Types in reductive -adic groups: The Hecke algebra of a cover

In this paper, is a non-Archimedean local field and is the group of -points of a connected reductive algebraic group defined over . Also, is an irreducible representation of a compact open subgroup of , the pair being a type in . The pair is assumed to be a cover of a type in a Levi subgroup of . We give conditions, generalizing those of earlier work, under which the Hecke algebra is the tensor product of a canonical image of and a sub-algebra , for a compact open subgroup of containing .

     

Minimax kernels for density estimation with biased data

This paper considers the asymptotic properties of two kernel estimates % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\], which have been proposed by Bhattacharyya et al. (1988, Comm. Statist. Theory Methods, A17, 3629–3644) and Jones (1991, Biometrika, 78, 511–519), respectively, for estimating the underlying density f at a point under a general selection biased model. The asymptotic optimality of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]is measured by the corresponding asymptotic minimax mean squared errors under a compactly supported Lipschitz continuous family of the underlying densities. It is shown that, in general, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]is a superior local estimate than % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]in the sense that the asymptotic minimax risk of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]is lower than that of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]. The minimax kernels and bandwidths of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]are computed explicity and shown to have simple forms and depend on the weight functions of the model.     

DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.     

Concentration for self‐bounding functions and an inequality of Talagrand

We see that the entropy method yields strong concentration results for general self‐bounding functions of independent random variables. These give an improvement of a concentration result of Talagrand much used in discrete mathematics. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Revised molecular constants and term values for the XΠ and BΣ states of OH

An improved set of molecular constants and term values are given for the X²Π (v = 0–13) and B²Σ⁺ (v = 0 and 1) states of the OH radical. They are derived from a fit of previously published laboratory data and additional lines taken from infrared solar spectra recorded on orbit.     

Fluoroquinolone Antimicrobials: Singlet Oxygen, Superoxide and Phototoxicity

The fluoroquinolone antibacterial agents possess photo-sensitizing properties that lead to phototoxic responses in both human and animal subjects. The phototoxicity order reported in humans is: fleroxacin > lomefloxacin, pefloxacin > ciprofloxacin ? enoxacin, norfloxacin and ofloxacin. Studies both in vivo and in vitro have related this phototoxicity to the generation of reactive oxygen species including hydrogen peroxide and the hydroxyl radical. We determined the quantum yields of singlet oxygen generation (φ_Δ,) by detection of the singlet oxygen (¹O₂) luminescence at 1270 tun for several fluoroquinolones, naphthyridines and other structurally related compounds. All the fluoroquinolones examined have low φ_Δ values ranging from 0.06 to 0.09 in phosphate buffer at pD 7.5. We also determined the ¹O₂ quenching constants for these compounds and their values were on the order of 10⁶M^?1 s¹, except for lomefloxacin whose rate constant was 1.8 × 10⁷M^?1 s^?1. The φ_Δ values were significantly decreased in a solvent of lower polarity such as methanol (0.007 ≤φ_Δ≤ 0.02). The production of ¹O₂ by these antibiotics did not correlate with the order reported for their phototoxicity. We also measured the photogeneration (λ > 300 nm) of superoxide by these antibacterials in dimethylsulfoxide using electron paramagnetic resonance and the spin trap 5,5-dimethyl-l-pyrroiine N-oxide. Although there is not a one-to-one correspondence between the relative rates of superoxide generation and the phototoxicity ranking of the fluoroquinolones, the more phototoxic compounds tended to produce superoxide at a faster rate. Nevertheless, the magnitudes of the observed differences do not appear sufficient to explain the range of fluoroquinolone phototoxicity potencies in human and animal subjects in general and the high activity of fleroxacin and lomefloxacin in particular. For these latter drugs the photoinduced loss of the F₈ atom as fluoride and the concomitant generation of a highly reactive carbene at C-8 provide a more plausible mechanism for their potent phototoxic and photocarcinogenic properties.     

The Effect of Static Magnetic Fields on the Photohemolysis of Human Erythrocytes by Ketoprofen

Ultraviolet irradiation (λ > 300 nm) of the nonsteroidal anti-inflammatory agent ketoprofen (KP, 3-benzoyl-α-methylbenzoacetic acid) in aqueous solution, pH 7.4, results in heterolytic decarboxylation of the drug to give 3-ethylbenzophenone (EtBP). Ketoprofen caused the photohemolysis of human erythrocytes probably as a result of lipid peroxidation. Application of a static magnetic field (250–1500 G) during UV (>300 nm) irradiation of KP and erythrocytes significantly decreased the time required for photohemolysis. This observation suggests that KP-induced photohemolysis involves the initial generation of a triplet radical pair derived from the reaction of triplet state KP (or 3-EtBP) with erythrocyte component(s) probably lipids. The magnetic field increases the concentration and/or lifetime of free radicals that escape from the radical pair so that the critical radical concentration needed to initiate membrane damage and cause cell lysis is reached sooner. Spin-trapping studies with 2,6-dibromo-1-nitrosobenzene-4-sulfonate confirmed that the application of an external static magnetic field increased the concentration of radicals released during the photolysis of either KP or 3-EtBP dissolved in organized media such as sodium dodecylsulfate micelles.     

A Computational and Experimental Approach Linking Disorder,High‐Pressure Behavior,and Mechanical Properties in UiO Frameworks

Whilst many metal–organic frameworks possess the chemical stability needed to be used as functional materials, they often lack the physical strength required for industrial applications. Herein, we have investigated the mechanical properties of two UiO‐topology Zr‐MOFs, the planar UiO‐67 ([Zr₆O₄(OH)₄(bpdc)₆], bpdc: 4,4′‐biphenyl dicarboxylate) and UiO‐abdc ([Zr₆O₄(OH)₄(abdc)₆], abdc: 4,4′‐azobenzene dicarboxylate) by single‐crystal nanoindentation, high‐pressure X‐ray diffraction, density functional theory calculations, and first‐principles molecular dynamics. On increasing pressure, both UiO‐67 and UiO‐abdc were found to be incompressible when filled with methanol molecules within a diamond anvil cell. Stabilization in both cases is attributed to dynamical linker disorder. The diazo‐linker of UiO‐abdc possesses local site disorder, which, in conjunction with its longer nature, also decreases the capacity of the framework to compress and stabilizes it against direct compression, compared to UiO‐67, characterized by a large elastic modulus. The use of non‐linear linkers in the synthesis of UiO‐MOFs therefore creates MOFs that have more rigid mechanical properties over a larger pressure range.     

Phorbasides A-E, cytotoxic chlorocyclopropane macrolide glycosides from the marine sponge Phorbas sp. CD determination of C-methyl sugar configurations

Five new cytotoxic macrolide glycosides phorbasides A-E (3-7), each possessing a macrolide ring appended to a rare ene-yne-trans-2-chlorocyclopropane, were isolated from the same Western Australian sponge (Phorbas sp.) that provided phorboxazoles A and B. The structures of 3-7 were solved by analysis of spectroscopic data including NMR, MS, and CD. A synthesis of methyl 2-O-methyl-alpha-L-evalose from L-rhamnose was completed and used for configurational assignment of the sugar residue in 3. Acid-catalyzed methanolysis of 3 followed by two-step derivatization of the liberated O-methyl glycoside gave a vicinal 4-O-naphthoyl/tertiary 3-N-(2-aminonaphthyl)carbamate derivative that exhibited exciton coupled CD identical with that of the derivative prepared from synthetic 1,2- O-dimethyl-alpha-L-evalose.