Side chain impacts on pH‐ and thermo‐responsiveness of tertiary amine functionalized polypeptides

The systemic investigation of the structural impacts of side chains on the pH‐ and thermo‐responsiveness of tertiary amine functionalized poly(l ‐glutamate)s (TA‐PGs) was carried out. The TA‐PGs polymers were effectively synthesized by Cu(I)‐catalyzed azide‐alkyne cycloaddition click reaction of azido tertiary amines with poly(γ‐propargyl‐l ‐glutamate) (PPLG). Turbimetric measurements were performed to characterize the pH‐ and temperature‐induced phase transition of TA‐PGs in aqueous solution, which suggested a structural dependence of the properties on the N‐substituted groups and the “linkers” between 1,2,3‐triazole ring and the tertiary amine groups in the side chains. In detail, the pH responsive properties of TA‐PGs were basically determined by the hydrophobicity of the N‐substituted groups in the side chains and the pH transition point (pH_t) decreased as the increasing hydrophobicity of the N‐substituted groups, while the temperature‐responsiveness of TA‐PGs were affected by either the N‐substituted groups or the “linkers.” TA‐PGs with a moderate N‐substituted amine group (e.g., DEA, PR, and PD) or a branched “linker” (e.g., iso‐propylene and 2‐methylpropylene group) were more likely to express the LCST‐type phase transition tuned by pH variation. These structure–property relationships revealed in this study would help to develop the applications of TA‐PGs in smart drug delivery systems. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 671–679     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Relations among five radii of circles in a triangle,its sides and other segments

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas relating the radii to the sides and the inequalities between the different averages. The activities described were conducted with pre-service teachers of mathematics, with empirical investigation of the relations using dynamical geometry software, and formal presentation of proofs.     

Nonlinear anisotropic elliptic equations in with variable exponents and locally integrable data

In this paper, we prove existence and regularity results for weak solutions in the framework of anisotropic Sobolev spaces for a class of nonlinear anisotropic elliptic equations in the whole with variable exponents and locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Copyright © 2016 John Wiley & Sons, Ltd.     

A posteriori error estimation for the Stokes–Darcy coupled problem on anisotropic discretization

This paper presents an a posteriori error analysis for the stationary Stokes–Darcy coupled problem approximated by finite element methods on anisotropic meshes in or 3. Korn's inequality for piecewise linear vector fields on anisotropic meshes is established and is applied to non‐conforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for non‐conforming case. With the obtained finite element solutions, the error estimators are constructed and based on the residual of model equations plus the stabilization terms. The lower error bound is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so‐called matching function is defined, and its discussion shows it to be useful tool. With its help, the upper error bound is shown by means of the corresponding anisotropic interpolation estimates and a special Helmholtz decomposition in both media. Copyright © 2016 John Wiley & Sons, Ltd.     

Geometric Design of Anode-Supported Micro-Tubular Solid Oxide Fuel Cells by Multiphysics Simulations

High volumetric power density (VPD) is the basis for the commercial success of micro-tubular solid oxide fuel cells (mtSOFCs). To find maximal VPD (MVPD) for anode-supported mtSOFC (as-mtSOFC), the effects of geometric parameters on VPD are analyzed and the anode thickness, t_an, and the cathode length, l_ca, are identified as the key design parameters. Thermo-fluid electrochemical models were built to examine the dependence of the electrical output on the cell parameters. The multiphysics model is validated by reproducing the experimental I-V curves with no adjustable parameters. The optimal l_ca and the corresponding MVPDs are then determined by the multiphysics model for 20 combinations of r_in, the inner tube radius, and t_an. And all these optimization are made at 1073.15 K. The results show that:(i) significant performance improvement may be achieved by geometry optimization, (ii) the seemingly high MVPD of 11 and 14 W/cm³ can be easily realized for as-mtSOFC with single-and double-terminal anode current collection, respectively. Moreover, the variation of the area specific power density with l_ca2(2 mm, 40 mm) is determined for three representative (r_in, t_an) combinations. Besides, it is demonstrated that the current output of mtSOFC with proper geometric parameters is comparable to that of planar SOFC.     

Facile synthesis methodology and characterization studies of silica-decorated hybridized anisotropic nanotubes and nanosheets

Carbonaceous nanomaterials and their derivatives have been inspired tremendous enthusiasm in the scientific community. They have been excogitated as the encouraging attributes and the qualified dispersed phase to develop multi-functional composites. Particularly, graphene and carbon nanotube (anisotropic fillers) have gained substantial research interest owing to their promising characteristics. This highlights an innovative technique to synthesize hybridized nanotube and nanosheet. Initially, parent materials have been synthesized: The pristine CNT has been modified by acid mixture solution, and reduced graphene oxide has been prepared by chemical reduction method. Henceforth, the self-assembly in situ sol–gel technique has been endorsed here. The synthesized nanohybrids have been characterized by different spectroscopic techniques: FTIR, Raman, UV, and XPS to confirm the attachment of multifunctionalities; meanwhile, the composition and stability have been investigated from XRD and TGA plots. The magnitude of surface charge and particle size distribution have been evaluated for the parent and hybridized products; further, morphology of all the samples has been authenticated from FESEM and TEM.     

Defect Engineering and Anisotropic Modulation of Ionic Transport in Perovskite Solid Electrolyte LixLa(1−x)/3NbO3

Solid electrolytes, such as perovskite Li_3xLa_2/1−xTiO₃, Li_xLa_(1−x)/3NbO₃ and garnet Li₇La₃Zr₂O₁₂ ceramic oxides, have attracted extensive attention in lithium-ion battery research due to their good chemical stability and the improvability of their ionic conductivity with great potential in solid electrolyte battery applications. These solid oxides eliminate safety issues and cycling instability, which are common challenges in the current commercial lithium-ion batteries based on organic liquid electrolytes. However, in practical applications, structural disorders such as point defects and grain boundaries play a dominating role in the ionic transport of these solid electrolytes, where defect engineering to tailor or improve the ionic conductive property is still seldom reported. Here, we demonstrate a defect engineering approach to alter the ionic conductive channels in Li_xLa_(1−x)/3NbO₃ (x = 0.1~0.13) electrolytes based on the rearrangements of La sites through a quenching process. The changes in the occupancy and interstitial defects of La ions lead to anisotropic modulation of ionic conductivity with the increase in quenching temperatures. Our trial in this work on the defect engineering of quenched electrolytes will offer opportunities to optimize ionic conductivity and benefit the solid electrolyte battery applications.     

Multidimensional persistence in biomolecular data

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudomultidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high‐dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness, and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryoelectron microscopy data, and the scale dependence of nanoparticles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace–Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti‐0 invariants and the relatively global characteristics of Betti‐1 and Betti‐2 invariants. © 2015 Wiley Periodicals, Inc.