A unique decomposition result for HT factors with torsion free core

We prove that II₁ factors M have a unique (up to unitary conjugacy) cross-product type decomposition around “core subfactors” N⊂M satisfying the property HT of [S. Popa, On a class of type II₁ factors with Betti numbers invariants, Ann. of Math. (2) 163 (2006) 809-899] and a certain “torsion freeness” condition. In particular, this shows that isomorphism of factors of the form Lαi(Z²)?Fni, i=1,2, for Fni⊂SL(2,Z) free groups of rank ni and αj=e2πitj, tj∉Q, implies n₁=n₂.     

Plasma-mediated grafting of poly(ethylene glycol) on polyamide and polyester surfaces and evaluation of antifouling ability of modified substrates

A simple cold plasma technique was developed to functionalize the surfaces of polyamide (PA) and polyester (PET) for the grafting of polyethylene glycol (PEG) with the aim of reducing biofilm formation. The surfaces of PA and PET were treated with silicon tetrachloride (SiCl4) plasma, and PEG was grafted onto plasma-functionalized substrates (PA-PEG, PET-PEG). Different molecular weights of PEG and grafting times were tested to obtain optimal surface coverage by PEG as monitored by electron spectroscopy for chemical analysis (ESCA). The presence of a predominant C-O peak on the PEG-modified substrates indicated that the grafting was successful. Data from hydroxyl group derivatization and water contact angle measurement also indicated the presence of PEG after grafting. The PEG-grafted PA and PET under optimal conditions had similar chemical composition and hydrophilicity; however, different morphology changes were observed after grafting. Both PA-PEG and PET-PEG surfaces developed under optimal plasma conditions showed about 96% reduction in biofilm formation by Listeria monocytogenes compared with that of the corresponding unmodified substrates. This plasma functionalization method provided an efficient way to graft PEG onto PA and PET surfaces. Because of the high reactivity of Si-Cl species, this method could potentially be applied to other polymeric materials.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Synthesis and structural characterization of amino-functionalized polysaccharides

A variety of carbohydrates, in particular polysaccharides can be subjected to chemical modification to obtain derivatives with amphiphilic properties, which enable biochemical or biological reactions at the polymer surface. In the present work, a polydisperse maltodextrin mixture of average molecular weight 3000 was coupled with 1,6-hexamethylenediamine (HMD) via reductive amination reaction. Resulting products were characterized by thermal analysis and positive nanoelectrospray quadrupole time-of-flight (Q-TOF) mass spectrometry (MS) and tandem mass spectrometry (MS/MS). Both thermal analysis and MS screening confirmed the formation of the HMD-polysaccharide coupling products. Moreover, HMD-linked polysaccharide chains containing 2 to 26 glucose building blocks were identified by nanoESI Q-TOF MS. MS/MS fragmentation using collision-induced dissociation (CID) at low ion acceleration energies provided strong evidence for HMD-maltodextrin linkage formation and the set of sequence ions diagnostic for the composition and structure of a HMD-linked chain containing 18 glucose residues.      

Blood oxygenation monitoring using hyperspectral imaging after flap surgery

In this paper, we present a new method for the assessment of skin flap perfusion based on the non-invasive monitoring of skin blood oxygenation using hyperspectral imaging. This method consists of generation of oxyhemoglobin and deoxyhemoglobin maps in skin flap from hyperspectral image using an analytic model based on Beer–Lambert law. The results obtained on a fasciocutaneous sural flap have revealed that the oxyhemoglobin and deoxyhemoglobin maps facilitate the visualization of some differences between different areas of the flap, an aspect that clinical examination fails to do. In conclusion, the proposed method could provide a new option for a more accurate assessment of flap survival.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.     

Explicit Semi-invariants and Integrals of the Full Symmetric {\mathfrak{sl}_n} Toda Lattice

We show how to construct semi-invariants and integrals of the full symmetric \({\mathfrak{sl}_n}\) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates in the corresponding projective spaces. Then we use these semi-invariants to construct the integrals. The existence of additional integrals which constitute a full set of independent non-involutive integrals was known but the chopping and Kostant procedures have crucial computational complexities already for low-rank Lax matrices and are practically not applicable for higher ranks. Our new approach solves this problem and results in simple explicit formulae for the full set of independent semi-invariants and integrals expressed in terms of the Lax matrix and its eigenvectors, and of eigenvalue matrices for the full symmetric \({\mathfrak{sl}_n}\) Toda lattice.     

Bioaccumulative and conchological assessment of heavy metal transfer in a soil-plant-snail food chain

Background

Alendronate (ALD) is a member of the bisphosphonate family which is used for the treatment of osteoporosis, bone metastasis, Paget's disease, hypocalcaemia associated with malignancy and other conditions that feature bone fragility. ALD is a non-chromophoric compound so its determination by conventional spectrophotometric methods is not possible. So two derivatization reactions were proposed for determination of ALD through the reaction with 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl) and 2,4-dinitrofluorobenzene (DNFB) as chromogenic derivatizing reagents.

Results

Three simple and sensitive spectrophotometric methods are described for the determination of ALD. Method I is based on the reaction of ALD with NBD-Cl. Method II involved heat-catalyzed derivatization of ALD with DNFB, while, Method III is based on micellar-catalyzed reaction of the studied drug with DNFB at room temperature. The reactions products were measured at 472, 378 and 374 nm, for methods I, II and III, respectively. Beer's law was obeyed over the concentration ranges of 1.0-20.0, 4.0-40.0 and 1.5-30.0 ??g/mL with lower limits of detection of 0.09, 1.06 and 0.06 ??g/mL for Methods I, II and III, respectively. The proposed methods were applied for quantitation of the studied drug in its pure form with mean percentage recoveries of 100.47 ± 1.12, 100.17 ± 1.21 and 99.23 ± 1.26 for Methods I, II and III, respectively. Moreover the proposed methods were successfully applied for determination of ALD in different tablets. Proposals of the reactions pathways have been postulated.

Conclusion

The proposed spectrophotometric methods provided sensitive, specific and inexpensive analytical procedures for determination of the non-chromophoric drug alendronate either per se or in its tablet dosage forms without interference from common excipients.

Graphical abstract

     

M2 Proton Channel Structural Validation from Full-Length Protein Samples in Synthetic Bilayers and E. coli Membranes

Validation: Membrane protein structures are sensitive to the environment used for structural characterization. NMR spectra of the full-length M2 proton channel from influenza?A were measured directly in E.?coli membranes and compared to spectra of the protein in synthetic lipid bilayers. The results demonstrate that these bilayers provide a native-like membrane environment.