One‐Step Multicomponent Self‐Assembly of a First‐Generation Sierpiński Triangle: From Fractal Design to Chemical Reality

A novel terpyridine‐based architecture that mimics a first‐generation Sierpiński triangle has been synthesized by multicomponent assembly and features tpy? Cd^II? tpy connectivity (tpy=terpyridine). The key terpyridine ligands were synthesized by the Suzuki cross‐coupling reaction. Mixing two different terpyridine‐based ligands and Cd^II in a precise stoichiometric ratio (1:1:3) produced the desired fractal architecture in near‐quantitative yield. Characterization was accomplished by NMR spectroscopy, mass spectrometry, and transmission electron microscopy.     

Mott–Hubbard transition in a 2D He fluid monolayer

We discuss recent observations of the heat capacity and magnetization of a fluid ³He monolayer adsorbed on graphite plated with a bilayer of HD. Approaching the density at which the monolayer solidifies into a commensurate solid, we observe an apparent divergence of the effective mass. However, the inferred values of F₀^a tend to a constant. We interpret this in terms of a Mott–Hubbard transition between a 2D Fermi liquid and a magnetically disordered solid occurring via the Brinkman–Rice–Anderson–Vollhardt scenario.     

First observation ofΩ * resonances

In a experiment at the CERN SPS charged hyperon beam using incident Ξ^?, we have obtained evidence for the production of two Ω^* resonances decaying into Ξ^?π⁺ K ^?, with the following parameters:M ₁=2251±12,Γ ₁=48±20 MeV/c², 78 ±23 events, andM ₂=2284±12,Γ ₂=26±23 MeV/c² 45±10 events. The first state is also observed as a 4.2σ effect in a subsample which contains an additionalK ⁺ orK ⁰ in the final state. Production cross sections and branching ratios to Ξ^* K ^? and Ξ^? K ^* are presented.     

A statistical model of horizontal auditory localization performance data

Horizontal localization experiments are used to evaluate the listener's ability to locate the position of a sound source, and determine how signal characteristics affect this ability. These experiments generate circular, bimodal, and repeated data that are challenging to statistically analyze. A two-part mixture of wrapped Cauchys is proposed for these data, with the effects of signal type and position on localization bias, precision, and front-back confusion modeled using regression. The model is illustrated using mid- (1.0-2.0 kHz) and high- (3.0-6.0 kHz) frequency narrow band noises localization collected among ten normal hearing listeners.     

A symmetric numerical range for matrices

Summary For each normv on ⁿ, we define a numerical rangeZ _v, which is symmetric in the sense thatZ _v=Z_vD, wherev ^D is the dual norm.We prove that, fora ⁿⁿ,Z _v(a) contains the classical field of valuesV(a). In the special case thatv is thel ₁-norm,Z _v(a) is contained in a setG(a) of Gershgorin type defined by C. R. Johnson.Whena is in the complex linear span of both the Hermitians and thev-Hermitians, thenZ _v(a),V(a) and the convex hull of the usualv-numerical rangeV _v(a) all coincide. We prove some results concerning points ofV(a) which are extreme points ofZ _v(a).Part of this research was done while the authors were at the Mathematische Institut, Technische Universität, München, West Germany. The first author presented these results at the Seminar on Matrix Theory (Positivity and Norms) held in Munich in December, 1974. The second author also acknowledges support from the National Science Foundation under grant GP 37978X.     

Synthesis of rare earth hydroxide nanorods by room temperature reaction of oxide precursors with water

In this study, solid state chemical reaction of anhydrous chloride precursors with Na₂CO₃ has been used to manufacture composite powders of nanocrystalline rare earth oxide grains embedded within a matrix of NaCl. Subsequent washing of these powders with deionised water resulted in removal of the NaCl matrix and hydration of the oxide nanoparticles. In the case of Nd₂O₃ and Sm₂O₃, the hydration process yielded hydroxide nanorods. In contrast, washing of the Gd₂O₃ yielded a powder consisting of irregularly shaped nanoparticles of Gd₂O₃ and GdOOH. Analysis using high resolution transmission electron microscopy revealed that the Nd₂O₃ and Sm₂O₃ nanorods were not single crystals but were composed of crystalline subunits with a common á 0001 ñ \left\langle {0001} \right\rangle growth direction. The results obtained in this study demonstrate that rare earth hydroxide nanorods can be synthesised from oxide precursors without the need for hydrothermal processing at elevated temperature and pressure.     

Zero-angle depolarized light scattering of a colloidal polymer

The potential of zero-angle depolarized scattering for measuring the size distributions of optically anisotropic particles is considered. To illustrate the method, an analysis of Fluon, a teflon latex suspension, is presented. Homodyne correlation functions having signal-to-noise characteristics every bit as good as conventional unpolarized finite-angle measurements enabled confident application of a smoothed exponential sampling algorithm to obtain the decay rate distribution, which was converted to a size distribution with certain approximations. The size distribution obtained from light scattering agrees well with that from electron microscopy.