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.     

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 .

     

Heritability of Stroop and flanker performance in 12-year old children

Background  

There is great interest in appropriate phenotypes that serve as indicator of genetically transmitted frontal (dys)function, such as ADHD. Here we investigate the ability to deal with response conflict, and we ask to what extent performance variation on response interference tasks is caused by genetic variation. We tested a large sample of 12-year old monozygotic and dizygotic twins on two well-known and closely related response interference tasks; the color Stroop task and the Eriksen flanker task. Using structural equation modelling we assessed the heritability of several performance indices derived from those tasks.     

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.     

The contribution of high frequencies to human brain activity underlying horizontal localization of natural spatial sounds

Background  

In the field of auditory neuroscience, much research has focused on the neural processes underlying human sound localization. A recent magnetoencephalography (MEG) study investigated localization-related brain activity by measuring the N1m event-related response originating in the auditory cortex. It was found that the dynamic range of the right-hemispheric N1m response, defined as the mean difference in response magnitude between contralateral and ipsilateral stimulation, reflects cortical activity related to the discrimination of horizontal sound direction. Interestingly, the results also suggested that the presence of realistic spectral information within horizontally located spatial sounds resulted in a larger right-hemispheric N1m dynamic range. Spectral cues being predominant at high frequencies, the present study further investigated the issue by removing frequencies from the spatial stimuli with low-pass filtering. This resulted in a stepwise elimination of direction-specific spectral information. Interaural time and level differences were kept constant. The original, unfiltered stimuli were broadband noise signals presented from five frontal horizontal directions and binaurally recorded for eight human subjects with miniature microphones placed in each subject's ear canals. Stimuli were presented to the subjects during MEG registration and in a behavioral listening experiment.