Perturbation of semi-Browder operators and stability of Browder's essential defect and approximate point spectrum

In the present paper we investigate the stability of closed densely defined semi-Browder operators under operator perturbations that belong to a perturbation class related to compact operators. Furthermore, we apply the obtained results to give a characterization and to study the stability of Browder's essential approximate point spectrum and Browder's essential defect spectrum.     

Single point measurements of magnetic field gradient waveform

Pulsed magnetic field gradients are fundamental to spatial encoding and diffusion weighting in magnetic resonance. The ideal pulsed magnetic field gradient should have negligible rise and fall times, however, there are physical limits to how fast the magnetic field gradient may change with time. Finite gradient switching times, and transient, secondary, induced magnetic field gradients (eddy currents) alter the ideal gradient waveform and may introduce a variety of undesirable image artifacts. We have developed a new method to measure the complete magnetic field gradient waveform. The measurement employs a heavily doped test sample with short MR relaxation times (T(1), T(2), and T(2)(*)<100 micros) and a series of closely spaced broadband radiofrequency excitations, combined with single point data acquisition. This technique, a measure of evolving signal phase, directly determines the magnetic field gradient waveform experienced by the test sample. The measurement is sensitive to low level transient magnetic fields produced by eddy currents and other short and long time constant non-ideal gradient waveform behaviors. Data analysis is particularly facile permitting a very ready experimental check of gradient performance.     

An embedding method for simulation of immobilized enzyme kinetics and transport in sessile hydrogel drops

A newly-developed embedding method for simulating enzyme kinetics and transport occurring within axisymmetric 3D domains is presented. The physical problem is pertinent to gel-pad microarrays for assessment of enzymatic activity. An enzyme is immobilized uniformly within a hydrogel which is spotted onto a solid surface in the form of a sessile drop, taking on a spherical cap shape. An aqueous solution containing substrate flows slowly past the porous drop. The substrate diffuses into the drop and is converted to product with the help of the enzyme. The product accumulates in and diffuses out of the drop and is taken away by the flow. Spatiotemporal distribution of the product, monitored via fluorescence, can be used to quantify the enzyme kinetics. This process is described by a system of nonlinear reaction-diffusion partial differential equations, modeling the diffusive transport and enzymatic reaction. The computational domain contains both the hydrogel drop and the bulk fluid phases. The embedding method is a computational technique that enables the use of finite differences on a regular Cartesian grid for simulation of multiphase problems with complex interfaces/boundaries. It uses a volume-fraction-based approach, similar to the volume-of-fluid (VOF) method, to implement the boundary conditions that must be applied at the interface between the phases. The main advantage of the embedding method is its simplicity, which results in code generation that can be highly optimized. In the present work, we apply the embedding method to the aforementioned two-phase reaction-diffusion problem and validate the results by comparing to a number of exact solutions available in simpler geometries and to results obtained using a finite-volume method on an unstructured body-fitted mesh. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness

Due to excessive service load, inappropriate operating conditions or simply end of life fatigue, damage can occur in gears. When a fault, either distributed or localised, is incurred by gears, the stiffness and consequently vibration characteristics of the damaged tooth will change. In this work an analytical formulation of the time varying gearmesh stiffness was derived. An original analytical modelling of tooth cracks is presented and the gearmesh stiffness reduction due to this fault is quantified. A comparison with finite element model is presented in order to validate the analytical formulation.     

Tonal prediction of a faulty axial fan

The current techniques for monitoring and diagnostics of rotating machines to their conditional predictive maintenance mainly are based on vibration monitoring. In this research, experimental and theoretical methods to predict the tonal noise of a faulty fan are developed and validated. These methods can be used on identifying defects of an axial fan based on an acoustic monitoring in situations where it is necessary to operate remotely due to the inaccessibility of the areas of event defects.     

Zoonotic MERS-CoV transmission: modeling,backward bifurcation and optimal control analysis

Nonlinear Dynamics - Middle East Respiratory Syndrome Coronavirus (MERS-CoV) can cause mild to severe acute respiratory illness with a high mortality rate. As of January 2020, more than 2500 cases...     

Synthesis and Antimicrobial Properties of Fluorinated 1,2-Aminopropanethiols

Reactions of 1,2-aminopropanethiols with methyl trifluoropyruvate were studied, and the antibacterial and fungicidal activity of the resulting trifluoromethyl derivatives as additives to lubricants was examined.     

Study of the supramolecular cooperativity in the multirecognition mechanism of cyclodextrins/cucurbituril/disubstituted diimidazolium bromides

N, N'-Disubstituted methylenediimidazolium bromide salts substituted with two aromatic groups present two different binding sites. In the binary complexes with cyclodextrins (CDs) or cucurbit[7]uril (CB[7]), the macrocycle is always positioned on the external aromatic residues. In the ternary complexes, CB[7] is positioned around the diimidazolium cation, where the external aromatic residue is included in the CD's cavity. The unfavored position of the CB[7] on the cationic site in the ternary complex is the result of its cooperative supramolecular interaction with the cyclodextrin. The obtained ternary complexes possess different interfacial properties, compared to those of the binary complexes. We demonstrate these hypotheses by NMR spectroscopy, ESI-HRMS spectrometry, molecular modeling simulation, and surface tension measurements.