Extremal functions for Moser's inequality

Let be a bounded smooth domain in , and a function with compact support in . Moser's inequality states that there is a constant , depending only on the dimension , such that

where is the Lebesgue measure of , and the surface area of the unit ball in . We prove in this paper that there are extremal functions for this inequality. In other words, we show that the

is attained. Earlier results include Carleson-Chang (1986, is a ball in any dimension) and Flucher (1992, is any domain in 2-dimensions).

     

Absorption Spectra of 5′-carboxy-2′-hydroxychalcone and its Derivatives

Ultraviolet absorption spectra and infrared absorption spectra of 5′-carboxy-2′-hydroxychalcone and eleven derivatives substituted at side benzene nucleus are measured to elucidate the spectroscopic effects of the 5′-carboxyl group in this series of compounds.     

A chemoenzymatic approach to glycopeptide antibiotics

Many biologically active natural products are constrained by macrocyclization and modified with carbohydrates. These two types of modifications are essential for their biological activities. Here we report a chemoenzymatic approach to make carbohydrate-modified cyclic peptide antibiotics. Using a thioesterase domain from the decapeptide tyrocidine synthetase, 13 head-to-tail cyclized tyrocidine derivatives were obtained with one to three propargylglycines incorporated at positions 3-8. These cyclic peptides were then conjugated to 21 azido sugars via copper(I)-catalyzed cycloaddition. Antibacterial and hemolytic assays showed that the two best glycopeptides, Tyc4PG-14 and Tyc4PG-15, have a 6-fold better therapeutic index than the natural tyrocidine. We believe this method will also be useful for modifying other natural products to search for new therapeutics.     

Photoexcitation and photodissociation lasers. III. mechanisms of CO laser emission from the vacuum UV photodissociation of CH2COO2 and CH2COSO2 mixtures

CO laser emission was detected in the vacuum UV flash photolysis of CH₂CO. The emission is attributed to the initial photodissociation reaction

Addition of O₂ to the CH₂CO system caused a pronounced enhancement in the laser intensity. This effect is believed to be due to the removal of the CH₂ + CH₂CO reaction, which produces uninverted CO molecules. A greater laser output was obtained when SO₂ was used instead of O₂. In the O₂-added system, a total of 16 transitions ranging from Δv(8→7) to (4→3) were identified. Addition of SO₂ increased the total number of lines to 34, lasing in the range between (11→10) and (4→3). This enhancement is ascribed to the occurrence of the reaction

In addition to these chemical effects, the effects of flash energy, inert gases and total pressures have been investigated.     

The Adsorption and Thermal Decomposition of CH2CO (CD2CO) on Si(111)-7 × 7

The adsorption and thermal decomposition of ketene on Si(l 11)-7 × 7 were investigated using various surface analysis techniques. When the surface was exposed to ketene at 120 K, two CO stretching modes at 220 and 273 meV appeared in HREELS, corresponding to two adsorbed ketene states. After the sample was annealed at ?250 K, the 273 and the 80 meV peaks vanished, indicating the disappearance of one of the adsorption states by partial desorption of the adsorbate. In a corresponding TPD measurement, a desorption peak for ketene species was noted at 220 K. Annealing the sample at 450 K caused the decomposition of the adsorbate, producing CH_x and O adspecies. Further annealing of the surface at higher temperatures resulted in the breaking of the CH bond, the desorption of H and O species and the formation of Si carbide. The desorption of H at 800 K was confirmed by the appearance of the D₂ (m/e = 4) TPD peak at that temperature when CD₂CO was used instead of CH₂CO.     

Synthesis of 9-(2,3-dihydroxy-1-propoxymethyl)guanine - a new potential antiviral agent

Coupling of tris(trimethylsilyl)guanine (4) with 1,2-di-$\text{O}$-acetyl-3-$\text{O}$chloromethyl glycerol (3), followed by removal of the protecting groups afforded 9-(2,3-dihydroxy-1-propoxy)guanine (1). Compound 1 exhibited potent antiviral activity.     

Laser-induced reactions of NO2 in the visible region

The reaction of NO₂ with isobutane, induced by 488 nm laser radiation, to form 2-nitro-2-methylpropane has been investigated and the results computer-modeled according to two possible reaction mechanisms. The first scheme involves the direct abstraction of H from isobutane by vibronically excited NO₂ (NO ₂ ^* ), and the second, abstraction by an intermediate NO₃ radial produced by NO ₂ ^* +NO₂. The modeling results strongly support the NO ₂ ^* scheme as the dominant reaction mechanism.     

The Study on the Thermal Stability of CLA in Egg Yolk

Conjugated linoleic acids (CLA) have been a subject of extensive investigation for their anticarcinogenic, hypolipidemic, antiatherosclerotic and immune-enhancing activities. Stability of CLA in foods has not received much attention by both academics and industry. Although CLA has shown many beneficial effects, its decomposition must be prevented when CLA in foods is processed, stored and transported. However, no study to date has addressed the stability of CLA in foods. The present study was carried out further to examine the stability of CLA in egg yolk during the storage and frying, using gas liquid chromatography (GLC) and silver ion high-performance liquid chromatography (Agt-HPLC). The eggs, containing 4.0% CLA per gramme of egg yolk, were 40s. Either storage for 6 months or frying for 40 s did not significantly change the composition of CLA in egg yolk. However, the degradation of CLA was statistically significant when the CLA components of egg yolk protected CLA from degradation. It is concluded that CLA is well preserved in egg before it is consumed.     

Properties of nanobelts and nanotubes measured by in situ TEM.

Characterizing the physical properties of individual nanostructures is challenging because of the difficulty in manipulating the objects of sizes from nanometers to micrometers. Most nanomeasurements have been carried using scanning probe microscopy. In this article, we demonstrate that transmission electron microscopy can be a powerful tool for quantitative measurements of the mechanical and electrical properties of a single nanostructure. Dual-mode resonance of an oxide nanobelt has been observed, and its bending modulus has been measured. An in situ technique was demonstrated for measuring the work function at the tip of a carbon nanotube. The ballistic quantum conductance of a multiwalled carbon nanotube was observed at room temperature using the setup in TEM. It is concluded that in situ measurement by directly linking structure with property is a future direction of electron microscopy.