On Besov spaces modelled on Zygmund spaces

Working on the d-torus, we show that Besov spaces Bps(Lp(logL)a) modelled on Zygmund spaces can be described in terms of classical Besov spaces. Several other properties of spaces Bps(Lp(logL)a) are also established. In particular, in the critical case s=d/p, we characterize the embedding of Bpd/p(Lp(logL)a) into the space of continuous functions.

Toward a skin-material interface with vacuum-integrated capped macroporous scaffolds

Avulsion, epidermal marsupialization, and infection cause failure at the skin-material interface. A robust interface would permit implantable robotics, prosthetics, and other medical devices; reconstruction of surgical defects, and long-term access to blood vessels and body cavities. Torus-shaped cap-scaffold structures were designed to work in conjunction with negative pressure to address the three causes of failure. Six wounds were made on the backs of each of four 3-month old pigs. Four unmodified (no caps) scaffolds were implanted along with 20 cap-scaffolds. Collagen type 4 was attached to 21 implants. Negative pressure then was applied. Structures were explanted and assessed histologically at day 7 and day 28. At day 28, there was close tissue apposition to scaffolds, without detectable reactions from defensive or interfering cells. Three cap-scaffolds explanted at day 28 showed likely attachment of epidermis to the cap or cap-scaffold junction, without deeper marsupialization. The combination of toric-shaped cap-scaffolds with negative pressure appears to be an intrinsically biocompatible system, enabling a robust skin-material interface. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2016.

On continuous families of geometric Seifert conemanifold structures

In this paper, dedicated to Prof. Lou Kauffman, we determine the Thurston’s geometry possesed by any Seifert fibered conemanifold structure in a Seifert manifold with orbit space (Formula presented.) and no more than three exceptional fibers, whose singular set, composed by fibers, has at most three components which can include exceptional or general fibers (the total number of exceptional and singular fibers is less than or equal to three). We also give the method to obtain the holonomy of that structure. We apply these results to three families of Seifert manifolds, namely, spherical, Nil manifolds and manifolds obtained by Dehn surgery on a torus knot (Formula presented.). As a consequence we generalize to all torus knots the results obtained in [Geometric conemanifolds structures on (Formula presented.), the result of (Formula presented.) surgery in the left-handed trefoil knot (Formula presented.), J. Knot Theory Ramifications 24(12) (2015), Article ID: 1550057, 38pp., doi: 10.1142/S0218216515500571] for the case of the left handle trefoil knot. We associate a plot to each torus knot for the different geometries, in the spirit of Thurston.