In situ fabrication of three-dimensional chemical patterns in fused silica separation capillaries with polymerized phospholipids

We report a new molecular approach for in situ generation of micron scale, chemically and biochemically functionalized patterns inside three-dimensional, completely enclosed fluidic channels. The formation of chemical patterns is based upon a combination of lipid bilayer self-assembly and UV photopolymerization of photoreactive, cross-linkable phospholipids. Using this approach, we have functionalized capillaries of varying inner diameters with a range of chemistries useful for protein and peptide immobilization. Here, we demonstrate the ability to produce small molecule and protein-based chemical patterns.     

Magnetic resonance imaging: applications of novel methods in studies of porous media.

NMR imaging is finding broad applications in nonbiological areas including the study of fluid flow and fluid ingress in porous media. The porous media include at the one end mineral rocks and various building materials through various solid plastic materials to foodstuffs at the other end of the spectrum. The fluids within these various media range from crude oil and water mixtures, and water itself, to a range of organic solvents in plastic materials. This paper is concerned with the flow and ingress of water through Bentheimer sandstone and Ninian reservoir specimens, and also in solid nylon blocks.     

On the variational characterization and convergence of bivariate splines

It is shown that bivariate interpolatory splines defined on a rectangleR can be characterized as being unique solutions to certain variational problems. This variational property is used to prove the uniform convergence of bivariate polynomial splines interpolating moderately smooth functions at data which includes interpolation to values on a rectangular grid. These results are then extended to bivariate splines defined on anL-shaped region.This research was supported by a University of Kansas General Research Grant.     

A magneto-optically modulated CH3OH laser for Faraday rotation measurements in Tokamaks

Distortion-free intracavity polarization modulation of an optically pumped CH₃OH laser is shown to be viable. The possible use of this modulation technique to make a multichannel Faraday rotation measurement on a Tokamak device is discussed. In addition, the CdTe Faraday modulator employed in this study is shown to have an anomalously large Verdet constant.     

Infrared and Raman imaging of biological and biomimetic samples

Established methods for imaging of biological or biomimetic samples, such as fluorescence and optical microscopy, magnetic resonance imaging (MRI), X-ray tomography or positron emission tomography (PET) are currently complemented by infrared (both near-IR and mid-IR) as well as Raman spectroscopic imaging, whether it be on a microscopic or macroscopic scale. These vibrational spectroscopic techniques provide a wealth of information without a priori knowledge of either the spectral data or the composition of the sample. Infrared radiation does not harm the organism, no electric potential needs to be applied, and the measurements are not influenced by electromagnetic fields. In addition, no extrinsic labeling or staining, which may perturb the system under investigation, has to be added. The immense volume of information contained in spectroscopic images requires multivariate analysis methodologies in order to effectively mine the chemical and spatial information contained within the data as well as to analyze a time-series of images in order to reveal the origin of a chemical or biochemical process. The promise and limitations of this new analytical tool are surveyed in this review.     

On Moving Frames and Noether’s Conservation Laws

Noether’s Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim of this paper is to explain the mathematical structure of both the Euler‐Lagrange system and the set of conservation laws, in terms of the differential invariants of the group action and a moving frame. For the examples, we demonstrate, knowledge of this structure allows the Euler‐Lagrange equations to be integrated with relative ease. Our methods take advantage of recent advances in the theory of moving frames by Fels and Olver, and in the symbolic invariant calculus by Hubert. The results here generalize those appearing in Kogan and Olver [ 1 ] and in Mansfield [ 2 ]. In particular, we show results for high‐dimensional problems and classify those for the three inequivalent SL(2) actions in the plane.     

Efficient knot group identification as a tool for studying entanglements of polymers

A technique is presented for the identification of the knot group of knots, links, and other embedded graphs as a tool in numerical studies of entanglements of polymers. With this technique, the knot group is simultaneously more discriminating and easier to calculate than the knot invariants that have been used in such studies in the past. It can be applied even in cases of very complex knot projections with hundreds of crossings. Starting from an arbitrary projection of an embedded graph, we generate a sequence of representations, any one of which is a full and complete representation of the knot group. Any two knot groups are isomorphic if they have identical representations. Therefore, we compare the sequence of representations of any given knot or link against a previously determined lookup table, and if the group of the knot or link is represented in this table we eventually find a match and identify the knot group.     

Lithium and aluminium complexes supported by chelating phosphaguanidinates

Diisopropylcarbodiimide, (i)PrN[double bond, length as m-dash]C[double bond, length as m-dash]N(i)Pr, inserts into the lithium-phosphorus bond of in situ prepared "Ph(2)PLi(THF)(n)" to afford the lithium salt, [Li(Ph(2)PC{N(i)Pr}(2))(THF)(n)](x)(2a); alternatively, this compound can be made by deprotonation of the neutral phosphaguanidine, Ph(2)PC{N(i)Pr}{NH(i)Pr}(1a) with (n)BuLi. Displacement of the THF solvate in 2a is readily achieved with TMEDA to afford Li(Ph(2)PC{N(i)Pr}(2))(TMEDA)(3a). X-Ray crystallographic analyses show that 2a exists as a dimer in the solid state with a folded ladder structure and an N,N' chelating phosphaguanidinate, while 3a is monomeric with N,P-coordination of the ligand to lithium. Compound 2a reacts via a transmetallation pathway with AlMe(2)Cl to afford the dimethylaluminium complex, Al(Ph(2)PC{N(i)Pr}(2))Me(2)(4a), which can also be prepared by protonation of a methyl group of AlMe(3) using 1a. The formation of a series of dialkylaluminium compounds has been investigated employing this latter pathway using both 1a and the N,N'-dicyclohexyl analogue, Ph(2)PC{NCy}{NHCy}(1b), affording Al(Ph(2)PC{NR}(2))Et(2)(5a,b), Al(Ph(2)PC{NR}(2))(i)Bu(2)(6a,b) and the diphenylaluminium compound Al(Ph(2)PC{N(i)Pr}(2))Ph(2)(7a). The oily nature of most of the dialkyl compounds and high sensitivity to oxygen and moisture lead to difficulty in manipulation and characterization; however, NMR spectroscopy indicated highly pure products (>95%) upon removal of the solvent. The molecular structures of the crystalline examples 4a and 7a are reported, showing monomeric aluminium species with symmetrically chelating phosphaguanidinate ligands. The series of aluminium compounds AlLCl(2){L=[EC{NiPr}(2)](-): A, E=Me; B, E=Me(2)N; C, E=(Me(3)Si)(2)N and D, E=Ph(2)P} were investigated using density functional theory. In the more simple cases A and B, the delocalized electron density of the metallacycle was represented by a combination of the HOMO and an orbital of lower energy (A, HOMO-5; B, HOMO-6). The HOMO-1 in B was pi-bonded across the Me(2)N-C bond suggesting delocalization of electron density into the metallacycle. In the more complex systems C and D, delocalization within the metallacycle was less extensive due to the (Me(3)Si)(2)N- and Ph(2)P-moieties. A number of occupied orbitals in D, however, display phosphorus 'lone-pair' characteristics, indicating that these species have the potential to behave as Lewis bases in the formation of poly(metallic) systems.