Admissible slopes for monotone and convex interpolation

Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC ¹ interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C ¹ monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.     

Optical characteristics of a transverse volume discharge in a helium-hydrogen chloride mixture

The emission characteristics of a transverse volume discharge in a He: HCl = 10: 1 mixture at a total pressure of 1–8 kPa were investigated. The plasma volume was 18 × 2.2 × 1 cm³, the interelectrode distance was d=2.2 cm, and the charging voltage of the main storage capacitor was 5–10 kV. The emission characteristics of the discharge were studied in the spectral range of 500–1000 nm. This type of discharge can be used in pulsed dry-etching plasmochemical reactors. The density of atomic chlorine radicals in the plasma was optimized in terms of the pressure of the initial working He-HCl mixture by measuring the relative radiation intensity of the Cl 837(5)-nm spectral line. The density of molecular radicals can be monitored indirectly by recording radiation from the excited chlorine-free decomposition products of HCl molecules (the H_α 656-nm line).     

Solvent-stabilized alkylrhodium(III) hydride complexes: a special mode of reversible C-H bond elimination involving an agostic intermediate

Reaction of the complex [Rh(coe)2(solv)n]BF4 (coe=cyclooctene) with the phosphane 1-di-tert-butylphosphinomethyl-2,4,6-trimethylbenzene (1) results in selective C-H bond activation, yielding the spectroscopically characterized solvento complexes [(solv)nRhH(CH2C6H2(CH3)2[CH2P(tBu)2]]]BF4 (solv = acetone, 2a; THF, 2b; methanol, 2c). The stability of these complexes is solvent dependent, alcohols providing significant stabilization. Although cis-alkylrhodium hydride complexes containing labile ligands are generally unstable, 2a-c are stable at room temperature. Complex [ (acetone)(ketol)RhH[CH2C6H2(CH3)2[CH2P(t-Bu)2]]]BF4 (2d, ketol 4-hydroxy-4-methyl-2-pentanone, the product of acetone aldol condensation), crystallized from a solution of 2a in acetone and was structurally characterized. Unusual solvent- and temperature-dependent selectivity in reversible C-H bond elimination of these complexes, most probably controlled by a special mode of strong agostic interactions, is observed by spin saturation transfer experiments.     

A new ligand system based on a bipyridine-functionalized calix[4]arene backbone leading to mono- and bimetallic complexes

The synthesis of a new ligand system for mono- and bimetallic complexes based on a calixarene is described. Ligand BBPC (3, bis(bipyridine)-calix[4]arene) is obtained in three steps in 40% overall yield by first brominating one of the methyl groups of the 4,4'-dimethyl-2,2'-bipyridine in two steps and subsequently reacting it with p-tert-butylcalix[4]arene under basic conditions. Reaction of BBPC (3) with 2 equiv of [Rh(NBD)(2)]BF(4) or [Rh(NBD)(CH(3)CN)(2)]BF(4) (NBD = norbornadiene) produces the bimetallic compound BBPC[Rh(NBD)BF(4)](2) (4). Treatment of the ligand with PdCl(2)(CH(3)CN)(2) leads to the isolation of the bimetallic complex BBPC[PdCl(2)](2) (5). When the nickel precursor NiBr(2)(DME) (DME = dimethoxyethane) is reacted with BBPC, the bimetallic complex BBPC[NiBr(2)](2) (6) is isolated which, upon crystallization from methanol, gives the mononuclear bis(bipyridine) complex BBPC[NiBr(OMe)] (7). Full characterization includes X-ray structural studies of complexes 4, 5, and 7. The bimetallic compounds 4 and 5 show metal to metal distances of 4.334 A (for 4) and 3.224 A (for 5). For all three complexes, unique molecular packing arrangements were found, based on hydrophobic/hydrophilic interactions.     

Effects of shape and size of cobalt ferrite nanostructures on their MRI contrast and thermal activation

Cobalt ferrite magnetic nanostructures were synthesized via a high temperature solution phase method. Spherical nanostructures of various sizes were synthesized with the help of seed mediated growth of the nanostructures in organic phase, while faceted irregular (FI) cobalt ferrite nanostructures were synthesized via the same method but in the presence of a magnetic field. Magnetic properties were characterized by SQUID magnetometry, relaxivity measurements and thermal activation under RF field, as a function of size and shape. The results show that the saturation magnetization of the nanostructures increases with an increase in size, and the FI nanostructures exhibit lower saturation magnetization than their spherical counterparts. The relaxivity coefficient of cobalt ferrite nanostructures increases with increase in size; while FI nanostructures show a higher relaxivity coefficient than spherical nanostructures with respect to their saturation magnetization. In the case of RF thermal activation, the specific absorption rate (SAR) of nanostructures increases with increase in the size. The contribution sheds light on the role of size and shape on important magnetic properties of the nanostructures in relation to their biomedical applications.     

Amended Formula for the Decay of Radioactive Material for Cosmic Times

An amended formula for the decay of radioactivematerial is presented. It is a modification of thestandard exponential formula. The new formula appliesfor long cosmic times comparable to the Hubble time. It reduces to the standard formula for shorttimes. It is shown that the material decays faster thanexpected. The application of the new formula to directmeasurements of the age of the universe and its implications are briefly discussed.     

Macroscopic Polarization Change of Mononuclear Valence Tautomeric Cobalt Complexes Through the Use of Enantiopure Ligand

The crystallization of a complex having electron transfer properties in a polar space group can induce the polarization switching of a crystal in a specific direction, which is attractive for the development of sensors, memory devices, and capacitors. Unfortunately, the probability of crystallization in a polar space group is usually low. Noticing that enantiopure compounds crystallize in Sohncke space groups, this paper reports a strategy for the molecular design of non-ferroelectric polarization switching crystals based on the use of intramolecular electron transfer and chirality. In addition, this paper describes the synthesis of a mononuclear valence tautomeric (VT) cobalt complex bearing an enantiopure ligand. The introduction of enantiomer enables the crystallization of the complex in the polar space group (P2₁). The polarization of the crystals along the b-axis direction is not canceled out and the VT transition is accompanied by a change in the macroscopic polarization of the polar crystal. Polarization switching via electron transfer is realized at around room temperature.