Modelling,simulation, animation,and real-time control (MoSART) for a class of electromechanical systems: a system-theoretic approach

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of ‘cart-pendulum’ electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts through computer-aided analysis, design, graphical visualization, and 3D animation. Referred to as Cart-Pendulum Control3D-Lab1Control3D-Lab-short for control 3D animation laboratory. The author to whom correspondence should be addressed., the environment is based on Microsoft Windows/Visual C++/Direct-3D and MATLAB/Simulink2MATLAB and Simulant are trademarks of The Masterworks, Inc.. Pull-down menus provide access to systems/models/control laws, exogenous signals, parameters, animation models and visual indicators, a suite of (easy-to-modify) Simulant diagrams containing models and control laws, MATLAB m-files for detailed analysis and design, and detailed documentation for each of the above. Three blocks enable animation, joystick inputs, and real-time animation within Simulant. Examples are presented to illustrate the utility of the environment as a valuable tool for analysing/visualizing the above class of electromechanical systems and for enhancing mathematics instruction.     

Sensitive Spectroscopic Detection of Large and Denatured Protein Aggregates in Solution by Use of the Fluorescent Dye Nile Red

The fluorescent dye Nile red was used as a probe for the sensitive detection of large, denatured aggregates of the model protein β-galactosidase (E. coli) in solution. Aggregates were formed by irreversible heat denaturation of β-galactosidase below and above the protein’s unfolding temperature of 57.4°C, and the presence of aggregates in heated solutions was confirmed by static light scattering. Interaction of Nile red with β-galactosidase aggregates led to a shift of the emission maximum (λ _max) from 660 to 611 nm, and to an increase of fluorescence intensity. Time-resolved fluorescence and fluorescence correlation spectroscopy (FCS) measurements showed that Nile red detected large aggregates with hydrodynamic radii around 130 nm. By steady-state fluorescence measurements, it was possible to detect 1 nM of denatured and aggregated β-galactosidase in solution. The comparison with size exclusion chromatography (SEC) showed that native β-galactosidase and small aggregates thereof had no substantial effect on the fluorescence of Nile red. Large aggregates were not detected by SEC, because they were excluded from the column. The results with β-galactosidase demonstrate the potential of Nile red for developing complementary analytical methods that overcome the size limitations of SEC, and can detect the formation of large protein aggregates at early stages.     

Molecular amplification of two different receptors using diastereomeric templates

Two different macrocyclic members of a pseudo-peptide hydrazone dynamic combinatorial library were amplified using the diastereomeric templates quinine and quinidine.     

The ultimate veal calf reference experiment: hormone residue analysis data obtained by gas and liquid chromatography tandem mass spectrometry

A lifetime controlled reference experiment has been performed using 42 veal calves, 21 males and 21 females which were fed and housed according to European regulations and common veterinary practice. During the experiment feed, water, urine and hair were sampled and feed intake and growth were monitored. Thus for the first time residue analysis data were obtained from guaranteed lifetime-untreated animals. The analysis was focused on the natural hormones estradiol and testosterone and their metabolites, on 17beta- and 17alpha-nortestosterone, on 17beta- and 17alpha-boldenone and androsta-1,4-diene-3,17-dione (ADD), and carried out by gas chromatography tandem mass spectrometry (GC/MS/MS), an estrogen bioassay and liquid chromatography (LC) MS/MS. Feed, water and hair samples were negative for the residues tested. Female calf urines showed occasionally low levels of 17alpha-estradiol and 17alpha-testosterone. On one particular sampling day male veal calf urines showed very high levels of 17alpha-testosterone (up to 1000 ng mL(-1)), accompanied by lower levels of estrone and 17beta-testosterone. Despite these extreme levels of natural testosterone, 17beta-boldenone was never detected in the same urine samples; even 17alpha-boldenone and ADD were only occasionally beyond CCalpha (maximum levels 2.7 ng mL(-1)). The data from this unique experiment provide a set of reference values for steroid hormones in calf urine and demonstrate that 17beta-boldenone is not a naturally occurring compound in urine samples.     

The {ell}1-norm of the Fourier transform on compact vector spaces

Suppose that G is a compact Abelian group. If A G, then howsmall can ||_A||_A(G) be? In general, there is no non-triviallower bound. In a recent preprint, Green and Konyagin show thatif has sparse small subgroup structure and A has density with (1 – ) >> 1, then||_A||_A(G) does admit a non-trivial lower bound. In this paperwe address the complementary case of groups with duals havingrich small subgroup structure, specifically the case when Gis a compact vector space over ₂. The results themselves arerather technical to state, but the following consequence capturestheir essence: if is a set of density as close to 1/3 as possible, then we show that . We include a number of examples andconjectures which suggest that what we have shown is very farfrom a complete picture.     

The Saffman-Taylor problem for an extremely shear-thinning fluid

We consider a steady flow driven by pushing a finger of gasinto a highly shear-thinning power-law fluid, with exponentn, in a Hele-Shaw channel. We formulate the problem in termsof the streamfunction , which satisfies the p-Laplacian equation (with ), and investigate travelling wave solutions in the large-n (extreme shear-thinning) limit.We take a Legendre transform of the free-boundary problem for, which reduces it to a linear problem on a fixed domain. The solution to this problem is foundby using matched asymptotic expansions and the resulting shapeof the finger deduced (being, to leading order, a semi-infinitestrip). The nonlinear problem for the streamfunction is alsotreated using matched asymptotic expansion in the physical plane.The finger-width selection problem is briefly discussed in termsof our results.     

Dynamic combinatorial libraries of hydrazone-linked pseudo-peptides: dependence of diversity on building block structure and chirality

Expanding on our earlier building block architecture [(MeO)(2)CH-Linker-Pro-X-NHNH(2) where X = Phe, Cha], we have produced a series of new pseudo-dipeptides [(MeO)(2)CH-Linker-Pro-X-NHNH(2) where X = Val, Leu, Ile, Ala] for use in hydrazone-based dynamic combinatorial libraries (DCLs); reverse order analogues [Phe-Pro and Val-Pro] and two enantio-analogues [Pro-Phe and Pro-Val] were also prepared. The behaviours of these building blocks in DCLs, as single components and in mixtures, were studied systematically using HPLC and mass spectrometry in order to gain insight into the relationship between building block structure and good library diversity. Subtle changes in building block structure lead to significant changes in library distribution and in the ability to produce diverse libraries in mixtures.     

A new transvectant algorithm for nilpotent normal forms

We offer an algorithm to determine the form of the normal form for a vector field with a nilpotent linear part, when the form of the normal form is known for each Jordan block of the linear part taken separately. The algorithm is based on the notion of transvectant, from classical invariant theory.     

Metal-free sequential [3 + 2]-dipolar cycloadditions using cyclooctynes and 1,3-dipoles of different reactivity

Although metal-free cycloadditions of cyclooctynes and azides to give stable 1,2,3-triazoles have found wide utility in chemical biology and material sciences, there is an urgent need for faster and more versatile bioorthogonal reactions. We have found that nitrile oxides and diazocarbonyl derivatives undergo facile 1,3-dipolar cycloadditions with cyclooctynes. Cycloadditions with diazocarbonyl derivatives exhibited similar kinetics as compared to azides, whereas the reaction rates of cycloadditions with nitrile oxides were much faster. Nitrile oxides could conveniently be prepared by direct oxidation of the corresponding oximes with BAIB, and these conditions made it possible to perform oxime formation, oxidation, and cycloaddition as a one-pot procedure. The methodology was employed to functionalize the anomeric center of carbohydrates with various tags. Furthermore, oximes and azides provide an orthogonal pair of functional groups for sequential metal-free click reactions, and this feature makes it possible to multifunctionalize biomolecules and materials by a simple synthetic procedure that does not require toxic metal catalysts.