The interaction of an osmium-carbon triple bond with copper(I), silver(I) and gold(I) to give mixed dimetallocyclopropene species and the structures of Os(AgCl) (CR) Cl(CO) (PPh3)2

The osmium carbyne complex, Os(CR)Cl(CO)(PPh₃)₂, (R  p-tolyl) reacts with Group I halides to form the mixed dimetallocyclopropene species, $\text{Os(Cul)(C}$R)Cl(CO)(PPh₃)₂, $\text{Os(AgCl)(C}$R)Cl(CO)(PPh₃)₂, $\text{Os(AuCl)(C}$R)Cl(CO)(PPh₃)₂, and [$\text{Os[Ag(OClO}{}_3\text{)](C}$R)Cl(CO)(MeCN)(PPh₃)₂] ClO₄ X-ray crystal structure determination of $\text{Os(AgCl)(C}$R)Cl(CO)(PPh₃)₂ confirms the presence of a three-membered ring and the structure can be viewed as the “acetylene-like” interaction of an osmium—carbon triple bond with AgCl. In acid solution AgCl is precipitated and an alkylidene complex results from proton addition to the carbyne ligand.     

Role of structure in amorphous magnetic materials: Dense random packing of hard spheres of two sizes

We investigate the structure of amorphous rare-earth transition-metal alloys and its influence on their magnetic properties in the context of a simple model. The packing fraction of the alloys is discussed using both ball-bearing assemblies and also computer-generated clusters of randomly close-packed hard spheres, and the latter clusters are used to discuss the radial distribution functions (RDF's) and the magnetic anisotropy. The computer-generated RDF's are compared with published neutron diffraction results on amorphous TbFe₂.     

Gaps between integers with the same prime factors

We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers is , and it is shown that this lower bound is best possible. Dressler's conjecture is verified for values of and up to .

     

Upper bounds on a two-term exponential sum*

We obtain upper bounds for mixed exponential sums of the type where p^m is a prime power with m⩾ 2 and X is a multiplicative character (mod p^m). If X is primitive or p⫮(a, b) then we obtain |S(χ,f,p ^m)| ⩽2np ^{2/3 m}. If X is of conductor p and p⫮( a, b) then we get the stronger bound |S(χ,f,p ^m)|⩽np ^m/2. This paper is dedicated to Prof. Wang Yuan on the occasion of his 70th birthday.     

Magnetism and disorder effects on muon spin rotation measurements of the magnetic penetration depth in iron-arsenic superconductors

It is shown that attempts to accurately deduce the magnetic penetration depth λ of overdoped BaFe(1.82)Co(0.18)As? single crystals by transverse-field muon spin rotation (TF μSR) are thwarted by field-induced magnetic order and strong vortex-lattice disorder. We explain how substantial deviations from the magnetic field distribution of a nearly perfect vortex lattice by one or both of these factors is also significant for other iron-arsenic superconductors, and this introduces considerable uncertainty in the values of λ obtained by TF μSR.     

Solid supported chemical syntheses of both components of the lantibiotic lacticin 3147

Lantibiotics are antimicrobial peptides produced by bacteria. Some are employed for food preservation, whereas others have therapeutic potential due to their activity against organisms resistant to current antibiotics. They are ribosomally synthesized and posttranslationally modified by dehydration of serine and threonine residues followed by attack of thiols of cysteines to form monosulfide lanthionine and methyllanthionine rings, respectively. Chemical synthesis of peptide analogues is a powerful method to verify stereochemistry and access structure-activity relationships. However, solid supported synthesis of lantibiotics has been difficult due to problems in generating lanthionines and methyllanthionines with orthogonal protection and good stereochemical control. We report the solid-phase syntheses of both peptides of a two-component lantibiotic, lacticin 3147. Both successive and interlocking ring systems were synthesized on-resin, thereby providing a general methodology for this family of natural products.     

Using Stepanov's method for exponential sums involving rational functions

For any additive character ψ and multiplicative character χ on a finite field F_q, and rational functions f,g in F_q(x), we show that the elementary Stepanov-Schmidt method can be used to obtain the corresponding Weil bound for the sum ∑_x∈Fq?Sχ(g(x))ψ(f(x)) where S is the set of the poles of f and g. We also determine precisely the number of characteristic values ω_i of modulus q^1/2 and the number of modulus 1.     

The connection between Hall effect and magnetism

Experimental measurements of Hall effect on amorphous metals and, in particular, alloys containing magnetic components, often exhibit a simple relationship between Hall coefficientR _H and magnetic susceptibility. The scattering times, however, do not seem to affect either sign or magnitude of the Hall coefficient. This is in strong contrast to conventional theories of the Hall effect in materials. The present paper demonstrates that a theoretical foundation can be found for the experimental observations.