Nonexistence of a Kruskal-Katona Type Theorem for Subword Orders

We consider the poset SO(n) of all words over an n-element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i. e. there is a theorem of Kruskal–Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip-order can be chosen.Daykin introduced the V-order which generalizes the vip-order to the n2 case. He conjectured that the V-order gives a Kruskal–Katona type theorem for SO(n).We show that this conjecture fails for all n3 by explicitly giving a counterexample. Based on this, we prove that for no n3 the subword order SO(n) is a Macaulay poset.     

Localization ability with bimodal hearing aids and bilateral cochlear implants

After successful cochlear implantation in one ear, some patients continue to use a hearing aid at the contralateral ear. They report an improved reception of speech, especially in noise, as well as a better perception of music when the hearing aid and cochlear implant are used in this bimodal combination. Some individuals in this bimodal patient group also report the impression of an improved localization ability. Similar experiences are reported by the group of bilateral cochlear implantees. In this study, a survey of 11 bimodally and 4 bilaterally equipped cochlear implant users was carried out to assess localization ability. Individuals in the bimodal implant group were all provided with the same type of hearing aid in the opposite ear, and subjects in the bilateral implant group used cochlear implants of the same manufacturer on each ear. Subjects adjusted the spot of a computer-controlled laser-pointer to the perceived direction of sound incidence in the frontal horizontal plane by rotating a trackball. Two subjects of the bimodal group who had substantial residual hearing showed localization ability in the bimodal configuration, whereas using each single device only the subject with better residual hearing was able to discriminate the side of sound origin. Five other subjects with more pronounced hearing loss displayed an ability for side discrimination through the use of bimodal aids, while four of them were already able to discriminate the side with a single device. Of the bilateral cochlear implant group one subject showed localization accuracy close to that of normal hearing subjects. This subject was also able to discriminate the side of sound origin using the first implanted device alone. The other three bilaterally equipped subjects showed limited localization ability using both devices. Among them one subject demonstrated a side-discrimination ability using only the first implanted device.     

Ab initio calculation of hyperfine and superhyperfine interactions for shallow donors in semiconductors

For the shallow group V donors in Si we show that the hyperfine interaction for the donor nucleus and the superhyperfine interactions for the first five shells of Si ligands can be quite accurately calculated using the local spin-density approximation of the density-functional theory. We treat the impurity problem in a Green's function approach. Since we have to truncate the long-ranged part of the defect potential, we do not obtain a localized gap state. Instead we identify the resonance above the conduction band with the paramagnetic defect state. We show that the hf and shf interactions thus obtained are at least as accurate as those obtained from one-electron theories with fitting parameters. Application of this first principles method to other shallow donors could be an essential help in defect identification.     

Grafted conjugated polymers: synthesis and characterization of a polyester side chain substituted poly(paraphenyleneethynylene)

The synthesis of a poly(paraphenyleneethynylene) with macromolecular side chains and its irreversible thermo-chromic behaviour are reported herein.     

Synthesis of a eta 2-2,3-diphosphabutadiene complex of zerovalent platinum from the corresponding eta 2-phosphaalkyne complex

Hydrozirconation of the eta 2-phosphaalkyne complex [Pt(dppe)(eta 2-tBuCP)] with [ZrHCl(eta 5-C5H5)2], followed by treatment with the chlorophosphaalkene ClP=C(SiMe3)2 affords the eta 2-2,3-diphosphabutadiene complex [Pt(dppe)(eta 2-tBuC(H)=PP=C(SiMe3)2]. In the presence of [Pt(PPh3)2] the latter undergoes an addition reaction with water to afford the structurally characterised Pt(II) complex [Pt(dppe)(tBuCH2P(O)HPC(SiMe3)2].     

The selective functionalisation and difunctionalisation of p-substituted calix[6]arene and calix[8]arenes using hydrophilic moieties

Methodologies to access water soluble large ringed calixarenes in good yield using efficient synthetic procedures have been investigated. Symmetrical partial functionalisations at the lower rim are described using activated [n]ethylene glycol chains and the addition behaviour contrasted with that of bromoalkanenitriles which proceeds with no observed regioselectivity. Full functionalisations of the calixarenes bearing hydrophilic groups are then investigated and a two-step procedure established which appears to be generally applicable for the addition of different [n]ethylene glycol chains. Furthermore, difunctionalisation under different reaction conditions are described. Throughout, strategies for the characterisation of these high mass compounds are outlined.