A new fluorescent calix crown ether: synthesis and complex formation with alkali metal ions

We synthesised a new N-benzylaza-21-crown-7 ether 5 with a dihydroxy coumarin as a fluorescence sensor and investigated the binding behaviour towards alkali metal cations in methanol by fluorescence titrations. The association constants are within one order of magnitude, with the exception of sodium. Potassium is the preferred binding partner (K(Na)=330 M(-1); K(K)=8600 M(-1); K(Rb)=8200 M(-1); K(Cs)=4400 M(-1)). The corresponding aza-21-crown-7 ether (6) was attached by a methylene unit to a resorcarene to give fluorescent calix crown ether 12. The binding abilities of the calix crown ether towards alkali metal ions in methanol have also been investigated, and an increasing complex stability, distinct for potassium and rubidium in comparison with 5, was found: K(Na)=440 M(-1); K(K)=110,000 M(-1); K(Rb)=63,000 M(-1); K(Cs)=20,000 M(-1). Like bis(crown ether)s, a cooperative complexation of the crown ether and the cavitand scaffold can be assumed. The proposed complex geometry is supported by Kohn-Sham DFT calculations for the potassium and caesium complexes.     

Polar actions on compact Euclidean hypersurfaces

Given an isometric immersion of a compact Riemannian manifold of dimension n ≥ 3 into Euclidean space of dimension n + 1, we prove that the identity component Iso ⁰(M ⁿ ) of the isometry group Iso(M ⁿ ) of M ⁿ admits an orthogonal representation such that for every . If G is a closed connected subgroup of Iso(M ⁿ ) acting polarly on M ⁿ , we prove that Φ(G) acts polarly on , and we obtain that f(M ⁿ ) is given as Φ(G)(L), where L is a hypersurface of a section which is invariant under the Weyl group of the Φ(G)-action. We also find several sufficient conditions for such an f to be a rotation hypersurface. Finally, we show that compact Euclidean rotation hypersurfaces of dimension n ≥ 3 are characterized by their underlying warped product structure.      

Model‐based analysis of a dielectrophoretic microfluidic device for field‐flow fractionation

We present the development of a dynamic model for predicting the trajectory of microparticles in microfluidic devices, employing dielectrophoresis, for Hyperlayer field‐flow fractionation. The electrode configuration is such that multiple finite‐sized electrodes are located on the top and bottom walls of the microchannel; the electrodes on the walls are aligned with each other. The electric potential inside the microchannel is described using the Laplace equation while the microparticles' trajectory is described using equations based on Newton's second law. All equations are solved using finite difference method. The equations of motion account for forces including inertia, buoyancy, drag, gravity, virtual mass, and dielectrophoresis. The model is used for parametric study; the geometric parameters analyzed include microparticle radius, microchannel depth, and electrode/spacing lengths while volumetric flow rate and actuation voltage are the two operating parameters considered in the study. The trajectory of microparticles is composed of transient and steady state phases; the trajectory is influenced by all parameters. Microparticle radius and volumetric flow rate, above the threshold, do not influence the steady state levitation height; microparticle levitation is not possible below the threshold of the volumetric flow rate. Microchannel depth, electrode/spacing lengths, and actuation voltage influence the steady‐state levitation height.     

Synthesis and metal cation complexing properties of crown-annelated terthiophenes containing 3,4-ethylenedioxythiophene

Macrocyclic systems derived from crown-annelated terthiophene involving a median EDOT unit have been synthesized by coupling diiodooligooxyethylene chains and bis(2-cyanoethylsulfanyl)terthiophene under high dilution conditions. The metal cation complexing properties of the compounds have been analyzed using 1H NMR, UV-vis spectroscopy, and cyclic voltammetry. These various experiments provide consistent results showing that one of the compounds exhibits interesting complexing properties for Pb2+.     

Thermodynamic formalism of transcendental entire maps of finite singular type

We build a version of a thermodynamic formalism for maps of the form f(z) = ∑ _{j = 0} ^{p + q} a _j e ^(j−p)z where p, q > 0 and . We show in particular the existence and uniqueness of (t,α)-conformal measures and that the Hausdorff dimension HD(J _f ^r ) = h is the unique zero of the pressure function t ↦ P(t) for t > 1, where the set J _f ^r is the radial Julia set. Partially supported by NSF Grant DMS 0100078. Partially supported by Warsaw University of Technology Grant No. 504G11200023000, Polish KBN Grant No. 2PO3A03425 and Chilean FONDECYT Grant No. 11060280.     

Random quantum channels II: Entanglement of random subspaces, Rényi entropy estimates and additivity problems

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output Rényi entropies. We show that random channels obtained by randomly coupling the input to a qubit violate the additivity of the p-Rényi entropy, for all p>1. For some sequences of random quantum channels, we compute almost surely the limit of their Schatten S₁→Sp norms.     

Polyimides Containing Azobenzene Side Units: Properties and Correlation with Conformational Parameters

Two series of aromatic polyimides differing by the bridging group between imide rings, polymers a, b, and c, having C?O linkages and polymers d, e, and f, having C(CF₃)₂ groups, have been obtained by polycondensation reaction of aromatic dianhydrides with aromatic diamines containing substituted azobenzene groups. These polymers with good solubility in polar amidic solvents, were able to form transparent flexible films and showed high thermal stability. Conformational parameters of the polymers were calculated by the Monte Carlo method with allowance for hindered rotation. Several physical properties of these polymers, such as solubility, glass transition temperature (T_g), and initial decomposition temperature (T_onset) were measured and discussed in relation to the volume factor of the macromolecular chains. The volume factor is equal to ratio of the Van der Waals volume of the pendent group to the Van der Waals volume of the repeating unit of the main chain.     

About the Schur Index for Ambivalent Groups

An ambivalent group is a finite group all of whose irreducible characters are real valued. By Brauer–Speiser theorem, if G is an ambivalent group, then the absolute Schur index m _Q (χ) = m(χ) ≤2. In this note we shall prove that this property is true also for the derived subgroups of ambivalent groups. Also we will prove that there is a relation between the number of conjugacy classes of 2-regular cyclic subgroups of an ambivalent group and the irreducible characters with absolute Schur index 1.     

On an Aitken–Newton type method

We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes controlled by the Newton method. We obtain a local convergence result which shows that the q-convergence order of this method is 6 and its efficiency index is $\sqrt[5]{6},$ which is higher than the efficiency index of the Aitken or Newton methods. Monotone sequences are obtained for initial approximations farther from the solution, if they satisfy the Fourier condition and the nonlinear mapping satisfies monotony and convexity assumptions on the domain.     

CdS thin films obtained by thermal treatment of cadmium(II) complex precursor deposited by MAPLE technique

Thin films of [Cd{SSi(O-Bu^t)₃}(S₂CNEt₂)]₂, precursor for semiconducting CdS layers, were deposited on silicon substrates by Matrix-Assisted Pulsed Laser Evaporation (MAPLE) technique. Structural analysis of the obtained films by Fourier transform infrared spectroscopy (FTIR) confirmed the viability of the procedure. After the deposition of the coordination complex, the layers are manufactured by appropriate thermal treatment of the system (thin film and substrate), according to the thermal analysis of the compound. Surface morphology of the thin films was investigated by atomic force microscopy (AFM) and spectroscopic-ellipsometry (SE) measurements.