Wiener-Hope equations with the transmission property

Conditions on the kernel of the classical Wiener-Hopf equation are obtained which provide the same smoothness of any solution in terms of its inclusion in different spaces of smooth functions such as as the function in the right side of the equation.     

Mono- and dinuclear molybdenum complexes with sterically demanding cycloheptatrienyl ligands

Sterically demanding cycloheptatrienylium (tropylium) salts of the type (1,3,5-C7H4R3)BF4 [R = t-Bu, (3a)BF4; R = SiMe3, (3b)BF4] have been prepared from the corresponding 1,3,5-trisubstituted benzene derivatives 1 by ring expansion with diazomethane followed by hydride abstraction with triphenylcarbenium tetrafluoroborate, (Ph3C)BF4. Complexation can be achieved by arene exchange and Mo(CO)3 group transfer employing [(eta6-p-xylene)Mo(CO)3] (4) to yield the cationic complexes (5)BF4. In refluxing mesitylene, [(eta7-C7H4t-Bu3)Mo(CO)3]BF4, (5a)BF4, undergoes CO substitution to furnish the mesitylene sandwich complex (6a)BF4. A cyclic voltammetric study reveals that this complex exhibits a reversible one-electron oxidation to the dicationic 17e complex 6a2+, which can also be accessed by chemical oxidation with AgBF4. On the contrary, the reduction of 6a+ is irreversible and does not yield a stable 19e complex 6a. To study the fate of the reduced 19e form, (5a)BF4 was treated with Na2Hg to diastereoselectively afford the C-C coupled bicycloheptatriene complex 7a. Paramagnetic, dinuclear complexes of the type [(eta7-C7H4R3)Mo(mu-Cl)3Mo(eta7-C7H4R3)] (8) have been obtained from the reaction of (5)BF4 with Me3SiCl. These can be regarded as mixed-valence Mo(0)/Mo(+I) compounds with a metal-metal bond order of 0.5. Cyclic voltammetric studies reveal that both complexes 8a and 8b undergo reversible one-electron oxidation as well as reduction. Treatment with one equivalent of ferrocenium hexafluorophosphate leads to removal of the unpaired electron and formation of the diamagnetic complexes (8)PF6. Theoretical DFT calculations have been carried out to further elucidate the bonding in these systems. In addition, the X-ray crystal structures of (5b)BF4, (6a)BF4 x CH2Cl2, (6a)(BF4)2 x (acetone)2, 7a x CH2Cl2, 8a x 0.5C6H14, and (8a)PF6 x Et2O are reported.     

Tchebyshev systems that cannot be transformed into Markov systems

The linear hull of a Tchebyshev system is called a Haar-space. A basis f₁,...,f_n of an n-dimensional Haar-space is called a Markov basis if f₁,...,f_i form a Tchebyshev system for each i=l,...,n. It is shown by suitable examples that for all n3 there exist Haar-spaces without a Markov basis.     

Über die optimale Beleuchtung einer geraden Straße

The following problem is due toL. Fejes Tóth: For a given sort of lamps letf(x) be the intensity of brightness in each point having distancex from the foot of the lamp. How must infinitely many lamps of this kind be arranged on a both-side infinite rectilinear road, such that the infimum of the intensities of brightness, extended over the whole street, is maximal, subject to the condition that the average number of lamps per kilometer is bounded by a fixed number (“Best distributions”)? The main result of this paper is: Iff is strictly convex, the equidistant distribution is best.     

Pharmacomodulation of a ligand targeting the HBV capsid hydrophobic pocket

Hepatitis B virus (HBV) is a small enveloped retrotranscribing DNA virus and an important human pathogen. Its capsid-forming core protein (Cp) features a hydrophobic pocket proposed to be central notably in capsid envelopment. Indeed, mutations in and around this pocket can profoundly modulate, and even abolish, secretion of enveloped virions. We have recently shown that Triton X-100, a detergent used during Cp purification, binds to the hydrophobic pocket with micromolar affinity. We here performed pharmacomodulation of pocket binders through systematic modifications of the three distinct chemical moieties composing the Triton X-100 molecule. Using NMR and ITC, we found that the flat aromatic moiety is essential for binding, while the number of atoms of the aliphatic chain modulates binding affinity. The hydrophilic tail, in contrast, is highly tolerant to changes in both length and type. Our data provide essential information for designing a new class of HBV antivirals targeting capsid–envelope interactions.

Small-molecule binding to the Hepatitis B virus core protein hydrophobic pocket, a possible strategy for targeting viral particle assembly.     

Comment on “Density functional theory study of 1,2‐dioxetanone decomposition in condensed phase”

In the preceding paper results are presented, which are in serious conflict with state‐of‐the‐art ab initio method. Based on these new results the authors propose a new explanation of the reason for the preferential production of a phosphorescent state. Here we show that these controversial results are flawed, since the model use exclude biradical electron structures. © 2012 Wiley Periodicals, Inc.     

A Convenient Synthesis of Hydrophenanthrenes the Synthesis of Ferrugindl and Xanthoperol

We wish to report an approach (equation 1) to hydrophenanthrenes which shows considerable promise of providing a general synthetic route for diterpenes, steroids, triterpenes, and tetraterpenes. Herein we illustrate the utility of this Friedel-Crafts type of procedure^3,6 by describing a synthesis of ferruginol (6) ⁷ and xanthoperol (8).⁸