Tiling Lattices with Sublattices,I

Call a coset C of a subgroup of Z^d{\bf Z}^{d} a Cartesian coset if C equals the Cartesian product of d arithmetic progressions. Generalizing Mirsky–Newman, we show that a non-trivial disjoint family of Cartesian cosets with union Z^d{\bf Z}^{d} always contains two cosets that differ only by translation. Where Mirsky–Newman’s proof (for d=1) uses complex analysis, we employ Fourier techniques. Relaxing the Cartesian requirement, for d>2 we provide examples where Z^d{\bf Z}^{d} occurs as the disjoint union of four cosets of distinct subgroups (with one not Cartesian). Whether one can do the same for d=2 remains open.     

Transonic Shocks in Multidimensional Divergent Nozzles

We establish existence, uniqueness and stability of transonic shocks for a steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equation. In the process, we obtain unique solvability for a class of transport equations with velocity fields of weak regularity (non-Lipschitz), an infinite dimensional weak implicit mapping theorem which does not require continuous Fréchet differentiability, and regularity theory for a class of elliptic partial differential equations with discontinuous oblique boundary conditions.     

Mesoporous silica as a membrane for ultra-thin implantable direct glucose fuel cells

The design, fabrication and characterization of an inorganic catalyst based direct glucose fuel cell using mesoporous silica coating as a functional membrane is reported. The desired use of mesoporous silica based direct glucose fuel cell is for a blood vessel implantable device. Blood vessel implantable direct glucose fuel cells have access to higher continuous glucose concentrations. However, reduction in the implant thickness is required for application in the venous system as part of a stent. We report development of an implantable device with a platinum thin-film (thickness: 25 nm) deposited on silicon substrate (500 μm) to serve as the anode, and graphene pressed on a stainless steel mesh (175 μm) to serve as the cathode. Control experiments involved the use of a surfactant-coated polypropylene membrane (50 μm) with activated carbon (198 μm) electrodes. We demonstrate that a mesoporous silica thin film (270 nm) is capable of replacing the conventional polymer based membranes with an improvement in the power generated over conventional direct glucose fuel cells.     

Elastomer Nanocomposite; Properties

Polymer nanocomposites represent a class of materials that have assumed great importance in recent years and are the focus of extensive research. Unlike plastomer nanocomposites, the elastomer nanocomposites are in the stage of infancy in respect to their applications.

In general, in polymer composites, the matrix and the filler are bonded to each other by weak intermolecular forces and covalent bonding are rarely involved. If the filler could be dispersed in the polymer matrix at the nanometre level and is able to interact with the matrix by chemical bonding, nanocomposites with significant properties improvement are obtained. These improvements can include mechanical properties (module, strength, etc.), thermal resistance, decrease in gas permeability (barrier), flammability, etc.

This paper is a review of the property improvements of different elastomers using nanofillers like silicates, carbon black, metallic powders, cellulose crystals, mixture of nanofillers, etc, with the intention of obtaining elastomer nanocomposites.     

Human skin as arrays of helical antennas in the millimeter and submillimeter wave range

Recent studies of the minute morphology of the skin by optical coherence tomography showed that the sweat ducts in human skin are helically shaped tubes, filled with a conductive aqueous solution. A computer simulation study of these structures in millimeter and submillimeter wave bands show that the human skin functions as an array of low-Q helical antennas. Experimental evidence is presented that the spectral response in the sub-Terahertz region is governed by the level of activity of the perspiration system. It is also correlated to physiological stress as manifested by the pulse rate and the systolic blood pressure.     

Embodied language,best-fit analysis,and formal compositionality

This review brings together two fundamental, but unreconciled, aspects of human language: embodiment and compositionality.One major scientific advance in recent decades has been Embodiment – the realization that scientific understanding of mind and language entails detailed modeling of the human brain and how it evolved to control a physical body in a social community.The ability to learn and use language is one of the most characteristically human traits. Many animals signal, but only people can express and understand an essentially unbounded range of messages. The technical term for the ability of human language to support all these messages from a few dozen alphabetic symbols is Compositionality.Rigor is essential for the advancement of any science, but there has been essentially no overlap between efforts to formalize language compositionality and the manifest embodiment of thought. Recent developments suggest that it is feasible to formalize the compositionality of embodied language, but that this requires a focus on conceptual composition and better understanding of contextual best-fit.