Extremes of Shepp statistics for Gaussian random walk

Let (ξ _i , i ≥ 1) be a sequence of independent standard normal random variables and let be the corresponding random walk. We study the renormalized Shepp statistic and determine asymptotic expressions for when u,N and T→ ∞ in a synchronized way. There are three types of relations between u and N that give different asymptotic behavior. For these three cases we establish the limiting Gumbel distribution of when T,N→ ∞ and present corresponding normalization sequences.      

Postmetallocene lanthanide-hydrido chemistry: A new family of complexes [{Ln{(Me3Si)2NC(NiPr)2}2(mu-H)}2] (Ln = Y, Nd, Sm, Gd, Yb) supported by guanidinate ligands-synthesis, structure, and catalytic activity in olefin polymerization

The new family of Lewis base free hydrido complexes of rare-earth metals supported by guanidinate ligands [{Ln{(Me3Si)2NC(NiPr)2}2(mu-H)}2] (Ln = Y, Nd, Sm, Gd, Yb) was synthesized and structurally characterized. Single-crystal X-ray and solution NMR studies revealed that these complexes are dimeric in both solid state and in [D6]benzene. The dimeric hydrido complexes can adopt eclipsed (Nd, Sm, Gd) or staggered (Y, Yb, Lu) conformations depending on the metal-atom size. Catalytic activity of these [{Ln{(Me3Si)2NC(NiPr)2}2(mu-H)}2] complexes in the polymerization of ethylene, propylene, and styrene has been investigated. Complexes of Sm and Y have high catalytic activity in ethylene polymerization (1268 and 442 g mmol(-1) atm(-1) h(-1), respectively).     

Rational modulation of the periodicity in linear hydrogen-bonded assemblies of trimesic acid on surfaces

We demonstrate a surprising cooperative adsorption process at the liquid-solid interface, involving self-assembly in which a three-fold hydrogen-bonding unit (trimesic acid, TMA) is forced into a linear pattern by noncovalent interaction with an alcohol. Our work shows that the unexpected linear pattern formed by coadsorption of TMA and alcohols can be modulated in size by choosing alcohols with different chain lengths.     

Dipyrido[1,2-a;3′,4′-d]imidazole systems

Novel tricyclic dipyridoimidazole derivatives can be readily synthesised in one pot processes from various highly fluorinated pyridine systems such as pentafluoropyridine and relatively nucleophilic 2-aminopyridine derivatives. Further nucleophilic aromatic substitution reactions of the novel tricyclic scaffolds allow the regioselective synthesis of various nitrogen, oxygen, carbon and sulfur-functionalised dipyridoimidazole products.     

Distinct methylalumoxane(MAO)-derived Me-MAO- anions in contact with a zirconocenium cation--a 13C-NMR study

Zirconocenium cations of the type [(MeC5H4)2ZrMe]+, formed by excess methylalumoxane (MAO) from (MeC5H4)2ZrCl2 or (MeC5H4)2ZrMe2 with 13C-labelled ring ligands, are found to form ion pairs with two types of anions, Me-MAO(A)- and Me-MAO(B)-, which differ in their coordinative strengths: More strongly coherent ion pairs [(MeC5H4)2ZrMe+...Me-MAO(B)-] are converted to more easily separable ion pairs [(MeC5H4)2ZrMe+...Me-MAO(A)-] by a sufficient excess of MAO. These react with Al2Me6 to form outer-sphere ion pairs containing the cationic AlMe3 adduct [(MeC5H4)2Zr(mu-Me)2AlMe2]+; formation of the more easily separable ion pairs might be required also for polymerisation catalysis.     

Mechanical unfolding of segment-swapped protein G dimer: results from replica exchange molecular dynamics simulations

The protein G dimer (pdb code 1Q10) is a mutated dimeric form of the immunoglobulin-binding domain B1 of streptococcal protein G, in which the two monomeric units have swapped elements of their secondary structure. We have used replica exchange molecular dynamics simulations to study how this dimer responds to a mechanical force that pulls the N-terminus of one unit and the C-terminus of the other apart. We have further compared the mechanical response of the dimer to that of the protein G monomer. When the pulling force is low enough, the mechanical unfolding can be viewed as a thermally activated barrier crossing process. For each protein, we have computed the corresponding free energy barrier and its dependence on the pulling force. While the dimer is found to be less resistant to mechanical unfolding than its monomeric counterpart, the two proteins exhibit essentially the same mechanical unfolding mechanism involving separation of the terminal parallel strands. On the basis of our results, we speculate that the mechanical properties of natural adhesives, composites, fibers, and other materials may be optimized not only at a single molecule level but also at the mesoscopic level through the interactions among individual chains.     

Convenient asymmetric synthesis of beta-substituted alpha,alpha-difluoro-beta-amino acids via Reformatsky reaction between Davis' N-sulfinylimines and ethyl bromodifluoroacetate

The enantiopure Davis' N-sulfinylimines were found to be efficient as chiral imine equivalents in the high-temperature Reformatsky-type additions with BrZnCF(2)COOEt affording an efficient approach to the enantiomerically pure alpha,alpha-difluoro-beta-amino acids. High chemical and stereochemical yields (drs > 9:1, and as high as 99:1) render this method immediately useful for preparing the target amino acids.     

A new simple synthesis of poly(thiophene-methine)s

Acid-promoted polycondensation of 3,4-(ethylenedioxy)thiophene-2-carbaldehyde leads to a conjugated heavily p-doped poly(thiophene-methine), which can be dedoped leading to a low band-gap neutral polymer.     

Mono- and bis-(2-dimethylaminoethyl)tetramethylcyclopentadienyl zirconium(IV) complexes: synthesis and structural studies in crystalline state and in solutions

A novel half-sandwich Zr(IV) complex [η⁵:η¹-N-C₅(CH₃)₄CH₂CH₂N(CH₃)₂]ZrCl₃ (6) together with zirconocene dichlorides [η⁵-C₅(CH₃)₄CH₂CH₂N(CH₃)₂][η⁵-C₅(CH₃)₅]ZrCl₂ (4) and [η⁵-C₅(CH₃)₄CH₂CH₂N(CH₃)₂]₂ZrCl₂ (5) have been prepared. Complex 6 has been isolated and characterized in three different forms, namely, as an adduct with THF 6a, an adduct with tetrahydrothiophene 6b, and a solvent-free form 6c. Molecular structures of complexes 4, 6b, and 6c have been established by X-ray diffraction analysis. Complex 6c has been shown to be a monomeric solvent-free half sandwich Zr(IV) complex. The dynamic behavior of complex 6a in a non-solvating medium (an equilibrium between 6a and 6c along with a degenerate interconversion of the Zr-C_cp-CH₂-CH₂-N(CH₃)₂-(Zr) pseudo-five-member metallacycle) have been studied by the variable-temperature ¹H and ¹³C{¹H} NMR spectroscopy. The activation parameters for the degenerate five-member cycle interconversion have been elucidated.