Homotopy Structures for Algebras over a Monad

Let T be a monad over a category A. Then a homotopy structure for A, defined by a cocylinder P : A content/n22515404j423847/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> A, or path-endofunctor, can be lifted to the category A ^T of Eilenberg–Moore algebras over T, provided that P is consistent with T in a natural sense, i.e. equipped with a natural transformation content/n22515404j423847/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0"> : T P content/n22515404j423847/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> P T satisfying some obvious axioms. In this way, homotopy can be lifted from well-known, basic situations to various categories of content/n22515404j423847/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">algebrascontent/n22515404j423847/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> for instance, from topological spaces to topological semigroups, or spaces over a fixed space (fibrewise homotopy), or actions of a fixed topological group (equivariant homotopy); from categories to strict monoidal categories; from chain complexes to associative chain algebras. The interest is given by the possibility of lifting the content/n22515404j423847/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">homotopy operationscontent/n22515404j423847/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> (as faces, degeneracy, connections, reversion, interchange, vertical composition, etc.) and their axioms from A to A ^T , just by verifying the consistency between these operations and content/n22515404j423847/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0"> : T P content/n22515404j423847/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> P T. When this holds, the structure we obtain on our category of algebras is sufficiently powerful to ensure the main general properties of homotopy.     

The first cohomology group of trivial extensions of special biserial algebras

Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A×DA in terms of the combinatorics of the quiver and relations is determined.     

Synthesis and characterization of tercopolymers derived from ε‐caprolactone,trimethylene carbonate,and lactide

A series of tri‐components copolymers with different molar ratios were synthesized via bulk ring‐opening copolymerization of trimethylene carbonate (TMC), L ‐lactide (LLA), and ε‐caprolactone (ε‐CL), using stannous octoate as catalyst. The sequence structure of the tercopolymer chain was characterized by ¹H and ¹³C nuclear magnetic resonance (NMR), Fourier transform infrared (FTIR), and gel permeation chromatography (GPC). The results showed that although block sequence of the corresponding monomers still existed in the tercopolymer chain, the random tercopolymers were ultimately obtained due to the transesterification during polymerization. For the samples TP1 and TP2, longer sequence of LLA existed in the molecular chains. The thermal properties of tercopolymers were investigated by differential scanning calorimetry (DSC) and the mechanical properties of the resulting copolymers were studied by using a tensile tester. The results indicated that the properties of these copolymers could be adjusted by changing the compositions of the copolymers. The resulting tercopolymers are expected to have potential uses as nerve regeneration and other biomedicine materials. Copyright © 2007 John Wiley & Sons, Ltd.     

Binary Interaction Parameters,Ternary Systems: Realistic Modeling of Liquid/Liquid Phase Separation

The phase behavior of ternary systems (either a polymer solution in a mixed solvent or a polymer blend in a single solvent) was modeled theoretically. The modeling considers two specific features of polymers explicitly: chain connectivity and the ability to respond to changes in the molecular environment by conformational reorientation. Previously, this approach has been applied to polymer solutions in single solvents. Here it is generalized and the number of parameters is reduced to two per binary system. The calculation of the Gibbs energies of the ternary mixtures accounts for the composition dependencies of the binary interaction parameters. The following phenomena are reproduced realistically for polymer solutions in a mixed solvent and for solutions of two polymers in a common solvent: simplicity, co‐solvency, and co‐non‐solvency. The results nourish the hope that the new approach is capable of modeling phase diagrams for ternary systems by means of binary interaction parameters only.

     

Patterned co-culture of primary hepatocytes and fibroblasts using polyelectrolyte multilayer templates

This paper describes the formation of patterned cell co-cultures using the layer-by-layer deposition of synthetic ionic polymers and without the aid of adhesive proteins/ligands such as collagen or fibronectin. In this study, we used synthetic polymers, namely poly(diallyldimethylammonium chloride) (PDAC) and sulfonated polystyrene (SPS) as the polycation and polyanion, respectively, to build the multilayer films. We formed SPS patterns on polyelectrolyte multilayer (PEM) surfaces either by microcontact printing PDAC onto SPS surfaces or vice-versa. To create patterned co-cultures on PEMs, we capitalize on the preferential attachment and spreading of primary hepatocytes on SPS as opposed to PDAC surfaces. In contrast, fibroblasts readily attached to both PDAC and SPS surfaces, and as a result, we were able to obtain patterned co-cultures of fibroblast and primary hepatocytes on synthetic PEM surfaces. We characterized the morphology and hepatic-specific functions of the patterned cell co-cultures with microscopy and biochemical assays. Our results suggest an alternative approach to fabricating controlled co-cultures with specified cell-cell and cell-surface interactions; this approach provides flexibility in designing cell-specific surfaces for tissue engineering applications.     

High Catalytic Activity of Nitrogen and Sulfur Co‐Doped Nanoporous Graphene in the Hydrogen Evolution Reaction

Chemical doping has been demonstrated to be an effective way to realize new functions of graphene as metal‐free catalyst in energy‐related electrochemical reactions. Although efficient catalysis for the oxygen reduction reaction (ORR) has been achieved with doped graphene, its performance in the hydrogen evolution reaction (HER) is rather poor. In this study we report that nitrogen and sulfur co‐doping leads to high catalytic activity of nanoporous graphene in HER at low operating potential, comparable to the best Pt‐free HER catalyst, 2D MoS₂. The interplay between the chemical dopants and geometric lattice defects of the nanoporous graphene plays the fundamental role in the superior HER catalysis.     

Co‐continuous Polyamide 6 (PA6)/Acrylonitrile‐Butadiene‐Styrene (ABS) Nanocomposites

Summary: Polyamide 6 (PA6)/acrylonitrile‐butadiene‐styrene (ABS) (40/60 w/w) nanocomposites with a novel morphology were prepared by the melt mixing of PA6, ABS and organoclay. The blend nanocomposites had a co‐continuous structure, in which both PA6 and styrene‐acrylonitrile (SAN) were continuous phases. It was found that the toughening rubber particles were only located in the SAN phase and the strengthening clay platelets were selectively dispersed in the PA6 phase. The co‐continuous nanocomposites showed greatly improved mechanical properties over the whole temperature range when compared with the same blend sample without clay.

Schematic diagram for the co‐continuous ABS/PA6 blend nanocomposite.     

A finite volume method for numerical grid generation

A novel method to generate body‐fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables ξ, η and ζ is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re‐zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid‐correction procedure. The scalar variables are re‐mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet–Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local‐boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point‐by‐point and whole‐field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright © 1999 National Research Council of Canada.     

Influence of thermal annealing on the structural and optical properties of maghemite (γ‐Fe2O3) nanoparticle thin films

In this study, maghemite (γ‐Fe₂O₃) nanoparticles were initially synthesized via chemical co‐precipitation and then deposited by spray pyrolysis as thin films on white glass substrates. The thin films were annealed for 8 h at 400, 450, 500, 550, and 600 °C in an oven. The structural studies of maghemite nanoparticles were carried out using X‐ray diffractometer. Structural properties that we investigated by X‐ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, SEM, and Energy dispersive X‐ray analysis (EDS). Optical properties of the samples were also investigated by ultraviolet‐visible (UV–vis) spectroscopy. The results showed that maghemite nanoparticles have crystalline structure with domain that increases in size with increasing annealing temperature. The optical band gap values were found to reduce from 2.9 to 2.4 eV with increase in annealing temperature. Copyright © 2015 John Wiley & Sons, Ltd.     

Poly[lactic‐co‐(glycolic acid)]‐Grafted Hyaluronic Acid Copolymer Micelle Nanoparticles for Target‐Specific Delivery of Doxorubicin

PLGA‐grafted HA copolymers were synthesized and utilized as target specific micelle carriers for DOX. For grafting hydrophobic PLGA chains onto the backbone of hydrophilic HA, HA was solubilized in an anhydrous DMSO by nano‐complexing with dimethoxy‐PEG. The carboxylic groups of HA were chemically grafted with PLGA, producing HA‐g‐PLGA copolymers. Resultant HA‐g‐PLGA self‐assembled in aqueous solution to form multi‐cored micellar aggregates and DOX was encapsulated during the self‐assembly. DOX‐loaded HA‐g‐PLGA micelle nanoparticles exhibited higher cellular uptake and greater cytotoxicity than free DOX for HCT‐116 cells that over‐expressed HA receptor, suggesting that they were taken up by the cells via HA receptor‐mediated endocytosis.

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