Some aspects of shift-like automorphisms of $$\pmb {\mathbb {C}}^{\varvec{k}}$$

The goal of this article is two fold. First, using transcendental shift-like automorphisms of \(\mathbb C^k, ~k \ge 3\) we construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of \(\mathbb C^k, ~k \ge 3\) whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon–Esterle in \(\mathbb C^2.\) The second example shows the existence of a Fatou–Bieberbach domain in \(\mathbb C^k,~k \ge 3\) that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay–Rudin. In the second part we compute the order and type of entire mappings that parametrize one dimensional unstable manifolds for shift-like polynomial automorphisms and show how they can be used to prove a Yoccoz type inequality for this class of automorphisms.     

Synthesis and trans-cis isomerization of azobenzene dendrimers incorporating 1,2-isopropylidenefuranose rings

Azobenzene dendrimer 2 was synthesized from a known dendritic azo-tetracarboxylic acid and a dendritic amine incorporating 1,2-isopropylidenefuranose rings, and its trans-cis isomerization was studied by UV-vis absorption spectroscopy.     

Alternate Proof of Shô Iseki's Functional Equation

Iseki's functional equation, a valuable tool in the transformation theory of the Dedekind modular function, has heretofore been derived using complex integration and the residue calculus. This paper gives a different and shorter proof using Fourier series.     

MATHEMATICAL MODEL FOR THE DEFORMATION IN A MODIFIED GREEN–LINDSAY THERMOELASTIC MEDIUM WITH NONLOCAL AND TWO-TEMPERATURE EFFECTS

Journal of Applied Mechanics and Technical Physics - The present study elaborates the response of a heat source along with thermomechanical loading in a modified Green–Lindsay generalized...     

Electrophoretically Deposited Bismuth Iron Oxide Nanoparticles Film for Supercapacitor Application

Russian Journal of Electrochemistry - Bismuth iron oxide (BFO) nanoparticles film prepared by electrophoretic deposition (EPD) process has been explored for supercapacitor application. EPD process...     

Matching Static and Dynamic Compliance of Small‐Diameter Arteries,with Poly(lactide‐co‐caprolactone) Copolymers: In Vitro and In Vivo Studies

Mechanical mismatch between vascular grafts and blood vessels is a major cause of smaller diameter vascular graft failure. To minimize this mismatch, several poly‐l ‐lactide‐co‐ε‐caprolactone (PLC) copolymers are evaluated as candidate materials to fabricate a small diameter graft. Using these materials, tubular prostheses of 4 mm inner diameter are fabricated by dip‐coating. In vitro static and dynamic compliance tests are conducted, using custom‐built apparatus featuring a closed flow system with water at 37 °C. Grafts of PLC monomer ratio of 50:50 are the most compliant (1.56% ± 0.31?mm Hg^?2), close to that of porcine aortic branch arteries (1.56% ± 0.43?mm Hg^?2), but underwent high continuous dilatation (87 µm min^?1). Better matching is achieved by optimizing the thickness of a tubular conduit made from 70:30 PLC grafts. In vivo implantation and function of a PLC 70:30 conduit of 150 µm wall‐thickness (WT) are tested as a rabbit aorta bypass. An implanted 150 µm WT PLC 70:30 prosthesis is observed over 3 h. The recorded angiogram shows continuous blood flow, no aneurysmal dilatation, leaks, or acute thrombosis during the in vivo test, indicating the potential for clinical applications.     

Tuning stability of mesoporous silica films under biologically relevant conditions through processing with supercritical CO2

Mesoporous materials have been proposed for use in numerous biological environments such as substrates for cell culture and controlled release for drug delivery. Although mesoporous silica synthesis is facile, recent reports (Dunphy et al. Langmuir 2003, 19, 10403; Bass et al. Chem. Mater. 2007, 19, 4349) have demonstrated instability (dissolution) of pure mesoporous silica films under biologically relevant conditions. In this work, we demonstrate a simple processing handle (pressure) to control the dissolution of mesoporous silica films that are synthesized using preformed template films and supercritical CO 2. Spectroscopic ellipsometry is utilized to quantify changes in both the film thickness and porosity; these properties provide insight into the dissolution mechanism. The pore size increases as the films are exposed to phosphate-buffered saline (PBS) through preferential dissolution at the pore wall in comparison to the film surface; a mechanism reminiscent of bulk erosion of scaffolds for drug delivery. Thin mesoporous silica film lifetimes can be extended from several hours using traditional sol-gel approaches to days by using CO 2 processing for identical film thickness. Osteoblast attachment and viability on these films was found to correlate with their increased stability. This enhanced stability opens new possibilities for the utilization of mesoporous silica for biological applications, including drug delivery and tissue engineering.     

Augmentation of the step‐by‐step Energy‐Scanning EXAFS beamline BL‐09 to continuous‐scan EXAFS mode at INDUS‐2 SRS

An innovative scheme to carry out continuous‐scan X‐ray absorption spectroscopy (XAS) measurements similar to quick‐EXAFS mode at the Energy‐Scanning EXAFS beamline BL‐09 at INDUS‐2 synchrotron source (Indore, India), which is generally operated in step‐by‐step scanning mode, is presented. The continuous XAS mode has been implemented by adopting a continuous‐scan scheme of the double‐crystal monochromator and on‐the‐fly measurement of incident and transmitted intensities. This enabled a high signal‐to‐noise ratio to be maintained and the acquisition time was reduced to a few seconds from tens of minutes or hours. The quality of the spectra (signal‐to‐noise level, resolution and energy calibration) was checked by measuring and analysing XAS spectra of standard metal foils. To demonstrate the energy range covered in a single scan, a continuous‐mode XAS spectrum of copper nickel alloy covering both Cu and Ni K‐edges was recorded. The implementation of continuous‐scan XAS mode at BL‐09 would expand the use of this beamline in in situ time‐resolved XAS studies of various important systems of current technological importance. The feasibility of employing this mode of measurement for time‐resolved probing of reaction kinetics has been demonstrated by in situ XAS measurement on the growth of Ag nanoparticles from a solution phase.     

On the exact solutions of nonlinear diffusion-reaction equations with quadratic and cubic nonlinearities

Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.