Amalgamated free products of weakly rigid factors and calculation of their symmetry groups

We consider amalgamated free product II₁ factors M = M _1*B M _2*B … and use “deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von Neumann subalgebra Q ⊂ M can be unitarily conjugated into one of the M _i ’s. We apply this to the case where the M _i ’s are w-rigid II₁ factors, with B equal to either C, to a Cartan subalgebra A in M _i , or to a regular hyperfinite II₁ subfactor R in M _i , to obtain the following type of unique decomposition results, àla Bass–Serre: If M = (N _1 * CN_2*C …) ^t , for some t > 0 and some other similar inclusions of algebras C ⊂ N _i then, after a permutation of indices, (B ⊂ M _i ) is inner conjugate to (C ⊂ N _i ) ^t , for all i. Taking B = C and , with {t _i } _i⩾1 = S a given countable subgroup of R ₊ ^*, we obtain continuously many non-stably isomorphic factors M with fundamental group equal to S. For B = A, we obtain a new class of factors M with unique Cartan subalgebra decomposition, with a large subclass satisfying and Out(M) abelian and calculable. Taking B = R, we get examples of factors with , Out(M) = K, for any given separable compact abelian group K.     

Approximation of Analytic Functions with an Arbitrary Order by Generalized Baskakov–Faber Operators in Compact Sets

By using a sequence \(\lambda _{n}>0\), \(n\in \mathbb {N}\) with the property that \(\lambda _{n}\rightarrow 0\) as fast we want, in this paper we obtain the approximation order \(O(\lambda _{n})\) for a generalized Baskakov–Faber operator attached to analytic functions of exponential growth in a continuum \(G\subset \mathbb {C}\). Several concrete examples of continuums G are given for which this operator can explicitly be constructed.     

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.     

Quantitative ferroelectric characterization of single submicron grains in Bi-layered perovskite thin films

The local polarization state and the electromechanical properties of ferroelectric thin films can be probed via the converse piezoelectric effect using scanning force microscopy (SFM) combined with a lock-in technique. This method, denominated as piezoresponse SFM, was used to characterize at the nanoscale level ferroelectric SrBi₂Ta₂O₉ and Bi₄Ti₃O₁₂ thin films, grown by pulsed laser deposition. Two types of samples were studied: polycrystalline films, with grains having random orientations, and epitaxial films, consisting of (100)_orth- or (110)_orth-oriented crystallites, 100 nm to 2 7m in lateral size, which are embedded into a (001)-oriented matrix. The ferroelectric domain structure was imaged and the piezoelectric response under different external conditions was locally measured for each type of sample. Different investigation procedures are described in order to study the ferroelectric properties via the electromechanical response. A distinct ferroelectric behavior was found for single grains of SrBi₂Ta₂O₉ as small as 200 nm in lateral size, as well as for 1.2 7m쏿 nm crystallites of Bi₄Ti₃O₁₂. By probing separately the crystallites and the matrix the investigations have demonstrated at the nanoscale level that SrBi₂Ta₂O₉ has no spontaneous polarization along its crystallographic c-axis, whereas Bi₄Ti₃O₁₂ exhibits a piezoelectric behavior along both the a- and c-directions. The electrostriction coefficients were estimated to be 3᎒^-2 m⁴/C² for polycrystalline SrBi₂Ta₂O₉ and 7.7᎒^-3 m⁴/C² for c-orientedBi₄Ti₃O₁₂. Quantitative measurements at the nanoscale level, within the experimental errors give the same values for remanent polarization and coercive field as macroscopic ferroelectric measurements performed on the same samples.     

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.