Bang-bang optimal control for the dam problem

The dam problem with general geometry is considered. Fluid is drawn from the bottomS ₁ at a ratek where 0 k N, _{S 1} k M; the objective is to minimize the total pressure of the fluid in the dam. A bang-bang principle is established for any optimal controlk ₀, that is,k ₀ = 0 on a setA andk ₀ =N on the complement setS ₁ A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk ₀ is established.This work is partially supported by National Science Foundation Grants DMS-8501397 and DMS-8420896.     

Conclusive evidence of the trapping of primary ozonides

[reaction: see text] Anomalous ozonolysis of strained bicyclic allylic alcohols yields alpha-hydroxymethyl ketones. The proposed mechanism involves an unusual trapping of the primary ozonide that undergoes a Grob-like fragmentation instead of dissociating into the Criegee intermediates.     

Concise synthesis of acyl migration-blocked 1,1-difluorinated analogues of lysophosphatidic acid

Lysophosphatidic acid (LPA, 1- or 2-acyl-sn-glycerol 3-phosphate) is an important phospholipid mediator produced by activated platelets and by ovarian cancer cells. Efforts to understand LPA signaling through G-protein-coupled receptors are hampered by the facile acyl migration that results in equilibration to a mixture of the 1- or 2-acyl species under physiological conditions. We describe a new and efficient route to enantiomerically homogeneous lysophospholipid analogues from D-mannitol 1,2:5,6-bis-acetonide to give two 1,1-difluorodeoxy analogues of (2R)-acyl-sn-glycerol 3-phosphate. These compounds are migration-blocked analogues of the labile sn-2 LPA species. The (19)F NMR of diastereotopic fluorines of the difluoromethyl group shows an unexpected solvent dependence.     

Electron paramagnetic resonance study of partially oriented clay platelets intercalated with copper(II) 1,4,8,11-tetraazacyclotetradecane

Electron paramagnetic resonance (EPR) spectra of powder and oriented films of montmorillonite, hectorite, and saponite intercalated with [Cu(cyclam)](2+) (cyclam = 1,4,8,11-tetraazacyclotetradecane) exhibit three components: an orientation-dependent component without hyperfine features, an orientation-dependent component with hyperfine features, and an orientation-independent component without hyperfine feature. EPR spectra of [Cu(cyclam)](2+)-saponite, which exhibit only two components and the best resolved hyperfine features, were simulated. The spectra indicate that a large portion of the saponite platelets are inclined to the glass surface, although they tend to align with their basal planes parallel to the glass surface. The orientation-dependent spectra could be simulated by introducing a Gaussian distribution with a standard deviation of 20 degrees for the inclination angle. The standard deviation may be used as a disorder parameter for the microcrystals assembled on glass plates. Spectral simulation also shows that the CuN(4) plane of [Cu(cyclam)](2+) is parallel to the clay layers. EPR spectra of some other partially oriented systems are also discussed.     

Reversible binding of the HPLC6 isoform of type I antifreeze proteins to ice surfaces and the antifreeze mechanism studied by multiple quantum filtering-spin exchange NMR experiment

Antifreeze proteins (AFPs) protect organisms from freezing damage by inhibiting the growth of seed-ice crystals. It has long been hypothesized that irreversible binding of AFPs to ice surfaces is responsible for inhibiting the growth of seed-ice crystals as such a mechanism supports the popularly accepted Kelvin effect for the explanation of local freezing-point depression. However, whether the binding is reversible or irreversible is still under debate due to the lack of direct experimental evidence. Here, we report the first direct experimental result, by using the newly developed multiple quantum (MQ) filtering-spin exchange NMR experiment, that shows that the binding of HPLC6 peptides to ice surfaces is reversible. It was found that the reversible process can be explained by the model of monolayer adsorption. These results suggest that the Kelvin effect is not suitable for explaining the antifreeze mechanism, and direct interactions between the peptides and the ice-surface binding sites are the driving forces for the binding of AFPs to ice surfaces. We propose that there exists a concentration gradient of AFP from an ice-binding surface to the solution due to the affinity of ice surfaces to AFPs. This concentration gradient creates a dense layer of AFP in contact with the ice-binding surface, which depresses the local freezing point because of the colligative property, but not the Kelvin effect.     

Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups

In this paper, the author computes canonical connections and KobayashiNomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.