The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

The selective reductive acylation of a-keto imines

Reaction of α-keto imines with the $\text{in}$$\text{situ}$ generated acetylcobalt tetracarbonyl occurs only at the carbon—nitrogen double bond to give β-keto amides. An unexpected by-product was formed in several instances.     

Star-shaped azo-based dipolar chromophores: design, synthesis, matrix compatibility, and electro-optic activity

Three new azo-benzene-based push-pull chromophores with dendritic architecture were synthesized as active materials for electro-optic applications. These chromophores were synthesized in six or seven synthetic steps with an overall yield of around 80% per step and high purity. UV-vis spectroscopy showed significant influence of the transient dipole moment on the observed r(33) values. The chromophores were stable to photochemical oxidation in ambient light and air. The electrical poling conditions were optimized for each chromophore as the T(g) of the composite material varied significantly. The highest EO coefficient achieved was 22-25 pm/V at 1550 nm wavelength. STEM analysis of the blends enabled the correlation of the activity of these large chromophores with the blend morphology. An amorphous polycarbonate host effectively disperses the chromophores in 2-20 nm aggregates in the active materials. However, macrophase separation into 200-500 nm aggregates was observed in a methacrylate host matrix.     

One-dimensional rigorous hole theory of fluids: Internally constrained ensembles

A hole in a fluid is specified in a well-defined manner. The concentration of holes is a thermodynamic property of the fluid and we derive this concentration in three different ensembles for a one-dimensional fluid of hard rods. The thermodynamics of these rigorously defined holes is developed, and the properties of holes are explored. The ensemble in which the concentration of holes is maintained fixed exhibits dramatic properties. Finally, pair correlation functions for hard rods in the various ensembles are computed. Contrary to a frequently made assumption, the equilibrium number of holes is found to never be proportional to the probability of finding a single hole in the fluid. Constraining the concentration of holes as well as the density leads to dramatic structural effects prominently displayed by the pair correlation function. The ensemble in which the concentration of holes is fixed is an example of an internally constrained metastable system.     

Nitrato- and fluoroboracites M3B7O13NO3 and M3B7O13F

New boracites containing nitrato- or fluoroanions that appear to be true low-pressure phases have been synthesized at superatmospheric pressures. The M₃B₇O₁₃NO₃ compounds (M = Co, Ni, Cu, Zn, Cd) transform rapidly and reversibly in the temperature region 300–500°C between probable orthorhombic and face centered cubic symmetry, while the M₃B₇O₁₃F compounds (M = Mg, Mn, Fe, Co, Zn) appear to maintain rhombohedral symmetry up to their decomposition temperatures of 800–900°C. True high-pressure boracite-like phases containing F and Cr, Mn, Fe, or Co that decompose upon heating to M₃B₇O₁₃F have also been isolated.     

Obtaining partial widths from siegert wavefunctions

It is shown that a simple expression for the partial widths in a multichannel decay problem can be readily obtained from a Siegert wavefunction.     

Longest cycles in generalized Buckminsterfullerene graphs

It is shown that every regular 3-valent polyhedral graph whose faces are all 5-gons and 6-gons contains a cycle through at least 4/5 of its vertices.