Geometric obstruction of black holes

We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The completeness of the latter is then employed to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proof of these new results is preceded by a pedagogic review of the local aspects of sectional curvature bounds for Lorentzian manifolds, which extends and strengthens previous constructions.     

Single-crystal-like materials by the self-assembly of cube-shaped lead zirconate titanate (PZT) microcrystals

We demonstrated the formation of single-crystal-like materials that contain preferentially oriented arrays of lead zirconate titanate (PZT) cube-shaped particles by self-assembly. Hydrothermally synthesized PZT particles with a bulk composition of Zr/Ti = 70/30 were used in making microcrystal arrays. Spreading a suspension containing PZT cube-shaped particles, 2-propanol, and mineral oil at the air-water interface produced a one-dimensional planar array of PZT particles on the water surface. The array so formed was subsequently transferred onto a flat or curved substrate. X-ray diffraction and electron backscattered diffraction analyses revealed that most of the cube-shaped particles in the array were oriented with their pseudocubic (001) direction aligned parallel to the normal direction of the substrate surface. Filling the arrays with matrixes produced monolayer or multilayer textured composites. The piezoelectric properties of oriented cube-shaped micron-sized particles in the self-assembled arrays were measured using a modified atomic force microscope to reveal the ferroelectric nature of the PZT arrays.     

Reagent-free Nazarov cyclisations

A new protocol for Nazarov cyclisation is described that involves simple heating of dienones in the absence of any external Lewis acid.     

Directly diode-pumped Yb3+:SrY4(SiO4)3O regenerative amplifier

We report a regenerative amplifier based on an Yb-doped apatite crystal: Yb3+:SrY4(SiO4)3O (Yb:SYS). We obtained 420-fs pulses at a central wavelength of 1066 nm with an energy of 100 microJ at 300 Hz after compression. To the best of our knowledge, this system is the first regenerative amplifier based on an Yb:SYS crystal and provides duration among the shortest ones generated by a directly diode-pumped regenerative amplifier.     

Johnson-Kendall-Roberts theory applied to living cells

Johnson-Kendall-Roberts (JKR) theory is an accurate model for strong adhesion energies of soft slightly deformable material. Little is known about the validity of this theory on complex systems such as living cells. We have addressed this problem using a depletion controlled cell adhesion and measured the force necessary to separate the cells with a micropipette technique. We show that the cytoskeleton can provide the cells with a 3D structure that is sufficiently elastic and has a sufficiently low deformability for JKR theory to be valid. When the cytoskeleton is disrupted, JKR theory is no longer applicable.     

Carbon-13 NMR spectra of hydroxylated bile acid stereoisomers

Carbon-13 NMR signals were assigned for the complete set of the 26 theoretically possible isomers of methyl 5β-cholanates having one to three hydroxy groups at positions C-3, C-7 and/or C-12 in the nucleus. Substituent effects on the ¹³C NMR shielding data serving to characterize the position and configuration of the hydroxy groups are discussed.     

A characterization of state spaces of orthomodular lattices

It is shown that every rational polytope is affinely equivalent to the set of all states of a finite orthomodular lattice, and that every compact convex subset of a locally convex topological vector space is affinely homeomorphic to the set of all states of an orthomodular lattice.     

Optimal Forest Harvesting with Ordered Site Access

A long-standing problem in forestry management is the optimal harvesting of a growing population of trees to maximize the resulting discounted aggregate net revenue. For an ongoing forest, the trees are harvested and replanted repeatedly; for a once-and-for-all forest, there is no replanting after a single harvest. In this paper, we outline a new formulation for the optimal-harvest problem which avoids difficulties associated with functional-differential equations or partial differential equations of state in the relevant optimal-control problem encountered in recent studies of the ongoing-forest problem. Our new formulation is based on the observation that tree logging is necessarily ordered by practical and/or regulatory considerations (e.g., it is illegal to cut the younger trees first in some jurisdictions); random access to tree sites does not occur in practice. The new formulation is described here for the simpler problem of a once-and-for-all forest. New results for nonuniform initial age distributions and variable unit harvest costs for this simpler problem are reported herein; results for an ongoing forest will be reported in [10]. The new model is also of interest from a control-theoretic viewpoint, as it exhibits the unique feature of having time as a state variable, in contrast to its usual role as an independent variable in conventional control problems.     

The influence of reorientational collisions on coherent optical processes

Numerical calculations of pulse transmission in SF₆ are performed to appraise the role of reorientational collisions. No support is found for the recent postutate calling for thermally equilibrated magnetic sublevels in self-induced transparency.