Enzymatic and chemical hydrolysis of poly(ethylene terephthalate) fabrics

Alkaline and enzymatic hydrolyzes of poly(ethylene terephthalate) fabrics (PET) were mechanistically compared based on released degradation products (HPLC‐UV‐RI) and changes in surface properties [hydrophilicity, cationic dyeing, X‐ray photoelectron spectroscopy (XPS)]. Enzymatic hydrolysis led to an increase in the amount of hydroxyl and carboxyl groups on the surface resulting in an enhanced water absorption and dyeability. Enzymes partially adsorbed to PET fabrics during hydrolysis were completely removed by subsequent extraction according to XPS analysis. In contrast to the enzyme treatment, alkaline hydrolysis did not lead to an increase of hydroxyl and acid groups according to XPS while both treatments caused a substantial increase in hydrophilicity and were more effective on amorphous fibers. Alkaline hydrolysis led to a greater increase in the K/S value after cationic dyeing due to enlarged surface area. Consequently, ESEM‐images demonstrated that alkaline treatment drastically affected the surface morphology of the polymer resulting in crater‐like structures of the fibers, whereas after enzymatic treatment the morphology of the fibers remained unchanged. To reach similar benefits in hydrophilicity, drastically higher amounts of degradation products were released during alkaline hydrolysis as also indicated by >6% weight loss compared to <1% after enzyme treatment. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6435–6443, 2008     

Ternary Mn/Ge/Se anions from reactions of [Ba2(H2O)9][GeSe4]: synthesis and characterization of compounds containing discrete or polymeric [Mn6Ge4Se17]6- units

[Ba2(H2O)9][GeSe4] is suitable for the formation of novel M/14/16 anions [Mn6Ge4Se17]6- --discrete or linked in an as yet unprecedented porous network--with antiferromagnetically coupled Mn(II) centers and relatively small electronic excitation energies.     

Can We Compute the Similarity between Surfaces?

A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fréchet distance. Whereas efficient algorithms are known for computing the Fréchet distance of polygonal curves, the same problem for triangulated surfaces is NP-hard. Furthermore, it remained open whether it is computable at all. Using a discrete approximation, we show that it is upper semi-computable, i.e., there is a non-halting Turing machine which produces a decreasing sequence of rationals converging to the Fréchet distance. It follows that the decision problem, whether the Fréchet distance of two given surfaces lies below a specified value, is recursively enumerable.     

Metric intersection problems in Cayley graphs and the Stirling recursion

In Sym(n) with n ≥ 5 let H be a conjugacy class of elements of order 2 and let Γ be the Cayley graph whose vertex set is the group G generated by H (so G = Sym(n) or Alt(n)) and whose edge set is determined by H. We are interested in the metric structure of this graph. In particular, for ${g \in G}$ let B _r (g) be the metric ball in Γ of radius r and centre g. We show that the intersection numbers ${\Phi(\Gamma; r, g) := |\,B_{r}(e)\,\cap\,B_{r}(g)\,|}$ are generalized Stirling functions in n and r. The results are motivated by the study of error graphs in Levenshtein (Dokl Akad Nauk 354:593–596, 1997; IEEE Trans Inform Theory 47(1):2–22, 2001; (J Comb Theory Ser A 93(2):310–332, 2001) and related reconstruction problems.     

Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature

The polar Kerr effect in the high-T_(c) superconductor YBa2Cu3O6+x was measured at zero magnetic field with high precision using a cyogenic Sagnac fiber interferometer. We observed nonzero Kerr rotations of order approximately 1 microrad appearing near the pseudogap temperature T(*) and marking what appears to be a true phase transition. Anomalous magnetic behavior in magnetic-field training of the effect suggests that time reversal symmetry is already broken above room temperature.     

Polychromatic Colorings of Plane Graphs

We show that the vertices of any plane graph in which every face is incident to at least g vertices can be colored by ⌊(3g−5)/4⌋ colors so that every color appears in every face. This is nearly tight, as there are plane graphs where all faces are incident to at least g vertices and that admit no vertex coloring of this type with more than ⌊(3g+1)/4⌋ colors. We further show that the problem of determining whether a plane graph admits a vertex coloring by k colors in which all colors appear in every face is in ℘ for k=2 and is -complete for k=3,4. We refine this result for polychromatic 3-colorings restricted to 2-connected graphs which have face sizes from a prescribed (possibly infinite) set of integers. Thereby we find an almost complete characterization of these sets of integers (face sizes) for which the corresponding decision problem is in ℘, and for the others it is -complete. Research of N. Alon was supported in part by the Israel Science Foundation, by a USA–Israeli BSF grant, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. Research of R. Berke was supported in part by JSPS Global COE program “Computationism as a Foundation for the Sciences.” Research of K. Buchin and M. Buchin was supported by the Netherlands’ Organisation for Scientific Research (NWO) under BRICKS/FOCUS project no. 642.065.503. Research of P. Csorba was supported by DIAMANT, an NWO mathematics cluster. Research of B. Speckmann was supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 639.022.707.     

Electromechanical modelling of skeletal muscle contractions

In the present paper, the aim was to develop a numerical method for optimisation an existing mechanical material model [1] including muscle activation concerning the excitation of skeletal muscles. The modelling idea was a weak and non-monolithic coupling of an electric current expressed by Ohm's law with a hyperelastic muscle model with transversal isotropic characteristics, see [2]. We confirmed the ability of the proposed model by applying on real reconstructed complex muscle geometry. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)