Decay of correlations in surface models

A convergent low-temperature expansion for a variety of models of twodimensional surfaces is presented. It yields existence of the thermodynamic limit for the pressure and correlation functions as well as analyticity inz =e ^– In addition, the estimates give exponential decay of truncated correlations, which proves the existence of a gap in the spectrum of the transfer matrix below the ground state eigenvalue. Two particular examples included in the general framework are the solid-on-solid and discrete Gaussian models.Supported in part by the National Science Foundation under grant No. PHY 79-16812.     

New structures in the bi­pyridine–copper(II) nitrate–methanol system: [(bpy)2Cu(NO3)]NO3·CH3OH and [(bpy)2Cu(NO3)]NO3

Reaction of 2,2′‐bi­pyridine (bpy) and copper(II) nitrate in methanol results in two complexes, namely light‐blue bis(2,2′‐bi­pyridine)­nitrato­copper(II) nitrate methanol solvate, [Cu(NO₃)(C₁₀H₈N₂)₂]NO₃·CH₃OH, (I), which is unstable in air, and the product of its decomposition, catena‐poly­[[[bis(2,2′‐bi­pyridine)copper(II)]‐μ‐nitrato‐O:O′] nitrate], {[Cu(NO₃)(C₁₀H₈N₂)₂]NO₃}_n, (II). The crystal structures of both compounds were determined from one crystal at room temperature. Later, the structure of (I) was redetermined at low temperature. In (I) and (II), the Cu atom is coordinated by two bpy and one or two nitrate ions, respectively. The second nitrate ion in (I), along with the methanol solvent mol­ecule, is found in the outer coordination sphere, not bonded to Cu. The nitrate in (I) is chelating, while in (II), it bridges (bpy)₂Cu complexes, forming a one‐dimensional chain structure. The Cu cation in (II) lies on a twofold axis and the uncoordinated NO₃^? ion is located close to a twofold axis and is therefore disordered. Compound (I) converts into (II) upon loss of solvent.     

A multi-moment vortex method for 2D viscous fluids

In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33]. These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as they evolve without the added cost of computing the non-local Biot–Savart integral. We present three examples using MMVM. We first focus our attention on the implementation of a single particle, large number of Hermite moments case, in the context of quadrupole perturbations of the Lamb–Oseen vortex. At smaller perturbation values, we show the method captures the shear diffusion mechanism and the rapid relaxation (on Re^1/3 time scale) to an axisymmetric state. We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods. We perform numerical tests of convergence of the single particle method and show that at least in simple cases the method exhibits the exponential convergence typical of spectral methods. Lastly, we numerically investigate the spatial accuracy improvement from the inclusion of higher Hermite moments in the full MMVM.     

Lie geometry of linear Weingarten surfaces

We show how linear Weingarten surfaces appear as special Ω-surfaces and give a characterization of those linear Weingarten surfaces that allow a Weierstrass type representation.     

Spectroscopic and time-dependent density functional investigation of the role of structure on the acid-base effects of citrinin detection

A time-dependent density functional theory (TD-DFT) study was carried out on tautomers of the mycotoxin citrinin in the neutral, anionic, and cationic forms to gain insight into the role of chemical structure on detection. Steady-state fluorescence studies of citrinin in micellar aqueous solutions produced unusual results for ionic surfactants and the neutral Triton X-100 enhanced fluorescence emission. Ground-state and time-dependent density functional studies were carried out on five tautomers of citrinin using the B3LYP density functional and the 6-311+G(2df,2p) basis set. The investigation revealed that deprotonation is a major factor governing the shifts in fluorescence excitation and emission maxima. Moreover, the position of the lowest unoccupied molecular orbitals is removed from the fluorophore moiety of citrinin in the dianionic state which is consistent with the diminished fluorescence of the toxin in basic solutions. The ionic characteristics of certain chemosensors can influence the structure and intrinsic spectroscopic properties of citrinin.     

Muscle oxygenation measurement in humans by noninvasive optical spectroscopy and Locally Weighted Regression

We have developed a method to make real-time, continuous, noninvasive measurements of muscle oxygenation (Mox) from the surface of the skin. A key development was measurement in both the visible and near infrared (NIR) regions. Measurement of both oxygenated and deoxygenated myoglobin and hemoglobin resulted in a more accurate measurement of Mox than could be achieved with measurement of only the deoxygenated components, as in traditional near-infrared spectroscopy (NIRS). Using the second derivative with respect to wavelength reduced the effects of scattering on the spectra and also made oxygenated and deoxygenated forms more distinguishable from each other. Selecting spectral bands where oxygenated and deoxygenated forms absorb filtered out noise and spectral features unrelated to Mox. NIR and visible bands were scaled relative to each other in order to correct for errors introduced by normalization. Multivariate Curve Resolution (MCR) was used to estimate Mox from spectra within each data set collected from healthy subjects. A Locally Weighted Regression (LWR) model was built from calibration set spectra and associated Mox values from 20 subjects using 2562 spectra. LWR and Partial Least Squares (PLS) allow accurate measurement of Mox despite variations in skin pigment or fat layer thickness in different subjects. The method estimated Mox in five healthy subjects with an RMSE of 5.4%.     

Hysteresis of two interacting magnetic pairs with inequivalent perpendicular anisotropy

We consider a model for magnetic memory that consists of strongly coupled dipolar or antiferromagnetic (AF) pairs with inequivalent perpendicular anisotropy _K1$K_1$ and _K2$K_2$. For appropriate parameter values, determined in this work, they have two inequivalent storage states with zero net magnetic moment. Both analytical and numerical calculations are performed, in some cases yielding different results because of relaxation effects (i.e., a dependence on the damping parameter α$\alpha$). Hysteresis loops for a wide variety of parameter values are obtained, both for the AF case and the dipole case. An Appendix gives analytic results for slightly non-collinear spins in an applied field, which were used to test the numerical results.     

Synthesis of [18F]F-γ-T-3, a Redox-Silent γ-Tocotrienol (γ-T-3) Vitamin E Analogue for Image-Based In Vivo Studies of Vitamin E Biodistribution and Dynamics

Vitamin E, a natural antioxidant, is of interest to scientists, health care pundits and faddists; its nutritional and biomedical attributes may be validated, anecdotal or fantasy. Vitamin E is a mixture of tocopherols (TPs) and tocotrienols (T-3s), each class having four substitutional isomers (α-, β-, γ-, δ-). Vitamin E analogues attain only low concentrations in most tissues, necessitating exacting invasive techniques for analytical research. Quantitative positron emission tomography (PET) with an F-18-labeled molecular probe would expedite access to Vitamin E’s biodistributions and pharmacokinetics via non-invasive temporal imaging. (R)-6-(3-[¹⁸F]Fluoropropoxy)-2,7,8-trimethyl-2-(4,8,12-trimethyltrideca-3,7,11-trien-1-yl)-chromane ([¹⁸F]F-γ-T-3) was prepared for this purpose. [¹⁸F]F-γ-T-3 was synthesized from γ-T-3 in two steps: (i) 1,3-di-O-tosylpropane was introduced at C6-O to form TsO-γ-T-3, and (ii) reaction of this tosylate with [¹⁸F]fluoride in DMF/K₂₂₂. Non-radioactive F-γ-T-3 was synthesized by reaction of γ-T-3 with 3-fluoropropyl methanesulfonate. [¹⁸F]F-γ-T-3 biodistribution in a murine tumor model was imaged using a small-animal PET scanner. F-γ-T-3 was prepared in 61% chemical yield. [¹⁸F]F-γ-T-3 was synthesized in acceptable radiochemical yield (RCY 12%) with high radiochemical purity (>99% RCP) in 45 min. Preliminary F-18 PET images in mice showed upper abdominal accumulation with evidence of renal clearance, only low concentrations in the thorax (lung/heart) and head, and rapid clearance from blood. [¹⁸F]F-γ-T-3 shows promise as an F-18 PET tracer for detailed in vivo studies of Vitamin E. The labeling procedure provides acceptable RCY, high RCP and pertinence to all eight Vitamin E analogues.