A short note on the monotonicity of the Erlang C formula in the Halfin–Whitt regime

We prove a monotonicity condition satisfied by the Erlang C formula when computed in the Halfin?CWhitt regime. This property was recently conjectured in (Janssen et al., Queueing Syst. Theory Appl. 68:361?C363, 2011).     

Hybridized globally divergence-free LDG methods. Part I: The Stokes problem

We devise and analyze a new local discontinuous Galerkin (LDG) method for the Stokes equations of incompressible fluid flow. This optimally convergent method is obtained by using an LDG method to discretize a vorticity-velocity formulation of the Stokes equations and by applying a new hybridization to the resulting discretization. One of the main features of the hybridized method is that it provides a globally divergence-free approximate velocity without having to construct globally divergence-free finite-dimensional spaces; only elementwise divergence-free basis functions are used. Another important feature is that it has significantly less degrees of freedom than all other LDG methods in the current literature; in particular, the approximation to the pressure is only defined on the faces of the elements. On the other hand, we show that, as expected, the condition number of the Schur-complement matrix for this approximate pressure is of order in the mesh size . Finally, we present numerical experiments that confirm the sharpness of our theoretical a priori error estimates.

     

Complexation behaviour and stability of Schiff bases in aqueous solution. The case of an acyclic diimino(amino) diphenol and its reduced triamine derivative

The copper(II), nickel(II), and zinc(II) complexes of the acyclic Schiff base H(2)L(A), obtained by [1 + 2] condensation of 1,2-ethanediamine,N-(2-aminoethyl)-N-methyl with 3-ethoxy-2-hydroxybenzaldehyde, and of H(2)L(B), the reduced derivative of H(2)L(A), were prepared and their properties studied by IR, NMR and SEM-EDS. In these complexes, the metal ion is always located in the coordination chamber of the ligand delimited by two phenol oxygens and nitrogen atoms (either aminic or iminic). The coordination behaviour of H(2)L(A) and H(2)L(B) towards H(+), Cu(2+), Ni(2+) and Zn(2+) in aqueous solution at 298 K and mu = 0.1 mol dm(-3) (Na)ClO(4) was also studied by potentiometric, NMR and UV-VIS measurements. In particular, potentiometric equilibrium studies indicate that H(2)L(A) is not stable enough to have a pH range in which it is the sole species in aqueous solution. In such a solution, the Schiff base forms over a limited pH range, between 6 and 10, with a maximum formation percentage at pH approximately 9. In addition, the involvement of imine nitrogens in the complexes markedly stabilises the azomethylene linkage, so that the metal complexes of H(2)L(A), particularly those of copper(II), are the species largely prevailing in solutions with pH >3.5. The stability constants of the complexes formed by metal ions with H(2)L(A) and H(2)L(B) follow the order Cu(2+) > Ni(2+) > Zn(2+); distribution plots show that copper(II) gives complexes more stable with H(2)L(A), whereas Ni(2+) and Zn(2+) prefer the reduced ligand, H(2)L(B).     

Synthesis and reactivity of uranium(IV) amide complexes supported by a triamidotriazacyclononane ligand

Reaction of [U{(SiMe2NPh)3-tacn}Cl] with LiNEt2 or LiNPh2 affords the corresponding amide compounds, [U{(SiMe2NPh)3-tacn}(NR2)] (R = Et (1), R = Ph (2)). The complexes have been fully characterized by spectroscopic methods and the solid-state structure of 1 was determined by single-crystal X-ray diffraction analysis. The six nitrogen atoms of the tris(dimethylsilylanilide)triazacyclononane ligand are in a trigonal prismatic configuration with the nitrogen atom of the diethylamide ligand capping one of the trigonal faces of the trigonal prism. Crystallization of 2 from CH3CN solution gave crystals of the six-membered heterocycle [U{(SiMe2NPh)3-tacn}{kappa2-(HNC(Me))2CC[triple bond]N}] (3). The reactivity of the amides was investigated. Both compounds undergo acid-base reactions with protic substrates such as HOC6H2-2,4,6-Me3, 3,5-Me2pzH (pz = pyrazolyl) and HSC5H4N to give the corresponding [U{(SiMe2NPh)3-tacn}X] (X = OC6H2-2,4,6-Me3 (4), 3,5-Me2pzH (5), kappa2-SC5H4N (6)) complexes. The solid-state structures of and were determined by single-crystal X-ray diffraction and revealed that the compounds are eight-coordinate with dodecahedral geometry.     

CsF-promoted acetyl dance at the narrow rim of p-tert-butyl[3.1.3.1]homooxacalixarene

In the acetylation of an oxygenated calix[4]arene homologue in the presence of CsF as a base, relaxation of the reaction system to the equilibrium composition takes place through several intra- and intermolecular steps that can be easily controlled to obtain the various acetyl derivatives. The effect of different bases is also discussed.     

Sorption of Pollutant Traces by Nanoporous Crystalline Aerogels: Visualization by a Dye

Summary: The influence of the crystalline structure on the pollutant sorption properties of high porosity syndiotactic polystyrene (sPS) aerogels has been made visible by using azulene, a blue dye, capable to form a clathrate phase with sPS. The bluish coloration observed for aerogels with the nanoporous δ-form and the absence of coloration for aerogels with the densely-packed γ-form clearly establish that the crystalline nanopores play a key role for the removal of pollutant traces from water or air.     

On ideal convergence of double sequences in probabilistic normed spaces

The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general.     

Methoxy‐ether and crown‐ether ­derivatives of tetrahomodioxa‐ and octahomotetraoxacalix­[4]­arenes

Three methoxy­‐ether and one methoxy‐­ether/crown‐ether derivatives of p‐tert‐butyl­tetrahomodioxa‐ and p‐R‐octahomo­tetraoxacalix­[4]­arenes (R = methyl, tert‐butyl, H) have been investigated. The first three compounds, 7,15,21,27‐tetra‐tert‐butyl‐29,30,31,32‐tetra­methoxy‐3,11‐dioxapenta­cyclo­[23.3.­1.1^5,9.1^13,17.1^19,23]­ditriaconta‐1(29),5,7,­9(30),­13,15,‐17(31),­19,21,23(32),25,27‐dodecaene, C₅₀H₆₈O₆, 33,34,35,36‐tetra­methoxy‐7,15,23,31‐tetra­methyl‐3,11,19,27‐tetra­oxa­penta­cyclo[27.3.1.1^5,9.1^13,17.1^21,25]­hexa­tri­aconta‐1(33),5,7,9(34),13,15,­17(35),21,23,25(36),29,31‐dodecaene, C₄₀H₄₈O₈, and 7,23‐di‐tert‐butyl‐33,34,35,36‐tetra­methoxy‐3,11,19,27‐tetraoxapenta­cyclo­[27.3.1.1^5,9.1^13,17.1^21,25]­hexatriaconta‐1(33),5,7,9(34),13,15,­17(35),‐ 21,23,25(36),29,31‐dodecaene, C₄₄H₅₆O₈, in the partial‐cone or 1,2‐alternate conformations, present the common feature of methoxy‐­ether self‐inclusion, while the fourth, 42,43‐di­methoxy‐7,15,23,31‐tetra­methyl‐3,11,19,27,34,37,40‐heptaoxahexa­cyclo[15.15.9.1^5,9.1^21,25.0^13,41.0^29,33]­tritetra­conta‐5(42),6,8,13(41),­14,16,21(43),22,24,29(33),30,32‐dodecaene, C₄₂H₅₀O₉, adopts the 1,3‐alternate conformation owing to the presence of a 1,3‐polyether chain.     

Decomposition of spaces with geodesics contained in compact flats

We prove a decomposition result for analytic spaces all of whose geodesics are contained in compact flats. Namely, we prove that a Riemannian manifold is such a space if and only if it admits a (finite) cover which splits as the product of a flat torus with simply connected factors which are either symmetric (of the compact type) or spaces of closed geodesics.

     

Halogenation of a twisted non-polar π-system as a tool to modulate phosphorescence at room temperature

Halogenation of a twisted three-fold symmetric hydrocarbon with F, Cl or Br leads to strong modulation of triplet–triplet annihilation and dual phosphorescence, one thermally activated and the other very persistent and visible by eye, with different relative contributions depending on the halide. The room temperature phosphorescence is highly unusual given the absence of lone-pair-contributing heteroatoms. The interplay between the spin–orbit coupling matrix elements and the spatial configuration of the triplet state induces efficient intersystem crossing and thus room temperature phosphorescence even without relying on heteroatomic electron lone pairs. A ninefold increase of the ISC rate after introduction of three bromine atoms is accompanied by a much higher 34-fold increase of phosphorescence rate.

Twisted π-systems investigation showed a very unusual HAE, influencing independently the ISC and the dual phosphorescence emission, one being very persistent at room temperature and visible by eye in powder.