Diffusivity of a random walk on random walks

We consider a random walk with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor with respect to the case of the classical simple random walk without constraint. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 267–283, 2015     

A beneficial kinetic effect of an η(5)-C5Me4H ligand

C-H activation of benzene at 26 °C by (η(5)-C(5)Me(5))W(NO)(CH(2)CMe(3))(η(3)-CH(2)CHCHMe) results after 4 h in the production of five new organometallic complexes, only two of which are isomers of the desired (η(5)-C(5)Me(5))W(NO)(C(6)H(5))(η(3)-CH(2)CHCHMe) compound. In contrast, the identical reaction involving the η(5)-C(5)Me(4)H analogue affords only the phenyl complexes during the first 24 h, thereby facilitating their isolation in good yields. This striking difference in reactivity can be attributed to the lesser steric demands of the η(5)-C(5)Me(4)H ligand that result in its complexes reacting at a significantly slower rate.     

Compound set enrichment: a novel approach to analysis of primary HTS data

The main goal of high-throughput screening (HTS) is to identify active chemical series rather than just individual active compounds. In light of this goal, a new method (called compound set enrichment) to identify active chemical series from primary screening data is proposed. The method employs the scaffold tree compound classification in conjunction with the Kolmogorov-Smirnov statistic to assess the overall activity of a compound scaffold. The application of this method to seven PubChem data sets (containing between 9389 and 263679 molecules) is presented, and the ability of this method to identify compound classes with only weakly active compounds (potentially latent hits) is demonstrated. The analysis presented here shows how methods based on an activity cutoff can distort activity information, leading to the incorrect activity assignment of compound series. These results suggest that this method might have utility in the rational selection of active classes of compounds (and not just individual active compounds) for followup and validation.     

Inside Cover: Challenging the Metallocene Dominance in Actinide Chemistry with a Soft PNP Pincer Ligand: New Uranium Structures and Reactivity Patterns (Angew. Chem. Int. Ed. 20/2009)

A standing iceberg illustrates how the soft PNP pincer ligand challenges the metallocene dominance (ship) in actinide chemistry, as described by J. L. Kiplinger and co‐workers in their Communication on page 3681 ff. Replacement of C₅Me₅ by the PNP ligand is a successful strategy for the promotion of new reactivities and to support new actinide structures. The specific electronic and steric properties of the PNP ligand enable access to structures not available for the C₅Me₅ ligand set and as yet unreported for uranium. (We thank Mr. Anthony Mancinco for the design of the graphic.)

     

A versatile new monomer family: functionalized 4-vinyl-1,2,3-triazoles via click chemistry

Using facile, highly modular synthetic approaches, a new monomer family based on a 1,2,3-triazole-4-vinyl building block has been prepared, and various functional derivatives have been obtained. Subsequent homo- and copolymerization of these novel functionalized monomers gives polymeric materials with unique physical properties, combining many attractive features of more traditional monomers, such as styrene, vinylpyridine, and meth/acrylates.     

Dipole blockade at Förster resonances in high resolution laser excitation of Rydberg states of cesium atoms

High resolution laser excitation of np Rydberg states of cesium atoms shows a dipole blockade at F?rster resonances corresponding to the resonant dipole-dipole energy transfer of the np+np --> ns+(n+1)s reaction. The dipole-dipole interaction can be tuned on and off by the Stark effect, and such a process, observed for relatively low n(25-41), is promising for quantum gate devices. Both Penning ionization and saturation in the laser excitation can limit the range of observation of the dipole blockade.     

EPR and DFT studies of the one-electron reduction product of phospholium cations

Cyclic voltammetry and EPR spectroscopy show that cationic phospholium groups are good electron acceptors whose reduction leads to a neutral radical where the unpaired electron is mainly delocalized on the carbon atoms of the five-membered ring. DFT calculations together with the crystal structure of phospholiums indicate that the electron addition causes a drastic diminution of the exocyclic CPC angle. The SOMO of reduced phospholium is compared to the SOMO of the phosphole radical anion.     

Scalarization of Tangential Regularity of Set-Valued Mappings

A set-valued mapping M from a topological vector space E into a normed vector space F is tangentially regular at a point in its graph g p h M if the Clarke tangent cone to g p h M at is equal to the Bouligand contingent cone to g p h M at . In this paper we characterize, in several cases, this tangential regularity as the directional regularity of the scalar function _M defined by _M (x, y) : = d(y, M(x)). The results allow us to express, in a useful formula, the subdifferential of _M in terms of the normal cone to the graph of M.     

Convex composite functions in Banach spaces and the primal lower-nice property

Primal lower-nice functions defined on Hilbert spaces provide examples of functions that are ``integrable' (i.e. of functions that are determined up to an additive constant by their subgradients). The class of primal lower-nice functions contains all convex and lower- functions. In finite dimensions the class of primal lower-nice functions also contains the composition of a convex function with a mapping under a constraint qualification. In Banach spaces certain convex composite functions were known to be primal lower-nice (e.g. a convex function had to be continuous relative to its domain). In this paper we weaken the assumptions and provide new examples of convex composite functions defined on a Banach space with the primal lower-nice property. One consequence of our results is the identification of new examples of integrable functions on Hilbert spaces.