cos πρ theorems for δ-subharmonic functions

For ϕ a δ-subharmonic function, sharp results are obtained that connectA(r, ϕ), B(r, ϕ) andT(r, ϕ), whereA(r, ϕ)=inf_|z|=r ϕ(z),B(r, ϕ)=sup_|z|=r ϕ(z), andT(r, ϕ) is the Nevanlinna characteristics.     

The crystal and molecular structure of a dinuclear copper(II) complex of a Robson-type macrocycle, [Cu2(C26H30N4O2)(H2O)2](BF4)2

Summary The crystal structure of the dinuclear complex [Cu₂(C₂₆H₃₀-N₄O₂)(H₂O)₂](BF₄)₂ was determined by x-ray crystallography. The crystals are triclinic, P¯1, witha = 10.945(5),b = 8.703(5),c = 8.495(5) Å, = 103.86(3)°, = 105.73(3)°, = 85.77(3)°, V = 756 ų D_c = 1.65 g cm^–3 for Z = 1. The copper(II) atoms are 5-coordinate and square-pyramidal. Selected bond distances are: Cu-N, 1.91 Å (mean); Cu-O(base) = 1.90(1) and 1.91(1) Å; Cu-O(apical) = 2.47(1) Å; There are O(water)-H ... F interionic hydrogen bonds in the structure. The Cu .. Cu distance is 2.847 Å.     

Dinuclear Nickel(II) and Zinc(II) Complexes of 2,6-[N,N′-bis(2-hydroxyphenylmethyl)-N,N′-bis(2-pyridylmethyl)aminomethyl]-4-methylphenol

Abstract

The symmetric 'end-off' compartmental proligand 2,6-[N,N′-bis(2-hydroxy-phenylmethyl)-N,N′-bis(2-pyridylmethyl)aminomethyl]-4-methylphenol (H₃L) has been used to generate homodinuclear nickel(II) and zinc(II) complexes. The crystal structures of the complexes reveal that the di-nickel(II) complex is donor asymmetric and the di-zinc(II) complex is coordination number asymmetric. In both complexes non-coordinated acetic acid molecules are tightly hydrogen-bonded to the pendant phenols of the ligand generating a double acid salt of the type[CH₃COO…H…L…H…OOCCH₃]^3? in the dinickel complex and a single acid salt of the type [CH₃COO…H…L]^3? in the dizinc complex. In both cases the ligand periphery has been extended to provide a supraligand in which the donor potential of the original ligand has been enhanced.     

The synthesis and crystal structure of a new diprotonated Schiff base cryptand

Abstract

The synthesis and crystal structure of the diprotonated cryptand derived from the reaction of tren and 2,6-diacetyl pyridine is reported. The imino nitrogens of the Schiff base linkages are directed so that the dicarbimine functions are in trans, trans geometry relative to the pyridine C-N bond. This configuration has not previously been reported in related pyridine-derived Schiff base macrocycles.     

Metal Ion Recognition. Interaction of New Oxygen-Nitrogen Donor Macrocycles with Selected Transition and Post-Transition Metal Ions

As part of an ongoing investigation of the factors influencing metal ionrecognition, we have investigated structure/function relationships involvingthe metal-ion binding by three new N-benzyl-substituted, 15- and 16-membered,macrocyclic ligands incorporating N₂O ₃- and N ₃O ₃-donor sets (withthe N ₃O ₃-system consisting of a N ₂O ₃-macrocyclic ring with an attachedCH ₂CH ₂NCH ₂C ₆H ₅ pendant arm). Selected solid complexes of thelatter ligand were isolated and the X-ray structures of individual Ni(II) and Ag(I) complexeswere obtained.Where solubility permitted, potentiometric titration studies in 95% methanolwere employed to investigate the binding affinities of all three ligand derivativestowards Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Ag(I) and Pb(II). The 15-memberedN ₂O ₃-ring was found to be selective for Ag(I) over the other six metalsinvestigated, including Cu(II). However, the presence of a further nitrogen donorin the form of the pendant benzylamine functionality in the N ₃O ₃-donorsystem results in an increase in its binding affinity for Ag(I) but an even greaterincrease occurs for Cu(II). As a consequence, the latter ion is now more stronglybound than Ag(I). The factors influencing these respective selectivities are discussed.     

A digital image analysis method for diagnostic ultrasound calibration

Acoustic test objects are commonly used for quality assurance testing of diagnostic ultrasound machines. However, the accompanying calibration protocols rely heavily on the judgment of the sonographer, are dependent on machine settings and are semi-quantitative. In the current study, two unique test objects and protocols were designed to quantitatively determine diagnostic ultrasound parameters, namely axial resolution and geometric uniformity, and lateral resolution and geometric uniformity of the ultrasound field. The effect of focal zone, signal gain, and distance from the ultrasound probe on these parameters was assessed. The investigation was performed using a typical low-frequency diagnostic unit equipped with a 7.5 MHz linear pulse–echo probe. Results underline the need to ensure that sensitivity of routine testing regimes is adequate for the measurements to be made. This study is a preliminary part of a larger project developing an ultrasound technique to be used as an engineering design tool in a non-clinical industrial setting for quality assurance testing of total knee replacements immersed in water.