Stationary twists and energy minimizers on a space of measure preserving maps

Let be a bounded Lipschitz domain, a suitably quasiconvex integrand and consider the energy functional

over the space of measure preserving maps

In this paper we discuss the question of existence of multiple strong local minimizers for over . Moreover, motivated by their significance in topology and the study of mapping class groups, we consider a class of maps, referred to as twists, and examine them in connection with the corresponding Euler–Lagrange equations and investigate various qualitative properties of the resulting solutions, the stationary twists. Particular attention is paid to the special case of the so-called p-Dirichlet energy, i.e., when .     

Diagnostic Checks and Measures of Information in the Bayesian Design of Experiments with Complex Polymerizations

Summary: A case study is presented from the bimolecular nitroxide-mediated radical polymerization of styrene. A Bayesian approach is implemented in order to design two optimal sequences of 2-trials each, and compared with a standard fractional factorial design. The improved effectiveness of the Bayesian design is demonstrated through a discussion of diagnostic criteria (on the quality of prior knowledge and the significance of estimated effects) and enhanced information content measures.     

Anomeric effect for a 2,5,7‐triazabicyclo[2.2.1]heptane derivative

A new member of the polyazapolycyclic family of compounds, namely N³,N⁶,2,5,7‐pentaphenyl‐2,5,7‐triazabicyclo[2.2.1]heptane‐3,6‐diamine xylene solvate, C₃₄H₃₁N₅·C₈H₁₀, was synthesized for the first time and the crystal structure is reported. There are no hydrogen bonds joining the molecules. All four chiral C atoms have the same absolute configurations. With regard to the four N—C—N groups, anomeric effects are observed to cause a reduction of C—N bond length and N‐atom pyramidality.     

Spherical twists, stationary paths and harmonic maps from generalised annuli into spheres

Let X ì \mathbb Rⁿ{{\bf X} \subset {\mathbb R}^n} be a generalised annulus and consider the Dirichlet energy functional

Chaotic oscillations in a coupled system of bistable oscillators

The influence of the asymmetry of the nonlinear element characteristic on the chaotic oscillations of Chua’s bistable oscillator is studied. It is shown that such asymmetry causes asymmetry of a chaotic attractor that maps the switching of motions between two basins of attraction up to the concentration of oscillations in one basin. Oscillation control in a bistable chaotic self-oscillating system (two coupled Chua’s oscillators) is considered. It is demonstrated that oscillations excited in two basins of attraction may pass to one of them and that oscillations may build up in two basins when they are autonomously excited in different basins. It is also found that chaotic oscillations in a coupled system may be excited at parameter values for which the autonomous chaotic oscillations of partial oscillators are absent. The influence of external noiselike oscillations is investigated.     

Enhancing endothelial differentiation of human mesenchymal stem cells by culture on a nanofibrous polycaprolactone/(poly-glycerol sebacate)/gelatin scaffold

Cardiovascular diseases have always been one of the main causes of death worldwide and eventually one of the major medical concerns. Tissue engineering is promising strategies of treating cardiovascular, which can be an effective approach with the design of appropriate scaffold. In this study, to develop engineering basement membrane for endothelial differentiation with good cell attachment, we produced polycaprolactone (PCL)/poly (glycerol sebacate) (PGS)/gelatin nanofibrous scaffold via electrospinning. Attenuated total reflectance-Fourier transform infrared and the proton nuclear magnetic resonance results confirmed the chemical structure of synthesized PGS. Scanning electron microscope images of the electrospun scaffold revealed that the nanofibers are smooth, continues and uniform. Moreover, due to the presence of hydrophilic functional groups in the scaffold, the contact angle is in the appropriate range for cell adhesion especially endothelial cells. The elastic modulus and ultimate tensile stress of electrospun scaffold were calculated 1.32 ± 0.27 MPa and 1.23 ± 0.18 MPa respectively. Quantitative polymerase chain reaction was performed for evaluation of endothelial differentiation of mesenchymal stem cells cultured on standard plate and fibrous scaffold under chemical stimulation with growth factor. Specific endothelial gene expression results postulated that our modified scaffold could support and significantly promote endothelial differentiation of MSCs.