethylhexyl-4-dimethylaminobenzoate (EHDAB). Pressurized liquid extraction (PLE) was applied for the extraction of ITX and EHDAB from milk and milk-based beverages. Samples were homogenized with sea sand and anhydrous sodium sulfate, and were extracted with ethyl acetate at 100 °C and 10.3 × 10⁶ Pa in one cycle of 10 min at 90% flush. Both, GC-MS and LC-MS/MS were suitable to determine these photoinitiators in the PLE extracts, providing appropriate identification and quantification. The recoveries obtained ranged from 70 to 99% for ITX and from 70 to 95% for EHDAB. These recoveries were equal as those obtained by a conventional liquid–liquid partitioning with acetonitrile and tert-butyl methyl ether–hexane. The quantification limits using GC-MS, based on a signal-to-noise ratio of 10, were 0.5 μg/L for ITX and 1 μg/L for EHDAB. The repeatability of the method, as indicated by the relative standard deviations, was within the range 0.9–16.1%. The same parameters calculated using LC-MS/MS result in quantification limits of 0.1 μg/L for ITX and 0.02 μg/L for EHDAB and repeatability within the range 5.2–19.4%. These results pointed out that both techniques are appropriate to determine these compounds in food samples. The method was applied to milk and milk-based beverages from different supermarkets. The ITX and EHDAB contents ranged from 2.5 to 325 μg/L and from 8 to 126 μg/L, respectively. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Unexpected Self‐Sorting Self‐Assembly Formation of a [4:4] Sulfate:Ligand Cage from a Preorganized Tripodal Urea Ligand

The design and synthesis of tripodal ligands 1 – 3 based upon the N‐methyl‐1,3,5‐benzenetricarboxamide platform appended with three aryl urea arms is reported. This ligand platform gives rise to highly preorganized structures and is ideally suited for binding SO₄^2? and H₂PO₄^? ions through multiple hydrogen‐bonding interactions. The solid‐state crystal structures of 1 – 3 with SO₄^2? show the encapsulation of a single anion within a cage structure, whereas the crystal structure of 1 with H₂PO₄^? showed that two anions are encapsulated. We further demonstrate that ligand 4 , based on the same platform but consisting of two bis‐urea moieties and a single ammonium moiety, also recognizes SO₄^2? to form a self‐assembled capsule with [4:4] SO₄^2?: 4 stoichiometry in which the anions are clustered within a cavity formed by the four ligands. This is the first example of a self‐sorting self‐assembled capsule where four tetrahedrally arranged SO₄^2? ions are embedded within a hydrophobic cavity.