Software and hardware integration of a microprogrammable state machine for NMR imaging.

We have integrated a commercially available microprogrammable state machine (Tecmag PULSkit) for use as a magnetic resonance pulse programmer. Providing the capability for active research environment imaging protocols, it features timing resolution of 100 nsec, ten 16-bit loop counters, and individually addressable look-up tables. This integration involved hardware and software integration with a VAX 11/750 at several levels. Hardware: Each of the three gradient channels employs three digital-to-analog converters (DACs). An 8-bit, 4-quadrant, multiplying DAC generates the gradient waveform shape. A 12-bit DAC generates the multiplying DAC scaling voltage, controlling gradient amplitude and sign. A third 12-bit DAC produces a gradient offset (shim) voltage. An eddy current compensation network is present for each gradient channel. Software: The software design philosophy was to create a flexible interface (interactive window environment), while not constraining complex manipulation of the hardware (direct use of the pulse-sequence compiler primitives and microprogramming). The software levels include (a) pulse-sequence microprogramming, (b) pulse-sequence compiler, (c) interactive parameter specification, and (d) canned pulse-sequence microcode library.     

Formation of walls in cylindrical smectic C layers in the presence of a tilted magnetic field

A theoretical study of the elastic properties of a smectic C liquid-crystalline system consisting of cylindrical smectic layers is presented. We show that the ground state configuration of the c-director for such a system depends on the signs of two combinations of the relevant elastic constants. With these configurations as a starting point, we describe how a set of walls under certain conditions must be formed in the system if a magnetic field is applied at an angle to the cylinder axis. An estimate of the thickness of these walls is given. We also show that, depending on whether the angle between the magnetic field and the cylinder axis is larger or smaller than the tilt of the director with respect to the smectic layer normal, the system will exhibit two qualitatively different behaviours.     

On Pseudorandomness in Families of Sequences Derived from the Legendre Symbol

We construct a family of finite binary sequences which has a remarkable uniformity with respect to specification of several terms and which also has the property that every sequence in the family has small measures of normality, well distribution in arithmetical progressions and multiple correlations. We also construct a pseudorandom bit generator whose output consists of members of the family.     

Electrical and structural properties of iron-doped β-alumina

β-alumina containing 50 w/o Fe exhibits high electronic conductivity when sintered in air but Mössbauer studies have shown the presence of Fe₃O₄. Single-phase β-alumina containing 50 w/o Fe could be prepared by sintering at 1400°C for 4–4.5 h followed by annealing at 1300°C for 96 h encapsulated with coarse β-alumina powder enriched with Na₂CO₃. Mössbauer spectroscopy indicated that all iron was present as Fe(III). Complex-plane impedance data showed a maximum bulk $\text{σ}{}_{\mathrm{25°C}}\text{= 5.56 × 10}{}^{-4}\text{(Ω cm)}{}^{-1}$ with little electronic conductivity. Reduction treatments on Fe-doped β-alumina utilizing H₂:N₂ gas were successful in producing a mixed conductor containing Fe(II) and Fe(III) but also produced a distorted β-alumina lattice. This material exhibited an electronic conductivity $\text{σ}{}_{\mathrm{e,25°C}}\text{= 2 × 10}{}^{-4}\text{(Ω cm)}{}^{-1}$ and a bulk ionic conductivity $\text{σ}{}_{\mathrm{b,25°C}}\text{= 1.35 × 10}{}^{-4}\text{(Ω cm)}{}^{-1}$.     

Carbon-13 NMR spectra of monosulphones and disulphones: Substitution rules and conformational effects

Carbon-13 NMR spectra have been obtained for 27 aliphatic monosulphones and 13 aliphatic disulphones. Substitution rules have been formulated which allow the prediction of chemical shifts when a CH₂ group in a hydrocarbon is replaced by an SO₂ group, or when an H atom in a sulphone is replaced by an alkyl group. Carbon atoms β to a sulphone group show a marked upfield shift effect which is sensitive to the conformation about the C? S bond; atoms in the trans position experience an upfield shift (?9.39±1.64 ppm) compared with those in the gauche position. An assignment of the meso (m) and racemic (r) β-carbon peaks in di-sec-butyl sulphone was made by synthesis of the optically active compound. |δ_m–δL_r| decreases with increasing temperature for both β–carbon atoms; this effect was interpreted in terms of two available conformers for each of the m and r compounds, those for the m form having the same energy and entropy, and those for the r form having ΔS=0.6 J K^?1 mol^?1 and ΔH=0.8 kJ mol^?1. Observed chemical shifts for the disulphones were compared with those estimated by the application of the first set of substitution rules.     

Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue

Summary This paper concerns two closely related topics: the behavior of the eigenvalues of graded matrices and the perturbation of a nondefective multiple eigenvalue. We will show that the eigenvalues of a graded matrix tend to share the graded structure of the matrix and give precise conditions insuring that this tendency is realized. These results are then applied to show that the secants of the canonical angles between the left and right invariant of a multiple eigenvalue tend to characterize its behavior when its matrix is slightly perturbed.This work was supported in part by the Air Force Office of Sponsored Research under Contract AFOSR-87-0188