Sharp L^p bounds on spectral clusters for Lipschitz metrics

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses for$6<p\leq 8$. In higher dimensions we obtain best possible bounds for a limited range of p.Comment: 28 page

Subcritical Lp bounds on spectral clusters for Lipschitz metrics

We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.Comment: 10 page

Subcritical Lp bounds on spectral clusters for Lipschitz metrics

We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.Comment: 10 page

The pelican

https://digitalcommons.ithaca.edu/sheetmusic/1026/thumbnail.jp

Synthesis of 1,1,2,2,3,3-hexamethyl-4,5-bis(methylene)cyclopentane

An efficient synthesis of the title compound 14 is reported, which employs the ZnCl2/Et2O catalyzed addition of acetyl chloride (4) to 2-methyl-2-butene (5) and the [3+ + 2] cycloaddition of the 1,1,2,3-tetramethylallyl cation to 2,3-dimethyl-2-butene as key steps

Castigo y responsabilidad: ensayos de filosofía del derecho

- Divulgação dos SUMÁRIOS das obras recentemente incorporadas ao acervo da Biblioteca Ministro Oscar Saraiva do STJ. Em respeito à Lei de Direitos Autorais, não disponibilizamos a obra na íntegra.- Localização na estante: 343:340.12 H325

The Power of Feminist Judgments?

Recent years have seen the advent of two feminist judgment-writing projects, the Women’s Court of Canada, and the Feminist Judgments Project in England. This article analyses these projects in light of Carol Smart’s feminist critique of law and legal reform and her proposed feminist strategies in Feminism and the Power of Law (1989). At the same time, it reflects on Smart’s arguments 20 years after their first publication and considers the extent to which feminist judgment-writing projects may reinforce or trouble her conclusions. It argues that both of these results are discernible—that while some of Smart’s contentions have proved to be unsustainable, others remain salient and have both inspired and hold important cautions for feminist judgment-writing projects

American History Atlas, Adapted from the Large Wall Maps

https://digitalcommons.usm.maine.edu/oml_collections/1020/thumbnail.jp

Can a single molecule trap the electron?

We suggest that it might be possible to trap the electron in a cavity of a macrocycle molecule, in the same way this trapping occurs cooperatively, by several solvent molecules, in hydroxylic liquids. Such an encapsulated electron is a "molecular capacitor," in which the excess electron is largely decoupled from valence electrons in the trap. A specific design for such a trap that is based on calix[4]cyclohexanol is discussed in detail. It is shown theoretically, by ab initio and density functional theory (DFT) modeling, that one of the conformations of this molecule forms the optimum tetrahedral trap for the electron. The resulting "encapsulated electron" strikingly resembles the solvated electron in alcohols and water.Comment: 13 pages 2 tables 5 figures, submitted to Chem Phys Let

Buoyancy regulation and aggregate formation in Amoebobacter purpureus from Mahoney lake

Abstract The meromictic Mahoney Lake (British Columbia, Canada) contains an extremely dense layer of purple sulfur bacteria (Amoebobacter purpureus). The buoyant density of Amoebobacter cells grown in pure culture at saturating light intensity was significantly higher (1027–1034 kg m−3) than the density of lake water (1015 kg m−3). When stationary cultures were shifted to the dark, the gas-vesicle content increased by a factor of 9 and buoyant density decreased to 1002 kg m−3 within three days. A novel mechanism of cell aggregation was detected for the Mahoney Lake strain. Dense cell aggregates were formed after depletion of sulfide. Formation of aggregates was correlated with an increase in cell surface hydrophobicity. Cell aggregates could be disintegrated within less than 1 s by addition of sulfide or various thiol compounds. Mercaptanes with a branched structure in the vicinity of the terminal thiol group, compounds with esterified thiol groups (methylmercaptanes), reducing compounds lacking thiol groups and detergents did not influence aggregate stability. Cell aggregates disintegrated upon addition of urea or of proteinase K. Addition of various sugars had no effect on aggregation; this points to the absence of lectins. The results indicate that cell-to-cell adhesion in A, purpureus ML1 is mainly caused by a hydrophobic effect and includes a specific mechanism possibly mediated by a surface protein. Extrapolation of laboratory results to field conditions demonstrated that both regulation of buoyant density and formation of cell aggregates result in passive accumulation of cells at the chemocline and contribute to the narrow stratification of A. purpureus in Mahoney Lake