Ideals of Priestley powers of semilattices

Let X be a poset and Y an ordered space; X ^Y denotes the poset of continuous order-preserving maps from Y to X with the discrete (respectively, Scott, Lawson) topology. If S is a -semilattice, its ideal semilattice, and T a bounded distributive lattice with Priestley dual space P(T), it is shown that the following isomorphisms hold: Moreover, and sufficient conditions and necessary conditions for the isomorphism to hold are obtained (both necessary and sufficient if S is a distributive -semilattice). Received September 27, 1995; accepted in final form April 6, 1998.     

Trim-loss pattern rearrangement and its relevance to the flat-glass industry

An additional restriction upon the conventional two-dimensional trim-loss problem arises in the glass-industry. This restriction imposes limitations upon the positioning of cuts within the stock-plate, relative to other cuts. Two procedures are presented which take an existing pattern and attempt to rearrange it to meet the restrictions. One procedure is a heuristic while the other is a complete enumeration.     

Some investigations into the strength and flow properties of powders

Summary Results of investigations made of the strengths of powders have been found to fit a general eq. for a yield locus at constant bulk density of the form: (/C) ⁿ=/T+1, where is the applied compressive stress and is the applied shear stress. The parametern for any particular powder is independent of bulk density and can be used to classify powders according to their flow properties. Experimentally determined values of tensile strengthT and cohesionC are both shown to have a similar type of power law relationship with bulk density. The relationships between shear stress, normal stress and bulk density for powders are represented by surfaces in a 3-dimensional space analogous to a similar concept recently developed in soil mechanics. The relationships greatly simplify the laboratory measurements required for hopper design.Paper presented at a meeting of the British Society of Rheology, University of Nottingham, April 6–8, 1965.Dr. Jenike's helpful comments are appreciated.     

An EPR and ENDOR investigation of a series of diazabutadiene-group 13 complexes

Paramagnetic diazabutadienegallium(II or III) complexes, [(Ar-DAB)2Ga] and [{(Ar-DAB*)GaX}2] (X = Br or I; Ar-DAB = {N(Ar)C(H)}2, Ar = 2,6-diisopropylphenyl), have been prepared by reactions of an anionic gallium N-heterocyclic carbene analogue, [K(tmeda)][:Ga(Ar-DAB)], with either "GaI" or [MoBr2(CO)2(PPh3)2]. A related InIII complex, [(Ar-DAB*)InCl2(thf)], has also been prepared. These compounds were characterised by X-ray crystallography and EPR/ENDOR spectroscopy. The EPR spectra of all metal(III) complexes incorporating the Ar-DAB ligand, [(Ar-DAB(.))MX(2)(thf)(n)] (M = Al, Ga or In; X = Cl or I; n = 0 or 1) and [(Ar-DAB)2Ga], confirmed that the unpaired spin density is primarily ligand centred, with weak hyperfine couplings to Al (a = 2.85 G), Ga (a = 17-25 G) or In (a = 26.1 G) nuclei. Changing the N substituents of the diazabutadiene ligand to tert-butyl groups in the gallium complex, [(tBu-DAB*)GaI2] (tBu-DAB={N(tBu)C(H)}2), changes the unpaired electron spin distribution producing 1H and 14N couplings of 1.4 G and 8.62 G, while the aryl-substituted complex, [(Ar-DAB*)GaI2], produces couplings of about 5.0 G. These variations were also manifested in the gallium couplings, namely aGa approximately 1.4 G for [(tBu-DAB*)GaI2] and aGa approximately 25 G for [(Ar-DAB*)GaI2]. The EPR spectra of the gallium(II) and indium(II) diradical complexes, [{(Ar-DAB*)GaBr}2], [{(Ar-DAB*)GaI}2], [{(tBu-DAB*)GaI}2] and [{(Ar-DAB*)InCl}2], revealed doublet ground states, indicating that the Ga-Ga and In-In bonds prevent dipole-dipole coupling of the two unpaired electrons. The EPR spectrum of the previously reported complex, [(Ar-BIAN*)GaI2] (Ar-BIAN = bis(2,6-diisopropylphenylimino)acenaphthene) is also described. The hyperfine tensors for the imine protons, and the aryl and tert-butyl protons were obtained by ENDOR spectroscopy. In [(Ar-DAB*)GaI2], gallium hyperfine and quadrupolar couplings were detected for the first time.     

Synthesis and characterisation of the first carbene and diazabutadiene-indium(II) complexes

The reactions of IMes [:CN(Mes)C2H2N(Mes), Mes = mesityl] and DAB [(ArN=CH)2, Ar = C6H3Pri2-2,6] with indium(I) halides have afforded the first carbene and diazabutadiene indium(II) complexes, [In2Br4(IMes)2] and [In2Cl2(DAB.)2], both of which have been crystallographically characterised.     

A platinum acetylide polymer with sterically demanding substituents: effect of aggregation on the triplet excited state

The effect of interchain interaction on the triplet excited state is explored in two Pt-acetylide polymers of the type [-trans-Pt(PBu(3))(2)-C triple bond C-Ar-C triple bond C-](n), where Ar is either 1,4-phenylene or is based on the pentiptycene unit (polymers 2 and 3, respectively). To explore the effect of interchain interaction in Pt-acetylide materials, the optical properties of parent polymer 2 are compared with those of polymer 3 in which interchain interaction is precluded by the sterically bulky pentiptycene moiety. Insight into the effect of the pentiptycene unit on packing in the solid state comes from the X-ray structure of monomer 1b, Ph-C triple bond C-[trans-Pt(PBu(3))(2)]-C triple bond C-Ar-C triple bond C-[trans-Pt(PBu(3))(2)]-C triple bond C-Ph. Spectroscopic studies indicate that weak phosphorescence emission from an interchain aggregate is observed from parent polymer 2, both in solution and in the solid state. By contrast, the photophysics of 3 is dominated by the intrachain triplet exciton. Interestingly, the phosphorescence emission of polymer 3 in the solid state is nearly superimposable with that of a single crystal of monomer 1b, suggesting that the solid polymer experiences an environment that is similar to that of the monomer in the crystal.     

Coding of spectral fine structure in the auditory nerve. I. Fourier analysis of period and interspike interval histograms

The temporal fine structure of discharge patterns of single auditory-nerve fibers in adult cats was analyzed in response to signals consisting of a variable number of equal-intensity, in-phase harmonics of a common low-frequency fundamental. Two analytic methods were employed. The first method considered Fourier spectra of period histograms based on the period of the fundamental, and the second method considered Fourier spectra of interspike interval histograms (ISIH's). Both analyses provide information about fiber tuning properties, but Fourier spectra of ISIH's also allow estimates to be made of the degree of resolution of individual stimulus components. At low intensities (within 20-40 dB of threshold), indices of synchronization to individual components of complex tones were similar to those obtained for pure tones. This was true even when fibers were capable of responding to several signal components simultaneously. Response spectra obtained at low intensities resembled fibers' tuning curves, and fibers with low spontaneous discharge rates tended to provide better resolution of stimulus components than fibers with high spontaneous rates. Strongly nonlinear behavior existed at higher stimulus intensities. In this, information was transmitted about progressively fewer signal components and about frequencies not present in the acoustic stimulus, and the component eliciting the largest response shifted away from the fiber's characteristic frequency and toward the edges of the stimulus spectrum. This high-intensity "edge enhancement" can result from the combined effects of a compressive input-output nonlinearity, suppression, and the fortuitous addition of internally generated combination tones. The data indicate that sufficient information exists for the auditory system to determine the frequencies of narrowly spaced stimulus components from the temporal fine structure of nerve fiber's responses.     

The synthesis and structure of terpyridine-N-oxide complexes of copper(II) perchlorate

The co-ordination of a series of terpyridine-N-oxide ligands to the Cu(ii) ion is reported. Addition of two equivalents of ligand results in the formation of the expected 2 : 1 six co-ordinate product, while the addition of one equivalent of ligand allows the isolation of 1 : 1 species if the ligand has a meridonal binding mode. The five complexes isolated were characterised in the solid state by X-ray crystallography while they are studied in solution using EPR, UV-vis spectroscopy and IR spectroscopy.