Random self-decomposability and autoregressive processes

We introduce the notion of random self-decomposability and discuss its relation to the concepts of self-decomposability and geometric infinite divisibility. We present its connection with time series autoregressive schemes with a regression coefficient that randomly turns on and off. In particular, we provide a characterization of random self-decomposability as well as that of marginal distributions of stationary time series that follow this scheme. Our results settle an open question related to the existence of such processes.     

Generic properties of measures invariant with respect to the Wa?ewska partial differential equation

It is shown that measure with the concentration dimension equal to zero is typical in family of measures invariant with respect to the Wa?ewska equation.     

Commutators of contactomorphisms

The group of volume preserving diffeomorphisms, the group of symplectomorphisms and the group of contactomorphisms constitute the classical groups of diffeomorphisms. The first homology groups of the compactly supported identity components of the first two groups have been computed by Thurston and Banyaga, respectively. In this paper we solve the long standing problem on the algebraic structure of the third classical diffeomorphism group, i.e. the contactomorphism group. Namely we show that the compactly supported identity component of the group of contactomorphisms is perfect and simple (if the underlying manifold is connected). The result could be applied in various ways.     

Microcellular antibacterial polylactide‐based systems prepared by additive extrusion with ALUM

This work investigates preparation by extrusion of microcellular antimicrobial polylactide (PLA) with an additive, the latter comprising 1% potassium aluminum sulfate dodecahydrate (ALUM), and 3% or 5% of a mixture of sodium hydrogen carbonate and sodium dihydrogen phosphate (1:1). Study was made as to the properties of the materials, their hydrolysis, release profiles, and antimicrobial properties in comparison with the pure polymer. Measuring the molecular weight of samples by gel permeation chromatography revealed that, during thermal processing, the molecular weight of the PLA prepared with additives mentiond above had reduced by approximately 43%. A mechanical test confirmed a decline in mechanical properties after processing as compared with the pure PLA. Release of the antimicrobial compound and the subsequent antimicrobial activity against Staphylococcus aureus and Escherichia coli was evaluated according to ISO 22196:2007. The release of ALUM from the microcellular specimens took place in two steps. During the first 10 days, the rate of release was extremely high in contrast with the remaining period. However, the release rate of the nonporous sample was seen to equal less than 1% in the first 10 days, a phenomenon probably arising through its less active surface.     

An improved phosphoramidite approach for the chemical synthesis of 3′,5′-cyclic diguanylic acid

3′,5′-Cyclic diguanylic acid (c-di-GMP) plays important roles as a signaling and effector molecule in prokaryotes as well as inducing innate and adaptive immune responses in mammalian cells through activation of cell death pathways. An improved phosphoramidite method for the synthesis of c-di-GMP is reported herein. The method is based on the use of an unprecedented 5′-O-formyl ester, which can efficiently and chemoselectively be cleaved from a dinucleotide phosphoramidite intermediate to permit a 1H-tetrazole-mediated cyclocondensation reaction leading to a fully protected c-di-GMP product in a yield of 78%. The native c-di-GMP is isolated in an overall yield of 36% based on the commercial ribonucleoside used as starting material.     

Implementation of genetic algorithm for controlling the electromagnetic motor

The paper deals with the problem of implementing a genetic algorithm (GA) to calculate a pareto-optimal function of voltage in time-domain powering solenoids, used to control a linear electromagnetic motor (e.m.). The method proposed assumes minimising two criteria: the time of motion of the linear electromagnetic motor and the energy input. The results have been obtained for a set position with a narrow range of power supply. The work of electromagnetic motor is based on electromagnetic repulsion. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dry Spinning Based Spinneret Based Tunable Engineered Parameters (STEP) Technique for Controlled and Aligned Deposition of Polymeric Nanofibers

Polymeric nanofibers are finding increasing number of applications and hold the potential to revolutionize diverse fields such as tissue engineering, smart textiles, sensors, and actuators. Aligning and producing high aspect ratio fiber arrays (length/diameter > 2 000) in the sub‐micron and nanoscale diameters has been challenging due to fragility of polymeric materials, thus making it difficult to deposit them as one dimensional structures functionally interfaced with other systems. Here, we present a pseudo dry spinning technique which allows precise control on fiber diameters and further allows deposition of fiber arrays in aligned configurations. Control on fiber diameters ranging from 50–500 nm and having lengths of several millimeters is achieved by altering the polymeric solution concentration. In the dilute and semi‐dilute unentangled concentration domain droplets or beaded fibers are observed to form. Smooth uniform diameter fibers are observed to form at the onset of semi‐dilute entangled concentration regime. For a given molecular weight, the increase in fiber diameter with increasing solution concentration is attributed to both the increase in the entanglement density and the decrease in the radius of gyration of solvated polymer molecules. Using this technique polymeric fiber arrays in single and multiple layers are demonstrated which can be used towards developing strong textiles, biological scaffolds, and sensor networks.

     

Temperature dependence of the EPR lines in weakly doped LiNbO3:Yb—possible evidence of Yb ion pairs formation

The electron paramagnetic resonance (EPR) studies of LiNbO₃ single crystal doped with 1 wt% of Yb³⁺ are reported. To put the EPR results in perspective, a brief discussion of optical absorption spectroscopy investigations of LiNbO₃:Yb³⁺ is provided. The temperature behavior of the EPR lines intensity and linewidth for LiNbO₃:Yb³⁺ reveals antiferromagnetic coupling between Yb³⁺ ions. The deconvolution of the EPR lines indicates that EPR signals arise from both the isolated Yb³⁺ ions as well as the Yb³⁺-Yb³⁺ ion pairs; the latter signals dominate. Based on this indication, EPR spectra are interpreted using a spin Hamiltonian for the Yb³⁺ dissimilar ion pairs. The negative sign of the isotropic parameter J confirms the existence of the antiferromagnetic interactions within Yb³⁺-Yb³⁺ pairs. The value of J obtained based on the proposed pair model, assuming the dipole-dipole interactions, is used to identify the positions of the Yb³⁺-Yb³⁺ pairs in the unit cell. Our results suggest the ^evenYb³⁺-^evenYb³⁺ pairs are located at the neighboring Li⁺ and Nb⁵⁺ positions, whereas the pair axis is not parallel to the optical c-axis. Some alternative explanations of the observed EPR spectra are also considered.     

Non-homogeneous Polygonal Markov Fields in the Plane: Graphical Representations and Geometry of Higher Order Correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (Probab. Theory Relat. Fields 80:543–579, 1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic environment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalized dynamic representation, generalized and defective disagreement loop dynamics as well as a generalized contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime. Research supported by the Polish Minister of Science and Higher Education grant N N201 385234 (2008-2010).