The NMR reciprocity theorem for arbitrary probe geometry

It is shown that the NMR reciprocity theorem is a variant of a problem considered by Lorentz in 1895. This formulation is quite general and applies to electric-dipole-based as well as coil-based or resonator-based magnetic resonance probes. The reasoning is related to, but different from, the proof of the reciprocity theorem for radiofrequency networks and for transmit/receive antenna systems in telecommunications. The signal-to-noise ratio of the NMR experiment is also discussed in very general terms.     

Sharp Recovery Bounds for Convex Demixing,with Applications

Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis, and the problem of decomposing an observed matrix into a low-rank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these demixing problems, and many others. This work introduces a randomized signal model that ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, this approach identifies a summary statistic that reflects the complexity of a particular signal. The difficulty of separating two structured, incoherent signals depends only on the total complexity of the two structures. Some applications include (1) demixing two signals that are sparse in mutually incoherent bases, (2) decoding spread-spectrum transmissions in the presence of impulsive errors, and (3) removing sparse corruptions from a low-rank matrix. In each case, the theoretical analysis of the convex demixing method closely matches its empirical behavior.     

Authentication of black cohosh (Actaea racemosa) dietary supplements based on chemometric evaluation of hydroxycinnamic acid esters and hydroxycinnamic acid amides

Analytical and Bioanalytical Chemistry - Ester and amide derivatives of hydroxycinnamic acids are found in black cohosh (Actaea racemosa) and other Actaea plants. These two compound groups were...     

On the maximum of the k-dependent susceptibility for fixed k and T > Tc

We study the maximum occuring in ${}_{\mathrm{x}}\text{(}\text{k}\text{, T)}$ for fixed k at a temperature T_max > T_c. We examine the predictions of both Ornstein-Zernike and ?-expansions for the position of this maximum. These are compared with the exact results fot the two-dimensional Ising model.     

Observation of shallow residual donors in high purity epitaxial GaAs by means of photoluminescence spectroscopy

We report the first observation of three different residual donors in undoped high purity vapor phase epitaxial GaAs using the high resolution photoluminescence spectroscopy technique at temperatures ～ 2 K. The binding energies of these shallow donors were determined from the excited state transitions of excitons bound to neutral donors and they are found to be in very good agreement with corresponding values obtained from high-resolution far infrared Fourier transform spectroscopy, using the modulated photoconductivity technique.     

The sl2 Loop Algebra Symmetry of the Six-Vertex Model at Roots of Unity

We demonstrate that the six vertex model (XXZ spin chain) with =(q+q^-1)/2 and q^2N=1 has an invariance under the loop algebra of sl₂ which produces a special set of degenerate eigenvalues. For =0 we compute the multiplicity of the degeneracies using Jordan–Wigner techniques.     

General relationships between the mobility of a chain fluid and various computed scalar metrics

We performed molecular dynamics simulations of chain systems to investigate general relationships between the system mobility and computed scalar quantities. Three quantities were found that had a simple one-to-one relationship with mobility: packing fraction, potential energy density, and the value of the static structure factor at the first peak. The chain center-of-mass mobility as a function of these three quantities could be described equally well by either a Vogel-Fulcher type or a power law equation.     

Determination of azarole plus its reduction product by HPLC

An analytical methodology for the assay of azarole plus its reduced product in plasma was developed. The method consists of oxidation of the sample with potassium ferrocyanide, extraction, and subsequent analysis by high performance liquid chromatography. Assays of prepared plasma samples demonstrated an overall precision of +/- 6.2%; accuracy ranged from -9.1% low to 5.1% high, based on mean values at several concentrations. Analysis of variance for the effects of concentration, time, and the interactive term concentration X time were all insignificant.     

Relatively Hyperimmune Relations on Structures

Let be a computable structure and let R be an additional relation on its domain. We establish a necessary and sufficient condition for the existence of an isomorphic copy of such that the image of R is h-simple (h-immune) relative to .     

The Perturbation ϕ2, 1 of the M(p,p + 1) Models of Conformal Field Theory and Related Polynomial-Character Identities

Using q-trinomial coefficients of Andrews and Baxter along with the technique of telescopic expansions, we propose and prove a complete set of polynomial identities of Rogers-Ramanujan type for M(p, p + 1) models of conformal field theory perturbed by the operator _{2, 1}. The bosonic form of our polynomials is closely related to corner transfer matrix sums which arise in the computation of the order parameter in the regime 1⁺ of A _p–1 dilute models. In the limit where the degree of the polynomials tends to infinity our identities provide new companion fermionic representations for all Virasoro characters of unitary minimal series.