Optimal adaptive solution of initial-value problems with unknown singularities

The optimal solution of initial-value problems in ODEs is well studied for smooth right-hand side functions. Much less is known about the optimality of algorithms for singular problems. In this paper, we study the (worst case) solution of scalar problems with a right-hand side function having r   continuous bounded derivatives in R$\mathbf{R}$, except for an unknown singular point. We establish the minimal worst case error for such problems (which depends on r similarly as in the smooth case), and define optimal adaptive algorithms. The crucial point is locating an unknown singularity of the solution by properly adapting the grid. We also study lower bounds on the error of an algorithm for classes of singular problems. In the case of a single singularity with nonadaptive information, or in the case of two or more singularities, the error of any algorithm is shown to be independent of r.     

Adaptive mesh point selection for the efficient solution of scalar IVPs

We discuss adaptive mesh point selection for the solution of scalar initial value problems. We consider a method that is optimal in the sense of the speed of convergence, and we aim at minimizing the local errors. Although the speed of convergence cannot be improved by using the adaptive mesh points compared to the equidistant points, we show that the factor in the error expression can be significantly reduced. We obtain formulas specifying the gain achieved in terms of the number of discretization subintervals, as well as in terms of the prescribed level of the local error. Both nonconstructive and constructive versions of the adaptive mesh selection are shown, and a numerical example is given.     

The 1H NMR spectra of methylmethoxyaluminium chloride and methylmethoxyaluminium iodide

It has been shown by means of ¹H NMR, IR and cryometrical measurements that, with oxygen bridges, Me(OMe)AlCl and Me(OMe)AII are trimers in solutions.Two isomers, cis and trans, are present, which are responsible for the multiple ¹H NMR spectra. The proton signals of MeAl and OMe groups are assigned in each isomer.     

Convergent synthesis of leukotriene a methyl ester

A convergent total synthesis of methyl 5,6-oxido-7,9,11,14-eicosapentaenoate from oct-2-yn-l-ol and metyl 4-formylbutyrate is described.     

The phospholipid membrane compositions of bacterial cells,cancer cell lines and biological samples from cancer patients

While cancer now impacts the health and well-being of more of the human population than ever before, the exponential rise in antimicrobial resistant (AMR) bacterial infections means AMR is predicted to become one of the greatest future threats to human health. It is therefore vital that novel therapeutic strategies are developed that can be used in the treatment of both cancer and AMR infections. Whether the target of a therapeutic agent be inside the cell or in the cell membrane, it must either interact with or cross this phospholipid barrier to elicit the desired cellular effect. Here we summarise findings from published research into the phospholipid membrane composition of bacterial and cancer cell lines and biological samples from cancer patients. These data not only highlight key differences in the membrane composition of these biological samples, but also the methods used to elucidate and report the results of this analogous research between the microbial and cancer fields.

This review acts as a repository and comparison of cell membrane phospholipid composition data collected from microbial and cancer fields.     

Establishing the selective phospholipid membrane coordination,permeation and lysis properties for a series of ‘druggable’ supramolecular self-associating antimicrobial amphiphiles

The rise of antimicrobial resistance remains one of the greatest global health threats facing humanity. Furthermore, the development of novel antibiotics has all but ground to a halt due to a collision of intersectional pressures. Herein we determine the antimicrobial efficacy for 14 structurally related supramolecular self-associating amphiphiles against clinically relevant Gram-positive methicillin resistant Staphylococcus aureus and Gram-negative Escherichia coli. We establish the ability of these agents to selectively target phospholipid membranes of differing compositions, through a combination of computational host:guest complex formation simulations, synthetic vesicle lysis, adhesion and membrane fluidity experiments, alongside our novel ¹H NMR CPMG nanodisc coordination assays, to verify a potential mode of action for this class of compounds and enable the production of evermore effective next-generation antimicrobial agents. Finally, we select a 7-compound subset, showing two lead compounds to exhibit ‘druggable’ profiles through completion of a variety of in vivo and in vitro DMPK studies.

A combination of computational and synthetic phospholipid vesicle/nanodisc assays are used to investigate the mode of action for a class of antimicrobial agents, while a range of DMPK studies establish agent druggability.     

The influence of plastic deformation on the magnetoelastic properties of the CSN12021 grade steel

Magnetoelastic properties of materials are strongly influenced by changes of the dislocation structure that take place during the process of plastic deformation. Such changes can be used as a basis for a method of nondestructive evaluation (NDE) of the deformation level. So far, various methods, based on magnetic hysteresis loop properties as well as on the Barkhausen effect (BE), have been proposed. In the paper, the results obtained with the help of the abovementioned methods are compared with the results of the magnetoacoustic emission (MAE) signal measurements. The MAE signal is relatively easy to implement as a nondestructive method and unlike the BE effect signal gives information about the whole magnetized volume.     

Existence of a homoclinic point for the Hénon map

We prove analytically that for the Hénon map of the plane into itself (s, t)(t+1–1.4a ², 0.3s), there exists a transversal homoclinic point.     

New π-electron donor (1,4-thioxane-2,3-diyldithio)ethylenedithiotetrathiafulvalene (ETOEDT-EDT-TTF) and its derivatives. Synthesis and characterization

We report more efficient way for the synthesis of 4,5-(1,4-oxathiane-2,3-diyldithio)-1,3-dithiole-2-thione and three new TTF-derived nonsymmetrical electron donors: the (1,4-thioxane-2,3-diyldithio)ethylenedithiotetrathiafulvalene (ETOEDT-EDT-TTF), (1,4-thioxane-2,3-diyldithio)propylenedithiotetrathiafulvalene (ETOEDT-PDT-TTF), and (1,4-thioxane-2,3-diyldithio)dimethylenedithiotetrathiafulvalene (ETOEDT-DMDT-TTF). For the first time we also present extended studies of the molecular structure, vibrational and electronic excitations of the donors. Based on theoretical and experimental Raman and infrared spectra as well as analysis of electron excitations of three new TTF-derived donors their spectral properties were described and discussed.