Hydrogenation of lactic acid to propylene glycol over copper-containing catalysts

Catalytic properties of different copper-containing catalysts synthesized from different precursors were studied in the hydrogenation of lactic acid at mild conditions. The most active catalyst was found to be chrysocolla-like copper hydroxysilicate with the copper loading of about 50 at%. At the optimal reaction conditions (T = 473 K, WHSV = 0.08 h⁻¹), 95% conversion of lactic acid over this catalyst and 65% selectivity to 1,2-propylene glycol were achieved. The effect of the weight hourly space velocity (WHSV) on the lactic acid conversion and selectivity to propylene glycol was studied. It is found that the formation of propylene glycol and propanoic acid as a byproduct proceeds via parallel pathways.     

The Pentagram Map: A Discrete Integrable System

The pentagram map is a projectively natural transformation defined on (twisted) polygons. A twisted polygon is a map from \mathbb Z{\mathbb Z} into \mathbbRP²{{\mathbb{RP}}^2} that is periodic modulo a projective transformation called the monodromy. We find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable. For certain families of twisted polygons, such as those we call universally convex, we translate the integrability into a statement about the quasi-periodic motion for the dynamics of the pentagram map. We also explain how the pentagram map, in the continuous limit, corresponds to the classical Boussinesq equation. The Poisson structure we attach to the pentagram map is a discrete version of the first Poisson structure associated with the Boussinesq equation. A research announcement of this work appeared in [16].     

Growth induced anisotropy of cobalt in cobalt/organic semiconductor films

We present the study of Co/organic semiconductor (OS) stacks both from the morphological and magnetic point of view. Co has been successfully used up to now as top contact of hybrid vertical devices. While the properties of Co grown on amorphous layers are well established, its deposition on soft materials presents critical aspects such as interfacial damage that affects its electrical and magnetic properties. In this work we focus on the influence of the morphology of the organic underlayer in the magnetic behavior of a Co thin film: tris(8-hydroxyquinoline) aluminum (Alq₃) grown in different conditions by molecular beam evaporation have been considered. A further considered aspect is the effect of the presence of a thin oxide barrier (Al₂O₃) on the Co magnetic properties.     

Bubble Divergences from Cellular Cohomology

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang–Mills theory, the Ponzano–Regge model of 3d quantum gravity and discrete BF theory, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined in general, because of a phenomenon called ‘bubble divergences’. A common expectation is that the degree of these divergences is given by the number of ‘bubbles’ of the 2-complex. In this note, we show that this expectation, although not realistic in general, is met in some special cases: when the 2-complex is simply connected, or when the structure group is Abelian – in both cases, the divergence degree is given by the second Betti number of the 2-complex.     

Fibroblasts alter spiral wave stability

We consider a three-domain model of cardiac tissue consisting of fibroblasts, myocytes, and extracellular space. We show in the one dimensional case that the fibroblasts with different resting potentials may alter restitution properties of tissue. On this basis we demonstrated that in two dimensional slice of cardiac tissue, a spiral wave break up can be caused purely by the influence of fibroblasts and, vice-versa, initially unstable spiral can be stabilized by fibroblasts depending on the value of their resting potential.     

Extensions de fonctions d'un voisinage de la sphère à la boule

In this note, we are interested in the problem of extending a germ defined along the standard sphere and whose restriction to the sphere is Morse to a function F defined on the ball bounded by the sphere, without critical point. We give an algebraic necessary condition dealing with the Morse complexes of f with $\mathbb{Z}$ coefficients.     

Selections and hyperspaces of finite sets

It is demonstrated that the hyperspace of at most (n+1)-point sets has a Vietoris continuous selection if both the hyperspace of at most n-point sets and that of exactly (n+1)-point sets have Vietoris continuous selections. This result is applied to demonstrate that the hyperspace of at most (2n+2)-point sets has a Vietoris continuous selection provided that one of at most (2n+1)-point sets has such a selection. This settles some open questions.     

Feedback Differential Invariants

The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.     

Maximum thick paths in static and dynamic environments

We consider the problem of finding a large number of disjoint paths for unit disks moving amidst static or dynamic obstacles. The problem is motivated by the capacity estimation problem in air traffic management, in which one must determine how many aircraft can safely move through a domain while avoiding each other and avoiding “no-fly zones” and predicted weather hazards. For the static case we give efficient exact algorithms, based on adapting the “continuous uppermost path” paradigm. As a by-product, we establish a continuous analogue of Menger's Theorem.Next we study the dynamic problem in which the obstacles may move, appear and disappear, and otherwise change with time in a known manner; in addition, the disks are required to enter/exit the domain during prescribed time intervals. Deciding the existence of just one path, even for a 0-radius disk, moving with bounded speed is NP-hard, as shown by Canny and Reif [J. Canny, J.H. Reif, New lower bound techniques for robot motion planning problems, in: Proc. 28th Annu. IEEE Sympos. Found. Comput. Sci., 1987, pp. 49–60]. Moreover, we observe that determining the existence of a given number of paths is hard even if the obstacles are static, and only the entry/exit time intervals are specified for the disks. This motivates studying “dual” approximations, compromising on the radius of the disks and on the maximum speed of motion.Our main result is a pseudopolynomial-time dual-approximation algorithm. If K unit disks, each moving with speed at most 1, can be routed through an environment, our algorithm finds (at least) K paths for disks of radius somewhat smaller than 1 moving with speed somewhat larger than 1.     

Antibacterial Polysiloxane Polymers and Coatings for Cochlear Implants

Within this study, new materials were synthesized and characterized based on polysiloxane modified with different ratios of N-acetyl-l-cysteine (NAC) and crosslinked via UV-assisted thiol-ene addition, in order to obtain efficient membranes able to resist bacterial adherence and biofilm formation. These membranes were subjected to in vitro testing for microbial adherence against S. pneumoniae using standardized tests. WISTAR rats were implanted for 4 weeks with crosslinked siloxane samples without and with NAC. A set of physical characterization methods was employed to assess the chemical structure and morphological aspects of the new synthetized materials before and after contact with the microbiological medium.