Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed point set. In particular, the center of A acts by characters on the deformed standard modules, providing a “localization map”. We construct a universal graded deformation of A and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming from the algebra Koszul dual to A. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category O{\mathcal{O}} for \mathfrakgl_n{\mathfrak{gl}_n} is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the “category O{\mathcal{O}}” of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.     

A simple automatic titrator based on a digital balance

A computer-controlled automatic titrator incorporating a weight burette is described. The titration vessel is mounted on the pan of a zero-displacement digital balance which records the weight of added sample as well as the weight of titrant added during the titration.     

The determination of lithium in rocks by the method of stable isotope dilution

A method is described for the determination of lithium in rocks by the method of stable isotope dilution. 50 mg to 500 mg of the sample are used for each determination. The sample is mixed with a known quantity of enriched lithium and is then decomposed by a mixture of hydrofluoric and perchloric acids. The separation of the alkali metals from iron and aluminium is based on the thermal decomposition of the perchlorates. For mass spectrometric measurements it is not necessary to separate the lithium from the other alkali metals.The values obtained for the lithium contents of two standard rocks are: G-I, 21.3 p.p. m. ; W-I, 12.6 p.p.m. Independent determinations, made using both lithium 6 and lithium 7 as tracers, have established that no significant systematic errors are caused by isotopic fractionation.Results obtained for two clay samples containing 0.1–0.3% of lithium show good agreement with spectrographic values.     

Phase equilibria in the n-hexane + diethylamine system

Pressure-temperature-composition data for the binary system composed of n-hexane and diethylamine have been determined over a range of conditions extending into the critical region. Dew, bubble and critical points at six compositions are reported in this paper. Vapor pressures and liquid densities of pure diethylamine are also reported. Phase equilibria in this nonpolar+polar system have been correlated using the Peng-Robinson (PR) equation. The PR equation is shown to work well for this weakly associating system although it fails to reproduce the detailed behavior of the critical locus. A remarkable feature of this binary system is that the critical locus is also the locus of points of maximum temperature (maxcondentherm) and pressure (maxcondenbar). As a consequence, there is no retrograde region in the system. The critical locus also exhibits a minimum in temperature which is characteristic of azeotropic behavior in the critical region.     

Magnetic order in palladium-based Heusler alloys part 3: The effects of disorder in Pd2MnIn1−xSn and Pd2MnIn1−ySb

Magnetization, susceptibility, X-ray and neutron diffraction measurements have already been reported in parts 1 and 2 on the two alloy series Pd₂MnIn_1−xSn_x and Pd₂MnIn_1−ySb_y when chemically ordered in the Heusler structure, with the Mn atoms on an fcc sublattice and carrying a moment of about 4.2μ_B ordered antiferromagnetically or ferromagnetically depending upon the conduction electron concentration. Results are presented here of similar measurements on the same samples, but after heat-treatments designed to produce maximum disorder between the Mn and In/Sn or In/Sb sites, respectively, whilst retaining the Pd order. In this disordered, B2, structure the Mn atoms retain the same magnetic moment but now occupy a simple cubic sublattice and form a new antiferromagnetic structure, simple cubic type 1. The results are discussed in terms of current indirect double resonance exchange interactions.     

Study of the missing-mass spectra in the reactions π−d → K+ + MM and K−d → π+ + MM at 1.4 GeV/c to search for strange dibaryon states

The reactions π^?d → K⁺ + MM and K^?d → π⁺ + MM have been studied at 1.4 GeV/c to search for strange dibaryon states with quantum numbers Q = ?1, and S = ?1. No structures are found which could indicate the production of such states and upper limits for the cross sections are established.     

Ferrimagnetic transition in Fe0.9S: Magnetic,thermodynamic and kinetic aspects

Antiferromagnetic Fe_0.9S forms a ferrimagnetic superlattice in a narrow temperature range centred at 475 K (γ-transition). We have made a study in single crystals by specific heat, Mössbauer spectroscopy and magnetic susceptibility of the magnetic structure and kinetics and thermodynamics of formation of the ferrimagnetic component.The antiferromagnetic alignment and the spontaneous moment lie in the c-plane. The magnetic anisotropy energy is of the order of 0.4 K per Fe ion. Above 475 K and below T_N ≈ 598 K there is a change in ordering of the vacancies and a new antiferromagnetic structure is formed. At lower temperatures our value (100 kJ mol^?1) of the activation energy of diffusion of iron vacancies, determined from magnetic susceptibility, is in quite good agreement with the value (88 kJ mol^?1) obtained from radiotracer measurements by Condit et al.     

Surface and aggregation behavior of aqueous solutions of Ru(II) metallosurfactants. 3. Effect of chain number and orientation on the structure of adsorbed films of [Ru(bipy)2(bipy')]Cl2 complexes

The surface behavior of a range of surfactant [Ru(bipy)(2)(p,p'-dialkyl-2,2'-bipy)]Cl(2) complexes, which we express as Ru(q)(p)C(n) where n is the alkyl chain length, p refers to the substitution position on the bipyridine ligand (=4 or 5), and q (=1 or 2) is the number of substituted alkyl chains, has been examined using neutron reflectometry. The adsorption of the single-chain Ru(1)(4)C(19) and Ru(1)(5)C(19) surfactants is strongly time-dependent, taking in excess of 10 h to form an equilibrium film. It is suggested that the slow adsorption rate is related to the alkyl chain length rather than the low monomer concentration present in the solutions. At concentrations below the critical micelle concentration (cmc) of Ru(1)(4)C(19), the film of Ru(1)(5)C(19) is denser than that of Ru(1)(4)C(19) at comparable concentration, consistent with the mass densities of the bulk solids, whereas at concentrations close to and greater than this cmc the converse pertains. Close to the cmc, the adsorbed films possess an average area per molecule significantly less than the nominal headgroup area of the surfactants (approximately 30 angstroms(2) compared with approximately 100 angstroms(2)). This fact together with consideration of the thickness and density of the adsorbed films leads to the conjecture that surface aggregates may be the adsorbing units. The adsorption of the double-chain surfactant Ru(1)(p)C(19), in contrast to the behavior of the Ru(1)(p)C(19) surfactants, is weak and independent of time. This behavior is attributed to the alkyl chain orientation. The adsorption behavior of a racemic mixture of the Delta and Lambda isomers of Ru(2)(4)C(19) has been compared with that of the Delta isomer. It is found that the film of racemic material is more closely packed than that of the resolved complex.