An abstract averaging theorem

For each t ? 0, let A(t) generate a contraction semigroup on a Banach space L. Suppose the solution of u_t = ?A(t)u is given by an evolution operator V_?(t, s). Conditions are given under which $\text{V}{}_{\mathrm{?}}\text{(}\text{(t+s)}\text{?}\text{,}\text{s}\text{?}\text{)}$ converges strongly as ? → 0 to a semigroup T(t) generated by the closure of $\text{A}\text{?}\text{f ≡}\text{lim}{}_{\mathrm{T\to \infty }}\text{(}\text{1}\text{T}\text{) ∝}{}_0{}^{\mathrm{T}}\text{A(t)f dt}$.This result is applied to the following situation: Let B generate a contraction group S(t) and the closure of ?A + B generate a contraction semigroup S_?(t). Conditions are given under which $\text{S(?}\text{t}\text{?}\text{) S}{}_{\mathrm{?}}\text{(}\text{t}\text{?}\text{)}$ converges strongly to a semigroup generated by the closure of $\text{A}\text{?}\text{f ≡}\text{lim}{}_{\mathrm{T\to \infty }}\text{(}\text{1}\text{T}\text{) ∝ S(?t) AS(t)f dt}$. This work was motivated by and generalizes a result of Pinsky and Ellis for the linearized Boltzmann Equation.     

Reizvorrichtungen, Thermostaten

Ohne Zusammenfassung     

Comparing the electronic properties of the low-spin cyano-ferric [Fe(N4)(Cys)] active sites of superoxide reductase and p450cam using ENDOR spectroscopy and DFT calculations

Superoxide reductase (SOR) and P450 enzymes contain similar [Fe(N)4(SCys)] active sites and, although they catalyze very different reactions, are proposed to involve analogous low-spin (hydro)peroxo-Fe(III) intermediates in their respective mechanisms that can be modeled by cyanide binding. The equatorial FeN4 ligation by four histidine ligands in CN-SOR and the heme in CN-P450cam is directly compared by 14N ENDOR, while the axial Fe-CN and Fe-S bonding is probed by 13C ENDOR of the cyanide ligand and 1Hbeta ENDOR measurements to determine the spin density delocalization onto the cysteine sulfur. There are small, but notable, differences in the bonding between Fe(III) and its ligands in the two enzymes. The ENDOR measurements are complemented by DFT computations that support the semiempirical equation used to compute spin densities on metal-coordinated cysteinyl and shed light on bonding changes as the Fe-C-N linkage bends. They further indicate that H bonds to the cysteinyl thiolate sulfur ligand reduce the spin density on the sulfur in both active sites to a degree that exceeds the difference induced by the alternative sets of "in-plane" nitrogen ligands.     

Copper(II)-catalyzed amidations of alkynyl bromides as a general synthesis of ynamides and Z-enamides. An intramolecular amidation for the synthesis of macrocyclic ynamides

A general and efficient method for the coupling of a wide range of amides with alkynyl bromides is described here. This novel amidation reaction involves a catalytic protocol using copper(II) sulfate-pentahydrate and 1,10-phenanthroline to direct the sp-C-N bond formation, leading to a structurally diverse array of ynamides including macrocyclic ynamides via an intramolecular amidation. Given the surging interest in ynamide chemistry, this atom economical synthesis of ynamides should invoke further attention from the synthetic organic community.     

Interfacial rheology and structure of straight-chain and branched fatty alcohol mixtures

Langmuir monolayers of mixtures of straight-chain and branched molecules of hexadecanol and eicosanol were studied using surface pressure-area isotherms, Brewster angle microscopy, and interfacial rheology measurements. For hexadecanol mixtures below 30% branched molecules, the isotherms show a lateral shift to a decreasing area proportional to the fraction of straight chains. Above a 30% branched fraction, the isotherms are no longer identical in shape. The surface viscosities of both straight and mixed monolayers exhibit a maximum in the condensed untilted LS phase at pi = 20 mN/m. Adding branched chains results in a nonmonotonic increase in surface viscosity, with the maximum near 12% branched hexadecanol. A visualization of these immiscible monolayers using Brewster angle microscopy in the liquid condensed phase shows the formation of discrete domains that initially increase in number density and then decrease with increasing surface pressure. Eicosanol mixtures exhibit different rheological and structural behavior from hexadecanol mixtures. The addition of branched chains results in a lateral shift to increasing area, proportional to the fraction and projected area of both straight and branched chains. A phase transition is seen for all mixtures, including pure straight chains, at pi = 15 mN/m up to 50% branched chains. A second transition is seen at pi = 25 mN/m when the isotherms cross over. Above this transition, the isotherms shift in the reverse direction with increasing branched fraction. The surface viscosities of both straight and mixed monolayers show a maximum in the L2' phase near pi = 5 mN/m. The surface viscosity is constant for low branched fractions and decays beyond 15% branched chains.     

Monomer-on-monomer (MoM) Mitsunobu reaction: facile purification utilizing surface-initiated sequestration

A monomer-on-monomer (MoM) Mitsunobu reaction utilizing norbornenyl-tagged (Nb-tagged) reagents is reported, whereby purification was rapidly achieved by employing ring-opening metathesis polymerization, which was initiated by any of three methods utilizing Grubbs catalyst: (i) free catalyst in solution, (ii) surface-initiated catalyst-armed silica, or (iii) surface-initiated catalyst-armed Co/C magnetic nanoparticles.     

"Click"-capture, ring-opening metathesis polymerization (ROMP), release: facile triazolation utilizing ROMP-derived oligomeric phosphates

Soluble, high-load ring-opening metathesis polymerization (ROMP)-derived oligomeric triazole phosphates (OTP) are reported for application as efficient triazolating reagents of nucleophilic species. Utilizing a "Click"-capture, ROMP, release protocol, the efficient and purification-free, direct triazolation of N-, O-, and S-nucleophilic species was successfully achieved. A variety of OTP derivatives were rapidly synthesized as free-flowing solids on a multigram scale from commercially available materials.     

A giant planet orbiting the 'extreme horizontal branch' star V 391 Pegasi

After the initial discoveries fifteen years ago, over 200 extrasolar planets have now been detected. Most of them orbit main-sequence stars similar to our Sun, although a few planets orbiting red giant stars have been recently found. When the hydrogen in their cores runs out, main-sequence stars undergo an expansion into red-giant stars. This expansion can modify the orbits of planets and can easily reach and engulf the inner planets. The same will happen to the planets of our Solar System in about five billion years and the fate of the Earth is matter of debate. Here we report the discovery of a planetary-mass body (Msini = 3.2M(Jupiter)) orbiting the star V 391 Pegasi at a distance of about 1.7 astronomical units (au), with a period of 3.2 years. This star is on the extreme horizontal branch of the Hertzsprung-Russell diagram, burning helium in its core and pulsating. The maximum radius of the red-giant precursor of V 391 Pegasi may have reached 0.7 au, while the orbital distance of the planet during the stellar main-sequence phase is estimated to be about 1 au. This detection of a planet orbiting a post-red-giant star demonstrates that planets with orbital distances of less than 2 au can survive the red-giant expansion of their parent stars.