Optimally Decomposing Coverings with Translates of a Convex Polygon

We show that any k-fold covering using translates of an arbitrary convex polygon can be decomposed into Ω(k) covers. Such a decomposition can be computed using an efficient (polynomial-time) algorithm.     

Three-dimensional nanocarbon and the electrochemistry of nanocarbon/tin oxide for lithium ion batteries

In this work, the potential of using coconut shell, which is very cheap and readily available, for the production of graphitic nanocarbon three-dimensional networks is investigated. The three-dimensional carbon has been produced via the wet-impregnation of coconut shell powder with a transition metal catalyst. The novel process employed offers low costs and environmental advantages, with biological waste used in place of carbonaceous precursor as the feedstock. Nanocarbon/tin oxide composites were prepared via wet-impregnation and the solvothermal method, using tin chloride solution with the activated nanocarbon. The electrochemical performances of the three-dimensional nanocarbon doped with tin oxide and of activated nanocarbon alone as anode materials were investigated in rechargeable lithium ion batteries. One composite made by using the solvothermal method shows stable cyclic retention up to 100 cycles and delivers a high reversible capacity of about 405?mAh g^?1.     

A coated wire-type lead(II) ion-selective electrode based on a phosphorylated calix[4]arene derivative.

The preparation of a lead-selective electrode based on 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrakis-(diphenylphosphinoylmethoxy)calix[4]arene (1) as an ionophore is reported. The plasticized PVC membrane containing 30% PVC, 57% ortho-nitrophenyloctylether (NPOE), 4% sodium tetraphenylborate (NaTPB) and 9% ionophore 1 was directly coated on a graphite electrode. It exhibits a nearly Nernstian slope of 28.0 +/- 0.2 mV decade(-1) over a concentration range of 1 x 10(-5) - 1 x 10(-2) mol dm(-3) with a detection limit of 1.4 x 10(-6) mol dm(-3). The response time of the electrode was found to be ca. 17 s. The potential of the sensor was independent of the pH variation in the range 3.5 - 5.0. The selectivity of the electrode performance towards lead ions over Th4+, La3+, Sm3+, Dy3+, Y3+, Ca2+, Sr2+, Cd2+, Mn2+, Zn2+, Ni2+, Co2+, NH4+ Ag+, Li+, Na+ and K+ ions was investigated. The prepared electrode was used successfully as an indicator electrode for a potentiometric titration of a lead solution using a standard solution of EDTA. The applicability of the sensor for Pb2+ measurements in various synthetic water samples spiked with lead nitrate was also checked.     

Morphology of polyanhydride copolymers: Time‐resolved small‐angle X‐ray scattering studies of crystallization

Synchrotron small‐angle X‐ray scattering (SAXS) was used to study the isothermal crystallization kinetics of a family of polyanhydride copolymers consisting of 1,6‐bis(p‐carboxyphenoxy)hexane and sebacic acid monomers. In situ SAXS experiments permitted the direct observation of the crystallization kinetics. The structural parameters (the long period, lamellar thickness, and degree of crystallinity) were obtained from Lorentz‐corrected intensity profiles, one‐dimensional correlation functions, and interface distribution functions to form a comprehensive picture of the crystal morphology. The combination of these three analyses provided information not only on the lamellar dimensions but also on the polydispersity (nonuniformity) of these dimensions. Where possible, the crystallization kinetics were interpreted with a modified version of the Avrami equation. The results can be used to perform the rational design of controlled‐drug‐release formulations because crystallinity affects drug‐release kinetics. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 463–477, 2005     

Geometry optimization of crystals by the quasi-independent curvilinear coordinate approximation

The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid under periodic boundary conditions, enabling simultaneous relaxation of the lattice and atomic coordinates, as illustrated by tight optimization of polyethylene, hexagonal boron nitride, a (10,0) carbon nanotube, hexagonal ice, quartz, and sulfur at the Gamma-point RPBE/STO-3G level of theory.