Planar microcoil-based microfluidic NMR probes

Microfabricated small-volume NMR probes consisting of electroplated planar microcoils integrated on a glass substrate with etched microfluidic channels are fabricated and tested. 1H NMR spectra are acquired at 300 MHz with three different probes having observed sample volumes of respectively 30, 120, and 470 nL. The achieved sensitivity enables acquisition of an 1H spectrum of 160 microg sucrose in D2O, corresponding to a proof-of-concept for on-chip NMR spectroscopy. Increase of mass-sensitivity with coil diameter reduction is demonstrated experimentally for planar microcoils. Models that enable quantitative prediction of the signal-to-noise ratio and of the influence of microfluidic channel geometry on spectral resolution are presented and successfully compared to the experimental data. The main factor presently limiting sensitivity for high-resolution applications is identified as being probe-induced static magnetic field distortions. Finally, based on the presented model and measured data, future performance of planar microcoil-based microfluidic NMR probes is extrapolated and discussed.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

Cholinesterase sensors based on screen-printed electrodes for detection of organophosphorus and carbamic pesticides

Cholinesterase sensors based on screen-printed electrodes modified with polyaniline, 7,7,8,8-tetracyanoquinodimethane (TCNQ), and Prussian blue have been developed and tested for detection of anticholinesterase pesticides in aqueous solution and in spiked grape juice. The influence of enzyme source and detection mode on biosensor performance was explored. It was shown that modification of the electrodes results in significant improvement of their analytical characteristics for pesticide determination. Thus, the slopes of the calibration curves obtained with modified electrodes were increased twofold and the detection limits of the pesticides were reduced by factors of 1.6 to 1.8 in comparison with the use of unmodified transducers. The biosensors developed make it possible to detect down to 2×10^–8 mol L^–1 chloropyrifos-methyl, 5×10^–8 mol L^–1 coumaphos, and 8×10^–9 mol L^–1 carbofuran in aqueous solution and grape juice. The optimal conditions for grape juice pretreatment were determined to diminish interference from the sample matrix.Abbreviations ChE Cholinesterase - TCNQ 7,7,8,8-Tetracyanoquinodimethane - ChO Choline oxidase - AChE Acetylcholinesterase - BChE Butyrylcholinesterase - BSA Bovine serum albumin - 2-PAM 2-Pyridine aldoxime methiodide     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of ``generalized Souslin lines", i.e., linearly ordered spaces in which every collection of disjoint open intervals is -discrete, but which do not have a -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.

     

GO-spaces with -closed discrete dense subsets

In this paper we study the question ``When does a perfect generalized ordered space have a -closed-discrete dense subset?' and we characterize such spaces in terms of their subspace structure, -mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a -closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.

     

On Modeling of the Spectral Line Shape of Heavy Neutral Nonhydrogen-Like Emitters

A method of simulating the contour of the asymmetric spectral lines of neutral nonhydrogen-like atoms in a plasma is suggested. The methods of nonlinear regression are used to approximate the experimental data by a model function. The method has been checked on the spectral lines emitted by the electric arc stabilized by the walls. The method makes it possible to evaluate the Stark parameters directly from the experimentally obtained shapes of isolated or overlapping spectral lines.     

High-field high-speed MAS resolution enhancement in 1H NMR spectroscopy of solids

Resolution in ¹H NMR spectra of solids can be significantly enhanced with fast magic-angle spinning and high magnetic fields. A variable field and spinning speed study up to 25 T and 40 kHz shows that the homogeneous line broadening is inversely proportional to the product of magnetic field strength and spinning speed. The combination of high field and fast speed yields a ¹H linewidth approaching the intrinsic limit determined by anisotropy of magnetic susceptibility. An analysis of the anisotropic magnetic susceptibility line broadening is presented.     

On classification of polarized varieties with non-integral nef values

Let be an -dimensional normal projective variety with only Gorenstein, terminal, -factorial singularities. Let be an ample line bundle on . Let denote the nef value of . The classification of via the nef value morphism is given for the situations when satisfies or .

     

Numerical analysis of a quadratic matrix equation

The quadratic matrix equation AX²+ BX + C = 0in n x nmatricesarises in applications and is of intrinsic interest as oneof the simplest nonlinear matrix equations. We give a completecharacterization of solutions in terms of the generalized Schurdecomposition and describe and compare various numerical solutiontechniques. In particular, we give a thorough treatment offunctional iteration methods based on Bernoulli’s method.Other methods considered include Newton’s method with exact line searches, symbolic solution and continued fractions.We show that functional iteration applied to the quadraticmatrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem (²A + B + C)x = 0.